🧮 Fractions Unit Review

30 Practice Problems to Test Your Skills!

Word Problems • Equations • Multiple Choice

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📚 Table of Contents

1️⃣ Equivalent Fractions

Problems 1-4

2️⃣ Simplifying Fractions

Problems 5-8

3️⃣ Mixed Numbers & Improper

Problems 9-12

4️⃣ Finding LCM

Problems 13-16

5️⃣ Adding Mixed Numbers

Problems 17-20

6️⃣ Multiplying Fractions

Problems 21-24

7️⃣ Fractions & Money

Problems 25-27

8️⃣ Unit Rates

Problems 28-30
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Section 1: Equivalent Fractions

Problems 1-4 • Finding fractions that represent the same amount

1 Word Problem

Marcus ate 2 slices of pizza. The pizza was cut into 8 equal slices. His sister says he ate the same amount as if the pizza had been cut into 4 slices and he took 1. Is she correct?

✅ Answer

Yes, she is correct!

🔍 Skills Needed:
Identify fraction from context Create equivalent fractions
📝 Steps:
  1. Marcus's fraction: 2 out of 8 = 28
  2. Sister's fraction: 1 out of 4 = 14
  3. Check: 28 ÷ 22 = 14 ✓
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Equivalent Fractions

2 Equation

Find the missing number:

35 = ?20

✅ Answer

? = 12

🔍 Skills Needed:
Find the multiplier for denominator Apply same multiplier to numerator
📝 Steps:
  1. Find multiplier: 5 × ? = 20, so 20 ÷ 5 = 4
  2. Apply to numerator: 3 × 4 = 12
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Equivalent Fractions

3 Multiple Choice

Which fraction is equivalent to 46?

A. 810
B. 23
C. 68
D. 34

✅ Answer

B. 23

🔍 Skills Needed:
Simplify using GCF
📝 Steps:
  1. GCF of 4 and 6 = 2
  2. 4÷26÷2 = 23
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Equivalent Fractions

4 Word Problem

A recipe calls for three-fourths cup of flour. Jasmine only has a measuring cup that shows eighths. How many eighths of a cup does she need?

✅ Answer

68 cup (6 eighths)

🔍 Skills Needed:
Convert words to fractions Create equivalent with new denominator
📝 Steps:
  1. Three-fourths = 34
  2. 4 × 2 = 8, so multiply by 22
  3. 3×24×2 = 68
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Section 2: Simplifying Fractions

Problems 5-8 • Reducing fractions to lowest terms

5 Equation

Simplify to lowest terms:

1824

✅ Answer

34

🔍 Skills Needed:
Find GCF Divide both by GCF
📝 Steps:
  1. Factors of 18: 1, 2, 3, 6, 9, 18
  2. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
  3. GCF = 6
  4. 18÷624÷6 = 34
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Simplifying Fractions

6 Word Problem

During gym class, 15 out of 25 students completed all the exercises. What fraction of the class finished, written in simplest form?

✅ Answer

35 of the class

🔍 Skills Needed:
Write fraction from context Find GCF and simplify
📝 Steps:
  1. 15 out of 25 = 1525
  2. GCF of 15 and 25 = 5
  3. 15÷525÷5 = 35
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Simplifying Fractions

7 Multiple Choice

Which fraction is already in simplest form?

A. 812
B. 715
C. 921
D. 1416

✅ Answer

B. 715

🔍 Skills Needed:
Check if GCF = 1
📝 Steps:
  1. A: 8 and 12 share factor 4
  2. B: 7 is prime; 15 = 3×5. No shared factors! ✓
  3. C: 9 and 21 share factor 3
  4. D: 14 and 16 share factor 2
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Simplifying Fractions

8 Equation

Simplify to lowest terms:

3648

✅ Answer

34

🔍 Skills Needed:
Find GCF of larger numbers
📝 Steps:
  1. GCF of 36 and 48 = 12
  2. 36÷1248÷12 = 34
  3. Or simplify in steps: ÷2 → ÷2 → ÷3
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Section 3: Mixed Numbers & Improper Fractions

Problems 9-12 • Converting between forms

9 Equation

Convert to an improper fraction:

3 25

✅ Answer

175

🔍 Skills Needed:
Multiply whole × denominator Add numerator
📝 Steps:
  1. Multiply: 3 × 5 = 15
  2. Add numerator: 15 + 2 = 17
  3. Keep denominator: 175
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Mixed Numbers & Improper Fractions

10 Equation

Convert to a mixed number:

296

✅ Answer

456

🔍 Skills Needed:
Divide numerator by denominator Quotient = whole, remainder = numerator
📝 Steps:
  1. Divide: 29 ÷ 6 = 4 R 5
  2. Whole number: 4
  3. Fraction: 56
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Mixed Numbers & Improper Fractions

11 Word Problem

A baker has 23 cups of sugar divided equally into containers that hold 4 cups each. Express how many full containers she has, plus any leftover, as a mixed number.

