๐ŸŽฏ Word Problem Practice ๐ŸŽฏ

Master the Art of Solving Math Word Problems

5th Grade Mathematics

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๐Ÿ“š Table of Contents

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๐Ÿ“– How to Use This Slideshow

Welcome! This slideshow will help you practice solving word problems AND understanding what problems are asking you to do.

For each problem, you'll see two special buttons:

๐Ÿ’ก Pro Tip: Try to solve each problem on your own BEFORE clicking the solution button!
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๐Ÿ“– Tips for Success

  1. Read the problem carefully - at least twice!
  2. Look for key words that tell you what operation to use
  3. Identify the important numbers and what they represent
  4. Decide what type of problem it is before solving
  5. Show all your work step by step
  6. Check that your answer makes sense in the context of the problem
โš ๏ธ Watch Out: Not every problem uses obvious words like "total" or "difference." Sometimes you have to figure out the operation from the situation!
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๐Ÿ“– Keyboard Shortcuts

Use these shortcuts to navigate quickly:

๐Ÿ–ฅ๏ธ Fullscreen Mode: Press F for a better viewing experience on the Smartboard!
๐Ÿ“

Section 1: Area Problems

Finding how much space a flat surface covers

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Area Problems

Problem 1

Ms. Johnson wants to cover her classroom floor with new tile. The classroom is 24 feet long and 18 feet wide. How many square feet of tile does she need to buy?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "cover" and "square feet" tell us we need to find how much space the floor takes up.
๐Ÿ“ Important numbers: 24 feet (length) and 18 feet (width)
๐ŸŽฏ What type? Covering a flat rectangular surface = AREA
Skill: Area of a Rectangle

โœ“ Step-by-Step Solution

Step 1: Identify that this is an area problem (covering a flat surface)
Step 2: Write the formula: Area = length ร— width
Step 3: Plug in: Area = 24 ร— 18
Step 4: Calculate: 24 ร— 18 = 432
Step 5: Include units: square feet
Final Answer: 432 square feet of tile
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Area Problems

Problem 2

Marcus is helping his dad build a rectangular garden. The garden will be 15 feet long and 9 feet wide. How much space will the garden take up in the backyard?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "how much space" means we need to find the area
๐Ÿ“ Important numbers: 15 feet (length) and 9 feet (width)
๐ŸŽฏ What type? Finding space of a flat rectangle = AREA
Skill: Area of a Rectangle

โœ“ Step-by-Step Solution

Step 1: This is an area problem (finding space of a flat surface)
Step 2: Formula: Area = length ร— width
Step 3: Plug in: Area = 15 ร— 9
Step 4: Calculate: 15 ร— 9 = 135
Final Answer: 135 square feet
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Area Problems

Problem 3

Sofia wants to buy a new rug for her bedroom. The rug she likes is 8 feet long and 6 feet wide. What is the area of the rug?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "area" is directly stated!
๐Ÿ“ Important numbers: 8 feet (length) and 6 feet (width)
๐ŸŽฏ What type? Finding area of a rectangle
Skill: Area of a Rectangle

โœ“ Step-by-Step Solution

Step 1: Area = length ร— width
Step 2: Area = 8 ร— 6 = 48
Final Answer: 48 square feet
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Area Problems

Problem 4

The school is painting a mural on a wall that is 32 feet long and 12 feet high. How many square feet of wall will be covered with the mural?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "covered" and "square feet" indicate area
๐Ÿ“ Important numbers: 32 feet ร— 12 feet
๐Ÿ’ก Notice: A wall is still a flat rectangle, just vertical!
Skill: Area of a Rectangle

โœ“ Step-by-Step Solution

Step 1: Area = length ร— height (for a wall)
Step 2: Area = 32 ร— 12
Step 3: Calculate: 32 ร— 12 = 384
Final Answer: 384 square feet
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Area Problems

Problem 5

Aisha's mom is buying carpet for the living room. The room measures 14 feet by 11 feet. The carpet costs $3 per square foot. First, find how many square feet of carpet they need.

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "square feet" and covering a room = area
๐Ÿ“ Important numbers: 14 feet ร— 11 feet
โš ๏ธ Watch out: The price info is extra - we only need area!
Skill: Area of a Rectangle

โœ“ Step-by-Step Solution

Step 1: Area = length ร— width
Step 2: Area = 14 ร— 11 = 154
Final Answer: 154 square feet
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Area Problems

Problem 6

The basketball court at Jamal's school is 84 feet long and 50 feet wide. What is the area of the basketball court?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "area" is directly stated
๐Ÿ“ Important numbers: 84 feet ร— 50 feet
๐Ÿ’ก Challenge: These are bigger numbers - be careful!
Skill: Area of a Rectangle

โœ“ Step-by-Step Solution

Step 1: Area = length ร— width
Step 2: Area = 84 ร— 50
Step 3: Calculate: 84 ร— 50 = 4,200
Final Answer: 4,200 square feet
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Area Problems

Problem 7

Maya is wrapping a rectangular present. The top of the box is 16 inches long and 10 inches wide. How much wrapping paper does she need just for the top?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "how much" for covering a flat surface
๐Ÿ“ Important numbers: 16 inches ร— 10 inches
๐Ÿ’ก Notice: "just for the top" means one rectangle only
Skill: Area of a Rectangle

โœ“ Step-by-Step Solution

Step 1: Area = length ร— width
Step 2: Area = 16 ร— 10 = 160
Final Answer: 160 square inches
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Area Problems

Problem 8

The school playground has a rectangular sandbox that is 22 feet long and 18 feet wide. The PTA wants to replace the sand. How many square feet of sand do they need?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "square feet" covering a flat surface
๐Ÿ“ Important numbers: 22 feet ร— 18 feet
๐Ÿ’ก Think: Sand covers the bottom of the sandbox = flat area
Skill: Area of a Rectangle

โœ“ Step-by-Step Solution

Step 1: Area = length ร— width
Step 2: Area = 22 ร— 18
Step 3: Calculate: 22 ร— 18 = 396
Final Answer: 396 square feet of sand
๐Ÿ“ฆ

Section 2: Volume Problems

Finding how much space is inside a 3D shape

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Volume Problems

Problem 9

A storage container is 15 inches long, 10 inches wide, and 8 inches tall. How much space is inside the container?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "space inside" means we need to find how much the container can hold
๐Ÿ“ Important numbers: 15 in (length), 10 in (width), 8 in (height)
๐ŸŽฏ What type? THREE measurements = 3D shape = VOLUME
Skill: Volume of a Rectangular Prism

โœ“ Step-by-Step Solution

Step 1: This is a volume problem (space inside a 3D shape)
Step 2: Formula: Volume = length ร— width ร— height
Step 3: Volume = 15 ร— 10 ร— 8
Step 4: Calculate: 15 ร— 10 = 150, then 150 ร— 8 = 1,200
Final Answer: 1,200 cubic inches
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Volume Problems

Problem 10

Carlos is filling an aquarium with water. The aquarium is 24 inches long, 12 inches wide, and 16 inches deep. How many cubic inches of water can the aquarium hold?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "filling" and "cubic inches" and "how many...can hold"
๐Ÿ“ Important numbers: 24 ร— 12 ร— 16 inches
๐ŸŽฏ What type? Finding capacity of a 3D container = VOLUME
Skill: Volume of a Rectangular Prism

โœ“ Step-by-Step Solution

Step 1: Volume = length ร— width ร— height
Step 2: Volume = 24 ร— 12 ร— 16
Step 3: 24 ร— 12 = 288
Step 4: 288 ร— 16 = 4,608
Final Answer: 4,608 cubic inches
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Volume Problems

Problem 11

A shipping box measures 18 inches by 14 inches by 10 inches. What is the volume of the box?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "volume" is directly stated
๐Ÿ“ Important numbers: 18 ร— 14 ร— 10 inches
๐Ÿ’ก Notice: "by" between numbers means multiply
Skill: Volume of a Rectangular Prism

โœ“ Step-by-Step Solution

Step 1: Volume = 18 ร— 14 ร— 10
Step 2: 18 ร— 14 = 252
Step 3: 252 ร— 10 = 2,520
Final Answer: 2,520 cubic inches
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Volume Problems

Problem 12

Destiny's toy chest is 3 feet long, 2 feet wide, and 2 feet tall. How much space is inside the toy chest for storing toys?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "space inside" and "storing"
๐Ÿ“ Important numbers: 3 ft ร— 2 ft ร— 2 ft
๐ŸŽฏ What type? Interior space of a box = VOLUME
Skill: Volume of a Rectangular Prism

โœ“ Step-by-Step Solution

Step 1: Volume = length ร— width ร— height
Step 2: Volume = 3 ร— 2 ร— 2 = 12
Final Answer: 12 cubic feet
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Volume Problems

Problem 13

The swimming pool at the rec center is 50 feet long, 25 feet wide, and 6 feet deep. How many cubic feet of water does it take to fill the pool?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "cubic feet" and "fill"
๐Ÿ“ Important numbers: 50 ร— 25 ร— 6 feet
๐ŸŽฏ What type? Filling a 3D space = VOLUME
Skill: Volume of a Rectangular Prism

โœ“ Step-by-Step Solution

Step 1: Volume = 50 ร— 25 ร— 6
Step 2: 50 ร— 25 = 1,250
Step 3: 1,250 ร— 6 = 7,500
Final Answer: 7,500 cubic feet
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Volume Problems

Problem 14

A gift box has dimensions of 8 inches by 8 inches by 8 inches. What is the volume of this cube-shaped box?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "volume" and "cube-shaped"
๐Ÿ“ Important numbers: 8 ร— 8 ร— 8 inches (all sides equal!)
๐Ÿ’ก Special: When all sides are equal, it's a cube!
Skill: Volume of a Cube

โœ“ Step-by-Step Solution

Step 1: Volume = side ร— side ร— side (or sยณ)
Step 2: Volume = 8 ร— 8 ร— 8
Step 3: 8 ร— 8 = 64, then 64 ร— 8 = 512
Final Answer: 512 cubic inches
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Volume Problems

Problem 15

A moving truck has a cargo area that is 20 feet long, 8 feet wide, and 9 feet tall. How much space is available for loading furniture?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "space...available for loading"
๐Ÿ“ Important numbers: 20 ร— 8 ร— 9 feet
๐ŸŽฏ What type? Storage capacity of a 3D space = VOLUME
Skill: Volume of a Rectangular Prism

โœ“ Step-by-Step Solution

Step 1: Volume = 20 ร— 8 ร— 9
Step 2: 20 ร— 8 = 160
Step 3: 160 ร— 9 = 1,440
Final Answer: 1,440 cubic feet
๐ŸŽ

Section 3: Surface Area Problems

Finding the total area of ALL outside surfaces of a 3D shape

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Surface Area Problems

Problem 16

DeShawn is wrapping a present that is 12 inches long, 8 inches wide, and 4 inches tall. How many square inches of wrapping paper does he need to cover all sides of the box?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "cover ALL sides" = surface area (not just one face!)
๐Ÿ“ Important numbers: 12 ร— 8 ร— 4 inches
๐ŸŽฏ What type? Covering the OUTSIDE of a 3D shape = SURFACE AREA
๐Ÿ’ก Remember: A box has 6 faces (3 pairs of matching rectangles)
Skill: Surface Area of a Rectangular Prism

โœ“ Step-by-Step Solution

Step 1: Find the area of each pair of faces:
โ€ข Top & Bottom: 12 ร— 8 = 96, so 96 ร— 2 = 192 sq in
โ€ข Front & Back: 12 ร— 4 = 48, so 48 ร— 2 = 96 sq in
โ€ข Left & Right: 8 ร— 4 = 32, so 32 ร— 2 = 64 sq in
Step 2: Add all faces: 192 + 96 + 64 = 352
Final Answer: 352 square inches
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Surface Area Problems

Problem 17

Kenji needs to paint all six faces of a wooden block. The block is 6 inches long, 6 inches wide, and 6 inches tall. How many square inches will he paint?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "all six faces" and "paint"
๐Ÿ“ Important numbers: 6 ร— 6 ร— 6 inches (a cube!)
๐Ÿ’ก Shortcut: For a cube, all 6 faces are the same size!
Skill: Surface Area of a Cube