✅ Answer

534 containers

🔍 Skills Needed:
Set up improper fraction Convert to mixed number
📝 Steps:
  1. Set up: 234
  2. Divide: 23 ÷ 4 = 5 R 3
  3. Answer: 534
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Mixed Numbers & Improper Fractions

12 Multiple Choice

Which improper fraction equals 638?

A. 488
B. 518
C. 638
D. 548

✅ Answer

B. 518

🔍 Skills Needed:
whole × denominator + numerator
📝 Steps:
  1. Multiply: 6 × 8 = 48
  2. Add: 48 + 3 = 51
  3. Answer: 518
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Section 4: Finding LCM

Problems 13-16 • Least Common Multiple for common denominators

13 Equation

Find the Least Common Multiple (LCM) of 6 and 8.

✅ Answer

LCM = 24

🔍 Skills Needed:
List multiples Find smallest common one
📝 Steps:
  1. Multiples of 6: 6, 12, 18, 24...
  2. Multiples of 8: 8, 16, 24...
  3. First common: 24
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Finding LCM

14 Word Problem

Sarah waters her plants every 4 days. Her brother waters his every 6 days. They both watered today. In how many days will they both water on the same day again?

✅ Answer

12 days

🔍 Skills Needed:
Recognize LCM problem "Same time again" = LCM
📝 Steps:
  1. Multiples of 4: 4, 8, 12...
  2. Multiples of 6: 6, 12...
  3. LCM = 12
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Finding LCM

15 Multiple Choice

What is the LCM of 5 and 9?

A. 14
B. 45
C. 36
D. 90

✅ Answer

B. 45

🔍 Skills Needed:
No common factors = multiply
📝 Steps:
  1. 5 is prime; 9 = 3×3
  2. No shared factors!
  3. LCM = 5 × 9 = 45
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Finding LCM

16 Word Problem

To add 23 + 58, you need a common denominator. What is the least common denominator?

✅ Answer

LCD = 24

🔍 Skills Needed:
LCD = LCM of denominators
📝 Steps:
  1. Denominators: 3 and 8
  2. Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24
  3. Multiples of 8: 8, 16, 24
  4. LCD = 24
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Section 5: Adding Mixed Numbers

Problems 17-20 • Adding fractions with regrouping

17 Equation

Add:

214 + 324

✅ Answer

534

🔍 Skills Needed:
Add whole numbers Add fractions (same denominator)
📝 Steps:
  1. Add wholes: 2 + 3 = 5
  2. Add fractions: 1+24 = 34
  3. Combine: 534
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Adding Mixed Numbers

18 Equation

Add (watch for regrouping!):

456 + 246

✅ Answer

712

🔍 Skills Needed:
Add fractions Regroup improper fraction Simplify
📝 Steps:
  1. Add fractions: 5+46 = 96 = 136
  2. Add wholes: 4 + 2 + 1 = 7
  3. Simplify: 736 = 712
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Adding Mixed Numbers

19 Word Problem

A carpenter needs two pieces of wood. One is 312 feet and the other is 234 feet. What is the total length needed?

✅ Answer

614 feet

🔍 Skills Needed:
Find LCD (LCM of 2 and 4 = 4) Convert, add, regroup
📝 Steps:
  1. Convert: 12 = 24
  2. Add fractions: 2+34 = 54 = 114
  3. Add wholes: 3 + 2 + 1 = 6
📚 Back to TOC

Adding Mixed Numbers

20 Multiple Choice

What is 123 + 256?