โœ“ Step-by-Step Solution

Step 1: Find area of ONE face: 6 ร— 6 = 36 sq in
Step 2: Multiply by 6 faces: 36 ร— 6 = 216
Final Answer: 216 square inches
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Surface Area Problems

Problem 18

A cardboard box is 20 inches long, 15 inches wide, and 10 inches tall. The company wants to cover the entire outside with decorative paper. What is the total surface area they need to cover?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "entire outside" and "surface area"
๐Ÿ“ Important numbers: 20 ร— 15 ร— 10 inches
๐ŸŽฏ What type? Total outside = SURFACE AREA
Skill: Surface Area of a Rectangular Prism

โœ“ Step-by-Step Solution

Step 1: Find each pair of faces:
โ€ข Top & Bottom: 20 ร— 15 = 300, so 300 ร— 2 = 600 sq in
โ€ข Front & Back: 20 ร— 10 = 200, so 200 ร— 2 = 400 sq in
โ€ข Left & Right: 15 ร— 10 = 150, so 150 ร— 2 = 300 sq in
Step 2: Total: 600 + 400 + 300 = 1,300
Final Answer: 1,300 square inches
โœ‚๏ธ

Section 4: Simplifying Fractions

Using GCF to write fractions in simplest form

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Simplifying Fractions

Problem 19

Aaliyah ate 6 slices of a pizza that was cut into 8 slices. Write the fraction of pizza she ate in simplest form.

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "simplest form"
๐Ÿ“ The fraction: 68
๐ŸŽฏ What type? Find GCF and divide both parts
Skill: Simplifying with GCF

โœ“ Step-by-Step Solution

Step 1: Write the fraction: 68
Step 2: Find the GCF of 6 and 8
โ€ข Factors of 6: 1, 2, 3, 6
โ€ข Factors of 8: 1, 2, 4, 8
โ€ข GCF = 2
Step 3: Divide both by 2: 6รท28รท2 = 34
Final Answer: 34 of the pizza
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Simplifying Fractions

Problem 20

Marcus completed 15 out of 20 homework problems. What fraction of his homework did he complete? Write your answer in simplest form.

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "simplest form"
๐Ÿ“ The fraction: 1520
๐Ÿ’ก Hint: Both numbers end in 5 or 0, so 5 is a common factor!
Skill: Simplifying with GCF

โœ“ Step-by-Step Solution

Step 1: Write the fraction: 1520
Step 2: Find the GCF of 15 and 20
โ€ข Factors of 15: 1, 3, 5, 15
โ€ข Factors of 20: 1, 2, 4, 5, 10, 20
โ€ข GCF = 5
Step 3: Divide both by 5: 15รท520รท5 = 34
Final Answer: 34 of his homework
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Simplifying Fractions

Problem 21

A recipe calls for 12 ounces of flour from a 16-ounce bag. What fraction of the bag does the recipe use? Simplify your answer.

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "simplify"
๐Ÿ“ The fraction: 1216
๐Ÿ’ก Hint: Both are even numbers, so try dividing by 2 first
Skill: Simplifying with GCF

โœ“ Step-by-Step Solution

Step 1: Write the fraction: 1216
Step 2: Find the GCF of 12 and 16
โ€ข Factors of 12: 1, 2, 3, 4, 6, 12
โ€ข Factors of 16: 1, 2, 4, 8, 16
โ€ข GCF = 4
Step 3: Divide both by 4: 12รท416รท4 = 34
Final Answer: 34 of the bag
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Simplifying Fractions

Problem 22

The soccer team won 18 out of 24 games this season. What fraction of their games did they win? Write in lowest terms.

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "lowest terms" = simplest form
๐Ÿ“ The fraction: 1824
๐Ÿ’ก Hint: Both are divisible by 2, 3, AND 6!
Skill: Simplifying with GCF

โœ“ Step-by-Step Solution

Step 1: Write the fraction: 1824
Step 2: Find the GCF of 18 and 24
โ€ข Factors of 18: 1, 2, 3, 6, 9, 18
โ€ข Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
โ€ข GCF = 6
Step 3: Divide both by 6: 18รท624รท6 = 34
Final Answer: 34 of their games
๐Ÿ”„

Section 5: Mixed Numbers & Improper Fractions

Converting between different fraction forms

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Mixed Numbers & Improper Fractions

Problem 23

Isabella has 114 cups of sugar. Write this as a mixed number so she can measure it more easily.

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "write as a mixed number"
๐Ÿ“ The fraction: 114 (improper - top bigger than bottom)
๐ŸŽฏ What to do: Divide to find whole number and remainder
Skill: Improper Fraction โ†’ Mixed Number

โœ“ Step-by-Step Solution

Step 1: Divide numerator by denominator: 11 รท 4
Step 2: 11 รท 4 = 2 remainder 3
Step 3: Write as mixed number: 2 34
โ€ข Whole number = 2 (the quotient)
โ€ข Numerator = 3 (the remainder)
โ€ข Denominator = 4 (stays the same)
Final Answer: 234 cups of sugar
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Mixed Numbers & Improper Fractions

Problem 24

Tyler ran 325 miles. Write this as an improper fraction to compare with his friend's distance.

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "write as an improper fraction"
๐Ÿ“ The mixed number: 325
๐ŸŽฏ What to do: Multiply whole ร— denominator, then add numerator
Skill: Mixed Number โ†’ Improper Fraction

โœ“ Step-by-Step Solution

Step 1: Multiply whole number ร— denominator: 3 ร— 5 = 15
Step 2: Add the numerator: 15 + 2 = 17
Step 3: Keep the same denominator: 5
Final Answer: 175 miles
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Mixed Numbers & Improper Fractions

Problem 25

A recipe needs 196 cups of broth. Express this as a mixed number.

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "express as a mixed number"
๐Ÿ“ The fraction: 196
๐ŸŽฏ What to do: Divide 19 รท 6
Skill: Improper Fraction โ†’ Mixed Number

โœ“ Step-by-Step Solution

Step 1: Divide: 19 รท 6 = 3 remainder 1
Step 2: Write as mixed number: 3 16
Final Answer: 316 cups of broth
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Mixed Numbers & Improper Fractions

Problem 26

Jayden practiced piano for 234 hours. Convert this to an improper fraction.

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "convert to an improper fraction"
๐Ÿ“ The mixed number: 234
๐ŸŽฏ Formula: (whole ร— denominator) + numerator
Skill: Mixed Number โ†’ Improper Fraction

โœ“ Step-by-Step Solution

Step 1: Multiply: 2 ร— 4 = 8
Step 2: Add numerator: 8 + 3 = 11
Step 3: Keep denominator: 4
Final Answer: 114 hours
โž•

Section 6: Adding Fractions

Same denominators - just add the numerators!

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Adding Fractions (Same Denominators)

Problem 27

Jamal practiced piano for 25 of an hour before lunch and 25 of an hour after lunch. How long did he practice altogether?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key word: "altogether" means ADD
๐Ÿ“ Numbers: 25 + 25
๐Ÿ’ก Good news: Same denominators - just add tops!
Skill: Adding Fractions (Same Denominators)

โœ“ Step-by-Step Solution

Step 1: Check denominators - both are 5 โœ“
Step 2: Add numerators: 2 + 2 = 4
Step 3: Keep denominator: 5
Final Answer: 45 of an hour
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Adding Fractions (Same Denominators)

Problem 28

Mia drank 38 of a bottle of water in the morning and 48 in the afternoon. How much of the bottle did she drink in total?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "in total" means ADD
๐Ÿ“ Numbers: 38 + 48
๐Ÿ’ก Same denominators!
Skill: Adding Fractions (Same Denominators)

โœ“ Step-by-Step Solution

Step 1: Add numerators: 3 + 4 = 7
Step 2: Keep denominator: 8
Final Answer: 78 of the bottle
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Adding Fractions (Same Denominators)

Problem 29

Noah walked 510 of a mile to school and 310 of a mile to the library. How far did he walk combined?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key word: "combined" means ADD
๐Ÿ“ Numbers: 510 + 310
๐Ÿ’ก Bonus: Can we simplify the answer?
Skill: Adding Fractions (Same Denominators)

โœ“ Step-by-Step Solution

Step 1: Add numerators: 5 + 3 = 8
Step 2: Keep denominator: 10
Step 3: Simplify: 810 = 45 (GCF = 2)
Final Answer: 45 of a mile
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Adding Fractions (Same Denominators)

Problem 30

Ava ate 26 of a pie and her brother ate 36 of the same pie. What fraction of the pie did they eat together?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "together" means ADD
๐Ÿ“ Numbers: 26 + 36
๐Ÿ’ก Remember to simplify!
Skill: Adding Fractions (Same Denominators)

โœ“ Step-by-Step Solution

Step 1: Add numerators: 2 + 3 = 5
Step 2: Keep denominator: 6
Step 3: Check if it simplifies - 56 is already in simplest form!
Final Answer: 56 of the pie
โž•

Section 7: Adding Fractions

Different denominators - find a common denominator first!

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Adding Fractions (Different Denominators)

Problem 31

Emma used 12 cup of sugar and 14 cup of brown sugar in her recipe. How much sugar did she use in all?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "in all" means ADD
๐Ÿ“ Numbers: 12 + 14
โš ๏ธ Different denominators! Need common denominator
๐Ÿ’ก Hint: 4 is a multiple of 2
Skill: Adding Fractions (Different Denominators)

โœ“ Step-by-Step Solution

Step 1: Find common denominator: LCD of 2 and 4 is 4
Step 2: Convert 12 = 24
Step 3: Add: 24 + 14 = 34
Final Answer: 34 cup of sugar
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Adding Fractions (Different Denominators)

Problem 32

Liam spent 23 of an hour on math homework and 16 of an hour on reading. How much time did he spend on homework?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: Finding total time = ADD
๐Ÿ“ Numbers: 23 + 16
๐Ÿ’ก Hint: 6 is a multiple of 3
Skill: Adding Fractions (Different Denominators)

โœ“ Step-by-Step Solution

Step 1: Common denominator: 6
Step 2: Convert 23 = 46
Step 3: Add: 46 + 16 = 56
Final Answer: 56 of an hour
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Adding Fractions (Different Denominators)

Problem 33

Olivia ran 34 of a mile and then walked 25 of a mile. How far did she travel in total?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "in total" = ADD
๐Ÿ“ Numbers: 34 + 25
๐Ÿ’ก Hint: Neither is a multiple of the other, so multiply: 4 ร— 5 = 20
Skill: Adding Fractions (Different Denominators)

โœ“ Step-by-Step Solution

Step 1: Common denominator: 4 ร— 5 = 20
Step 2: Convert 34 = 1520 (ร—5)
Step 3: Convert 25 = 820 (ร—4)
Step 4: Add: 1520 + 820 = 2320
Step 5: Convert to mixed: 1320
Final Answer: 1320 miles
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Adding Fractions (Different Denominators)

Problem 34

For an art project, Aiden used 13 yard of red ribbon and 14 yard of blue ribbon. How much ribbon did he use altogether?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key word: "altogether" = ADD
๐Ÿ“ Numbers: 13 + 14
๐Ÿ’ก Hint: LCD of 3 and 4 is 12
Skill: Adding Fractions (Different Denominators)

โœ“ Step-by-Step Solution

Step 1: Common denominator: 12
Step 2: Convert 13 = 412 (ร—4)
Step 3: Convert 14 = 312 (ร—3)
Step 4: Add: 412 + 312 = 712
Final Answer: 712 yard of ribbon
โž–

Section 8: Subtracting Fractions

Finding the difference between fraction amounts

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Subtracting Fractions

Problem 35

Sofia had 78 of a pizza. She gave 38 to her brother. How much pizza does she have left?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "gave" and "left" mean SUBTRACT
๐Ÿ“ Numbers: 78 - 38
๐Ÿ’ก Same denominators! Just subtract numerators
Skill: Subtracting Fractions (Same Denominators)

โœ“ Step-by-Step Solution

Step 1: Subtract numerators: 7 - 3 = 4
Step 2: Keep denominator: 8
Step 3: Simplify: 48 = 12
Final Answer: 12 of the pizza left
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Subtracting Fractions