A. 379
B. 412
C. 416
D. 376

✅ Answer

B. 412

🔍 Skills Needed:
Find LCD = 6 Convert, add, simplify
📝 Steps:
  1. Convert: 23 = 46
  2. Add: 4+56 = 96 = 136
  3. Wholes: 1 + 2 + 1 = 4; Simplify: 36 = 12
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Section 6: Multiplying Fractions & Whole Numbers

Problems 21-24 • Finding a fraction of a number

21 Equation

Multiply:

34 × 12

✅ Answer

9

🔍 Skills Needed:
Multiply numerator × whole Divide by denominator
📝 Steps:
  1. Multiply: 3 × 12 = 36
  2. Divide: 36 ÷ 4 = 9
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Multiplying Fractions & Whole Numbers

22 Word Problem

A cookie recipe makes 24 cookies. Tyler only wants to make two-thirds of the recipe. How many cookies will he make?

✅ Answer

16 cookies

🔍 Skills Needed:
"Of" means multiply Fraction × whole number
📝 Steps:
  1. Set up: 23 × 24
  2. 24 ÷ 3 = 8, then 8 × 2 = 16
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Multiplying Fractions & Whole Numbers

23 Multiple Choice

What is 58 × 32?

A. 15
B. 20
C. 25
D. 40

✅ Answer

B. 20

🔍 Skills Needed:
Divide first, then multiply
📝 Steps:
  1. 32 ÷ 8 = 4
  2. 4 × 5 = 20
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Multiplying Fractions & Whole Numbers

24 Word Problem

A running track is 400 meters around. During practice, Elena ran three-fifths of the track. How many meters did she run?

✅ Answer

240 meters

🔍 Skills Needed:
"Of the track" = multiply
📝 Steps:
  1. Set up: 35 × 400
  2. 400 ÷ 5 = 80
  3. 80 × 3 = 240
📚 Back to TOC

Section 7: Fractions & Money

Problems 25-27 • Understanding fractions of a dollar

25 Word Problem

Marco has 3 quarters. What fraction of a dollar does he have? Write in simplest form.

✅ Answer

34 of a dollar ($0.75)

🔍 Skills Needed:
Quarter = 14 dollar
📝 Steps:
  1. Each quarter = 14
  2. 3 quarters = 3 × 14 = 34
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Fractions & Money

26 Word Problem

A video game costs $60. Destiny has saved two-fifths of the price. How much has she saved?

✅ Answer

$24

🔍 Skills Needed:
"Of the price" = multiply
📝 Steps:
  1. Set up: 25 × $60
  2. $60 ÷ 5 = $12
  3. $12 × 2 = $24
📚 Back to TOC

Fractions & Money

27 Multiple Choice

Emma spent 38 of her $40 allowance. How much did she spend?

A. $12
B. $15
C. $18
D. $25

✅ Answer

B. $15

🔍 Skills Needed:
Multiply fraction × money
📝 Steps:
  1. $40 ÷ 8 = $5
  2. $5 × 3 = $15
📚 Back to TOC

Section 8: Unit Rates

Problems 28-30 • Finding the cost per one item

28 Word Problem

A pack of 6 water bottles costs $4.50. What is the cost per bottle?

✅ Answer

$0.75 per bottle

🔍 Skills Needed:
Unit rate = total ÷ quantity
📝 Steps:
  1. Set up: $4.50 ÷ 6 bottles
  2. $4.50 ÷ 6 = $0.75
📚 Back to TOC

Unit Rates

29 Word Problem

Store A sells 4 notebooks for $6. Store B sells 5 notebooks for $8. Which store has the better buy?

✅ Answer

Store A is the better buy

🔍 Skills Needed:
Find unit rate for each Compare - lower is better
📝 Steps:
  1. Store A: $6 ÷ 4 = $1.50 per notebook
  2. Store B: $8 ÷ 5 = $1.60 per notebook
  3. $1.50 < $1.60, so Store A wins!
📚 Back to TOC

Unit Rates

30 Multiple Choice

If 3 pounds of apples cost $5.25, what is the unit rate per pound?

A. $1.50
B. $1.75
C. $2.00
D. $2.25

✅ Answer

B. $1.75

🔍 Skills Needed:
Divide total by quantity
📝 Steps:
  1. $5.25 ÷ 3 pounds
  2. $5.25 ÷ 3 = $1.75
📚 Back to TOC

🎉 Great Job!

🏆 ⭐ 🎯

You've reviewed all 30 problems covering:

📝 Skills Checklist

✅ Equivalent Fractions

✅ Simplifying Fractions (GCF)

✅ Mixed Numbers ↔ Improper Fractions

✅ Least Common Multiples (LCM)

✅ Adding Mixed Numbers

✅ Multiplying Fractions × Whole Numbers

✅ Fractions & Money

✅ Unit Rates

Keep practicing and you'll master fractions! 💪

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