Problem 36

Jackson walked 56 of a mile to school. His friend Cameron only walked 16 of a mile. How much farther did Jackson walk?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "how much farther" = difference = SUBTRACT
๐Ÿ“ Numbers: 56 - 16
๐Ÿ’ก Same denominators!
Skill: Subtracting Fractions (Same Denominators)

โœ“ Step-by-Step Solution

Step 1: Subtract numerators: 5 - 1 = 4
Step 2: Keep denominator: 6
Step 3: Simplify: 46 = 23
Final Answer: 23 mile farther
๐Ÿ“š Back to TOC

Subtracting Fractions

Problem 37

A container had 34 gallon of juice. After the party, only 18 gallon was left. How much juice was consumed?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "consumed" means taken away = SUBTRACT
๐Ÿ“ Numbers: 34 - 18
โš ๏ธ Different denominators! Need common denominator
Skill: Subtracting Fractions (Different Denominators)

โœ“ Step-by-Step Solution

Step 1: Common denominator: 8
Step 2: Convert 34 = 68
Step 3: Subtract: 68 - 18 = 58
Final Answer: 58 gallon consumed
๐Ÿ“š Back to TOC

Subtracting Fractions

Problem 38

Maya needs 56 yard of fabric but she only has 13 yard. How much more fabric does she need to buy?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "how much more" = SUBTRACT
๐Ÿ“ Numbers: 56 - 13
๐Ÿ’ก Hint: 6 is a multiple of 3
Skill: Subtracting Fractions (Different Denominators)

โœ“ Step-by-Step Solution

Step 1: Common denominator: 6
Step 2: Convert 13 = 26
Step 3: Subtract: 56 - 26 = 36
Step 4: Simplify: 36 = 12
Final Answer: 12 yard more
๐Ÿ“š Back to TOC

Subtracting Fractions

Problem 39

Ethan's water bottle was 45 full. He drank 12 of the bottle. How full is the bottle now?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "drank" means taken away = SUBTRACT
๐Ÿ“ Numbers: 45 - 12
๐Ÿ’ก Hint: LCD of 5 and 2 is 10
Skill: Subtracting Fractions (Different Denominators)

โœ“ Step-by-Step Solution

Step 1: Common denominator: 10
Step 2: Convert 45 = 810
Step 3: Convert 12 = 510
Step 4: Subtract: 810 - 510 = 310
Final Answer: 310 full
โž•

Section 9: Adding Mixed Numbers

Adding numbers with whole and fraction parts

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Adding Mixed Numbers

Problem 40

Destiny ran 214 miles on Monday and 124 miles on Tuesday. How far did she run altogether?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key word: "altogether" = ADD
๐Ÿ“ Numbers: 214 + 124
๐Ÿ’ก Same denominators! Add wholes, then add fractions
Skill: Adding Mixed Numbers

โœ“ Step-by-Step Solution

Step 1: Add whole numbers: 2 + 1 = 3
Step 2: Add fractions: 14 + 24 = 34
Step 3: Combine: 3 + 34
Final Answer: 334 miles
๐Ÿ“š Back to TOC

Adding Mixed Numbers

Problem 41

A recipe needs 134 cups of flour and 212 cups of sugar. How much total dry ingredients are needed?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "total...needed" = ADD
๐Ÿ“ Numbers: 134 + 212
โš ๏ธ Different denominators! Convert 12 to fourths first
Skill: Adding Mixed Numbers

โœ“ Step-by-Step Solution

Step 1: Convert 12 = 24
Step 2: Add wholes: 1 + 2 = 3
Step 3: Add fractions: 34 + 24 = 54
Step 4: 54 = 114, so add to whole: 3 + 114
Final Answer: 414 cups
๐Ÿ“š Back to TOC

Adding Mixed Numbers

Problem 42

Brandon studied 113 hours for math and 223 hours for science. How long did he study in total?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "in total" = ADD
๐Ÿ“ Numbers: 113 + 223
๐Ÿ’ก Same denominators! Watch for regrouping
Skill: Adding Mixed Numbers

โœ“ Step-by-Step Solution

Step 1: Add wholes: 1 + 2 = 3
Step 2: Add fractions: 13 + 23 = 33 = 1
Step 3: Add the extra whole: 3 + 1 = 4
Final Answer: 4 hours
๐Ÿ“š Back to TOC

Adding Mixed Numbers

Problem 43

A board is 358 feet long. Another board is 278 feet long. If you put them end to end, how long would they be together?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "end to end" and "together" = ADD lengths
๐Ÿ“ Numbers: 358 + 278
๐Ÿ’ก Watch out: 58 + 78 = 128 - needs regrouping!
Skill: Adding Mixed Numbers (with regrouping)

โœ“ Step-by-Step Solution

Step 1: Add wholes: 3 + 2 = 5
Step 2: Add fractions: 58 + 78 = 128
Step 3: Convert: 128 = 148 = 112
Step 4: Combine: 5 + 112 = 612
Final Answer: 612 feet
๐Ÿ”ข

Section 10: Finding LCM

Least Common Multiple in real-world situations

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Finding LCM

Problem 44

Hot dogs come in packs of 8. Buns come in packs of 6. What is the smallest number of hot dogs and buns you need to buy so you have the same number of each?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "smallest number" and "same number of each"
๐Ÿ“ Numbers: 8 and 6
๐ŸŽฏ What type? Finding when two cycles meet = LCM
Skill: Finding LCM

โœ“ Step-by-Step Solution

Step 1: List multiples of 8: 8, 16, 24, 32...
Step 2: List multiples of 6: 6, 12, 18, 24, 30...
Step 3: Find the LCM (first common multiple): 24
Step 4: That's 3 packs of hot dogs (3ร—8=24) and 4 packs of buns (4ร—6=24)
Final Answer: 24 of each (3 packs of hot dogs, 4 packs of buns)
๐Ÿ“š Back to TOC

Finding LCM

Problem 45

Train A leaves the station every 12 minutes. Train B leaves every 15 minutes. If both trains leave at 9:00 AM, when will they next leave at the same time?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "next leave at the same time"
๐Ÿ“ Numbers: 12 minutes and 15 minutes
๐ŸŽฏ What type? When do two schedules sync = LCM
Skill: Finding LCM

โœ“ Step-by-Step Solution

Step 1: Multiples of 12: 12, 24, 36, 48, 60...
Step 2: Multiples of 15: 15, 30, 45, 60...
Step 3: LCM = 60 minutes
Step 4: 60 minutes = 1 hour after 9:00 AM
Final Answer: 10:00 AM (60 minutes later)
๐Ÿ“š Back to TOC

Finding LCM

Problem 46

Maria visits her grandmother every 4 days. Her cousin visits every 6 days. If they both visit today, in how many days will they visit on the same day again?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "same day again"
๐Ÿ“ Numbers: 4 days and 6 days
๐ŸŽฏ What type? When patterns align = LCM
Skill: Finding LCM

โœ“ Step-by-Step Solution

Step 1: Multiples of 4: 4, 8, 12, 16...
Step 2: Multiples of 6: 6, 12, 18...
Step 3: LCM = 12
Final Answer: 12 days
โœ–๏ธ

Section 11: Multiplying Fractions

Finding a fraction OF a whole number

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Multiplying Fractions ร— Whole Numbers

Problem 47

There are 24 students in the class. 34 of them brought their lunch from home. How many students brought lunch?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key word: "OF" means MULTIPLY
๐Ÿ“ Numbers: 34 ร— 24
๐ŸŽฏ What type? Finding a fraction OF a number = MULTIPLY
Skill: Multiplying Fractions ร— Whole Numbers

โœ“ Step-by-Step Solution

Step 1: Write as multiplication: 34 ร— 24
Step 2: Multiply numerator ร— whole: 3 ร— 24 = 72
Step 3: Divide by denominator: 72 รท 4 = 18
Final Answer: 18 students
๐Ÿ“š Back to TOC

Multiplying Fractions ร— Whole Numbers

Problem 48

A recipe makes 36 cookies. Jaylen only wants to make 23 of the recipe. How many cookies will he make?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key phrase: "2/3 OF the recipe"
๐Ÿ“ Numbers: 23 ร— 36
๐Ÿ’ก Tip: "OF" almost always means multiply!
Skill: Multiplying Fractions ร— Whole Numbers

โœ“ Step-by-Step Solution

Step 1: 23 ร— 36
Step 2: Multiply: 2 ร— 36 = 72
Step 3: Divide: 72 รท 3 = 24
Final Answer: 24 cookies
๐Ÿ“š Back to TOC

Multiplying Fractions ร— Whole Numbers

Problem 49

The basketball team practiced for 60 minutes. They spent 25 of the time doing drills. How many minutes were spent on drills?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key phrase: "2/5 OF the time"
๐Ÿ“ Numbers: 25 ร— 60
๐ŸŽฏ What type? Fraction of a whole = MULTIPLY
Skill: Multiplying Fractions ร— Whole Numbers

โœ“ Step-by-Step Solution

Step 1: 25 ร— 60
Step 2: Multiply: 2 ร— 60 = 120
Step 3: Divide: 120 รท 5 = 24
Final Answer: 24 minutes on drills
๐Ÿ“š Back to TOC

Multiplying Fractions ร— Whole Numbers

Problem 50

A book has 150 pages. Amara has read 35 of the book. How many pages has she read?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key phrase: "3/5 OF the book"
๐Ÿ“ Numbers: 35 ร— 150
Skill: Multiplying Fractions ร— Whole Numbers

โœ“ Step-by-Step Solution

Step 1: 35 ร— 150
Step 2: Multiply: 3 ร— 150 = 450
Step 3: Divide: 450 รท 5 = 90
Final Answer: 90 pages
๐Ÿ’ต

Section 12: Fractions and Money

Connecting fractions to dollars and cents

๐Ÿ“š Back to TOC

Fractions and Money

Problem 51

Kira saved $48. She spent 14 of her savings on a book. How much did the book cost?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key phrase: "1/4 OF her savings"
๐Ÿ“ Numbers: 14 ร— $48
๐Ÿ’ก Think: What's one quarter of $48?
Skill: Fractions and Money

โœ“ Step-by-Step Solution

Step 1: 14 ร— 48 = 48 รท 4 = 12
Final Answer: $12
๐Ÿ“š Back to TOC

Fractions and Money

Problem 52

Marcus earned $60 mowing lawns. He put 25 of his earnings into savings. How much did he save?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key phrase: "2/5 OF his earnings"
๐Ÿ“ Numbers: 25 ร— $60
Skill: Fractions and Money

โœ“ Step-by-Step Solution

Step 1: 25 ร— 60
Step 2: 2 ร— 60 = 120
Step 3: 120 รท 5 = 24
Final Answer: $24
๐Ÿ“š Back to TOC

Fractions and Money

Problem 53

A skateboard costs $80. The store is having a sale for 14 off. How much money will you save with the discount?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key phrase: "1/4 OFF" means find 1/4 of the price
๐Ÿ“ Numbers: 14 ร— $80
โš ๏ธ Watch out: This asks for the SAVINGS, not the sale price!
Skill: Fractions and Money (Discounts)

โœ“ Step-by-Step Solution

Step 1: Find 14 of $80
Step 2: 80 รท 4 = 20
Final Answer: $20 savings
๐Ÿ“š Back to TOC

Fractions and Money

Problem 54

Four friends split a $36 dinner bill equally. Then one friend paid 13 of their share as a tip. How much tip did that friend leave?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "split equally" then "1/3 OF their share"
๐Ÿ“ Two steps: First divide $36 by 4, then find 13
๐ŸŽฏ What type? Multi-step with fractions and money
Skill: Fractions and Money (Multi-step)

โœ“ Step-by-Step Solution

Step 1: Find each person's share: $36 รท 4 = $9
Step 2: Find 13 of $9: 9 รท 3 = 3
Final Answer: $3 tip
๐Ÿ›’

Section 13: Unit Rates / Better Buy

Finding the best deal by comparing prices per unit

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Unit Rates / Better Buy

Problem 55

A 6-pack of juice boxes costs $4.50. An 8-pack of the same juice costs $5.60. Which is the better buy?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key phrase: "better buy" = compare unit prices
๐Ÿ“ Numbers: 6 for $4.50 vs. 8 for $5.60
๐ŸŽฏ Strategy: Find price PER juice box for each
Skill: Unit Rates / Better Buy

โœ“ Step-by-Step Solution

Step 1: Find unit price for 6-pack: $4.50 รท 6 = $0.75 each
Step 2: Find unit price for 8-pack: $5.60 รท 8 = $0.70 each
Step 3: Compare: $0.70 < $0.75
Final Answer: The 8-pack is the better buy ($0.70 vs $0.75 per box)
๐Ÿ“š Back to TOC

Unit Rates / Better Buy

Problem 56

Store A sells 5 notebooks for $8.75. Store B sells 4 notebooks for $7.20. Which store has the better deal on notebooks?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key phrase: "better deal" = lower unit price wins
๐Ÿ“ Numbers: 5 for $8.75 vs. 4 for $7.20
๐ŸŽฏ Strategy: Divide to find price per notebook
Skill: Unit Rates / Better Buy

โœ“ Step-by-Step Solution

Step 1: Store A: $8.75 รท 5 = $1.75 per notebook
Step 2: Store B: $7.20 รท 4 = $1.80 per notebook
Step 3: Compare: $1.75 < $1.80
Final Answer: Store A has the better deal ($1.75 vs $1.80 each)
๐Ÿ“š Back to TOC

Unit Rates / Better Buy

Problem 57

Brand X cereal: 15 oz for $4.50. Brand Y cereal: 12 oz for $3.00. Which brand costs less per ounce?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key phrase: "costs less per ounce"
๐Ÿ“ Numbers: 15 oz/$4.50 vs. 12 oz/$3.00
๐ŸŽฏ Strategy: Find price รท ounces
Skill: Unit Rates / Better Buy

โœ“ Step-by-Step Solution

Step 1: Brand X: $4.50 รท 15 = $0.30 per oz
Step 2: Brand Y: $3.00 รท 12 = $0.25 per oz
Step 3: Compare: $0.25 < $0.30
Final Answer: Brand Y costs less per ounce ($0.25 vs $0.30)
๐Ÿ“š Back to TOC

Unit Rates / Better Buy

Problem 58

Maya can buy a 3-pack of tennis balls for $5.97 or a 4-pack for $7.96. If she wants to spend her money wisely, which should she buy?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key phrase: "spend money wisely" = find better value
๐Ÿ“ Numbers: 3 for $5.97 vs. 4 for $7.96
๐ŸŽฏ Strategy: Lower unit price = wiser choice
Skill: Unit Rates / Better Buy

โœ“ Step-by-Step Solution

Step 1: 3-pack: $5.97 รท 3 = $1.99 per ball
Step 2: 4-pack: $7.96 รท 4 = $1.99 per ball
Step 3: They're the same price per ball!
Final Answer: Either pack is equally wise - both cost $1.99 per ball!
โœ–๏ธ

Section 14: Whole Number Multiplication

Multi-digit multiplication word problems

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Whole Number Multiplication

Problem 59

The school cafeteria serves 325 students each day. How many meals do they serve in a 5-day school week?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "each day" for 5 days = repeated groups
๐Ÿ“ Numbers: 325 ร— 5
๐ŸŽฏ What type? Equal groups = MULTIPLY
Skill: Multi-digit Multiplication

โœ“ Step-by-Step Solution

Step 1: 325 ร— 5
Step 2: 5 ร— 5 = 25 (write 5, carry 2)
Step 3: 5 ร— 2 = 10, +2 = 12 (write 2, carry 1)
Step 4: 5 ร— 3 = 15, +1 = 16
Final Answer: 1,625 meals
๐Ÿ“š Back to TOC

Whole Number Multiplication

Problem 60

A theater has 28 rows of seats. Each row has 32 seats. How many people can the theater hold?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "rows" with "seats in each" = array
๐Ÿ“ Numbers: 28 ร— 32
๐ŸŽฏ What type? Array/area model = MULTIPLY
Skill: Multi-digit Multiplication

โœ“ Step-by-Step Solution

Step 1: 28 ร— 32
Step 2: 28 ร— 2 = 56
Step 3: 28 ร— 30 = 840
Step 4: Add: 56 + 840 = 896
Final Answer: 896 people
๐Ÿ“š Back to TOC

Whole Number Multiplication

Problem 61

A factory produces 1,250 toys per hour. How many toys are produced in an 8-hour shift?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "per hour" for multiple hours = repeated addition
๐Ÿ“ Numbers: 1,250 ร— 8
Skill: Multi-digit Multiplication

โœ“ Step-by-Step Solution

Step 1: 1,250 ร— 8
Step 2: 8 ร— 0 = 0
Step 3: 8 ร— 5 = 40 (write 0, carry 4)
Step 4: 8 ร— 2 = 16, +4 = 20 (write 0, carry 2)
Step 5: 8 ร— 1 = 8, +2 = 10
Final Answer: 10,000 toys
๐Ÿ“š Back to TOC

Whole Number Multiplication

Problem 62

There are 365 days in a year. How many days are in 12 years?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "days in a year" ร— number of years
๐Ÿ“ Numbers: 365 ร— 12
Skill: Multi-digit Multiplication

โœ“ Step-by-Step Solution

Step 1: 365 ร— 12
Step 2: 365 ร— 2 = 730
Step 3: 365 ร— 10 = 3,650
Step 4: Add: 730 + 3,650 = 4,380
Final Answer: 4,380 days
๐Ÿ“š Back to TOC

Whole Number Multiplication

Problem 63

Each classroom at Lincoln Elementary has 24 desks. There are 18 classrooms. How many desks are there in total?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "each classroom has" ร— number of classrooms
๐Ÿ“ Numbers: 24 ร— 18
Skill: Multi-digit Multiplication

โœ“ Step-by-Step Solution

Step 1: 24 ร— 18
Step 2: 24 ร— 8 = 192
Step 3: 24 ร— 10 = 240
Step 4: Add: 192 + 240 = 432
Final Answer: 432 desks
๐Ÿ“š Back to TOC

Whole Number Multiplication

Problem 64

A bookstore ordered 45 boxes of books. Each box contains 36 books. How many books did they order?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "boxes" with "each contains" = groups
๐Ÿ“ Numbers: 45 ร— 36
Skill: Multi-digit Multiplication

โœ“ Step-by-Step Solution

Step 1: 45 ร— 36
Step 2: 45 ร— 6 = 270
Step 3: 45 ร— 30 = 1,350
Step 4: Add: 270 + 1,350 = 1,620
Final Answer: 1,620 books
๐Ÿ“š Back to TOC

Whole Number Multiplication

Problem 65

A parking garage has 6 levels. Each level has 125 parking spaces. What is the total capacity of the garage?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "each level has" ร— number of levels
๐Ÿ“ Numbers: 125 ร— 6
Skill: Multi-digit Multiplication

โœ“ Step-by-Step Solution

Step 1: 125 ร— 6
Step 2: 6 ร— 5 = 30 (write 0, carry 3)
Step 3: 6 ร— 2 = 12, +3 = 15 (write 5, carry 1)
Step 4: 6 ร— 1 = 6, +1 = 7
Final Answer: 750 parking spaces
๐Ÿ“š Back to TOC

Whole Number Multiplication

Problem 66

An apartment building has 15 floors with 24 apartments on each floor. How many apartments are in the building?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "on each floor" ร— number of floors
๐Ÿ“ Numbers: 15 ร— 24
Skill: Multi-digit Multiplication

โœ“ Step-by-Step Solution

Step 1: 15 ร— 24
Step 2: 15 ร— 4 = 60
Step 3: 15 ร— 20 = 300
Step 4: Add: 60 + 300 = 360
Final Answer: 360 apartments
๐Ÿ†

Section 15: Challenge Problems

Multi-step problems that combine multiple skills!

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๐Ÿ† Challenge Problems

Problem 67

A bakery made 84 cupcakes. They sold 23 of them in the morning and 14 of the original amount in the afternoon. How many cupcakes are left?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "sold" (subtract), "left" (what remains)
๐Ÿ“ Numbers: 84 total, 23 sold + 14 sold
๐ŸŽฏ Steps: Find each amount sold, add them, subtract from 84
Skill: Multi-step (Fractions ร— Whole Numbers, then Subtraction)

โœ“ Step-by-Step Solution

Step 1: Morning sales: 23 ร— 84 = 168 รท 3 = 56 cupcakes
Step 2: Afternoon sales: 14 ร— 84 = 84 รท 4 = 21 cupcakes
Step 3: Total sold: 56 + 21 = 77 cupcakes
Step 4: Remaining: 84 - 77 = 7 cupcakes
Final Answer: 7 cupcakes left
๐Ÿ“š Back to TOC

๐Ÿ† Challenge Problems

Problem 68

Jordan has a rectangular garden that is 12 feet long and 8 feet wide. He wants to build a fence around it and also put a path down the middle (lengthwise). How many total feet of material does he need for the fence AND the path?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "around it" = perimeter, "path down the middle (lengthwise)" = length
๐Ÿ“ Numbers: 12 ft ร— 8 ft rectangle
๐ŸŽฏ Steps: Find perimeter, add length of path
Skill: Multi-step (Perimeter + Addition)

โœ“ Step-by-Step Solution

Step 1: Perimeter = 2(length) + 2(width)
Step 2: Perimeter = 2(12) + 2(8) = 24 + 16 = 40 feet
Step 3: Path length = 12 feet (lengthwise)
Step 4: Total: 40 + 12 = 52 feet
Final Answer: 52 feet of material
๐Ÿ“š Back to TOC

๐Ÿ† Challenge Problems

Problem 69

A movie theater has 25 rows with 18 seats each. On Friday, 35 of the seats were filled. How many seats were empty?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "rows ร— seats" then "filled" vs "empty"
๐Ÿ“ Numbers: 25 ร— 18, then 35 filled
๐ŸŽฏ Steps: Find total, find filled, subtract to get empty
๐Ÿ’ก Shortcut: If 35 filled, then 25 empty!
Skill: Multi-step (Multiplication, Fractions, Subtraction)

โœ“ Step-by-Step Solution

Step 1: Total seats: 25 ร— 18 = 450
Step 2: Filled: 35 ร— 450 = 1,350 รท 5 = 270
Step 3: Empty: 450 - 270 = 180
OR use shortcut: 25 ร— 450 = 900 รท 5 = 180 โœ“
Final Answer: 180 empty seats
๐Ÿ“š Back to TOC

๐Ÿ† Challenge Problems

Problem 70

Mia ran 212 miles on Monday, 334 miles on Wednesday, and 114 miles on Friday. Her goal is to run 10 miles per week. How many more miles does she need to run to meet her goal?

๐Ÿ” Problem Clues

๐Ÿ”‘ Key words: "how many more" = subtract from goal
๐Ÿ“ Numbers: 212 + 334 + 114, goal = 10
๐ŸŽฏ Steps: Add mixed numbers, subtract from 10
Skill: Multi-step (Adding Mixed Numbers, Subtraction)

โœ“ Step-by-Step Solution

Step 1: Convert to common denominator (4):
โ€ข 212 = 224
โ€ข 334 stays the same
โ€ข 114 stays the same
Step 2: Add: 2 + 3 + 1 = 6 whole, 24 + 34 + 14 = 64 = 124 = 112
Step 3: Total: 6 + 112 = 712 miles
Step 4: Remaining: 10 - 712 = 212 miles
Final Answer: 212 more miles needed
๐Ÿ“š Back to TOC

๐ŸŽ‰ Congratulations! ๐ŸŽ‰

๐Ÿ† โญ ๐ŸŽฏ

You've completed all 70 word problems!

๐Ÿ“‹ Skills You Practiced:

  • Area & Volume & Surface Area
  • Simplifying Fractions with GCF
  • Mixed Numbers & Improper Fractions
  • Adding & Subtracting Fractions
  • Adding Mixed Numbers
  • Finding LCM
  • Multiplying Fractions ร— Whole Numbers
  • Fractions and Money
  • Unit Rates & Better Buy
  • Multi-digit Multiplication
  • Multi-step Problem Solving

Keep practicing and you'll become a word problem master! ๐Ÿ’ช

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