Multiplying Decimals & Ratio Tables

Using ratio tables, the fraction-decimal connection, and smart strategies to multiply with decimals

📚

Subject

Math

⏱️

Duration

60+ min

🎯

Standard

5.NBT.B.7

📋 Standards & Objectives

📜Standards

5.NBT.B.7Add, subtract, multiply, and divide decimals to hundredths.

5.NF.B.4Multiply a fraction or whole number by a fraction.

5.OA.B.3Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms.

5.NF.B.5Interpret multiplication as scaling (resizing).

🎯SWBAT

Use a ratio table to find the cost of multiple items when the unit price is a decimal
Choose smart strategies (doubling, ×10, combining rows) to fill ratio tables efficiently
Explain why multiplying by 0.25 gives the same result as finding ¼ of a number
Use the fraction-decimal connection to solve multiplication problems

📖 Key Vocabulary

📝Ratio Table

A table that shows pairs of numbers that have the same relationship. Each row multiplies by the same rule.

A ratio table for $3.00 per pound would show 1→$3, 2→$6, 5→$15, and so on.

You can use a ratio table to find any amount by building from rows you already know.

📝Unit Rate

The cost or value for one single unit — the "per 1" amount. It's always the starting row in a ratio table.

If a bag of chips costs $2.50, that $2.50 is the unit rate — the price for one bag.

Knowing the unit rate lets you figure out the cost for any number of items.

📝Product

The answer you get when you multiply two numbers together. In 4.25 × 3 = 12.75, the product is 12.75.

The product of 6 and 0.25 is 1.50 — you can find this by thinking "6 quarters."

Every cell in a ratio table is really a product — the unit rate times the number of items.

📝Equivalent

Having the same value, even though they look different. The fraction 14 and the decimal 0.25 are equivalent.

Equivalent means "equal in value" — 14 of 20 and 0.25 × 20 both give you 5.

Recognizing equivalent forms helps you pick the easiest way to solve a problem.

🚀 The Fudge Shop

A sweet problem to solve

Imagine you're opening a fudge shop at the Wellpinit Winter Market. Each pound of fudge costs $4.25 to make.

The Big Question

A customer walks in and orders 19 pounds of fudge. How much will it cost you to make?

You could multiply $4.25 × 19 with the standard algorithm... but is there a smarter way? Today we'll learn strategies that make problems like this way easier.

👨‍🏫 What Is a Ratio Table?

A ratio table is a tool that organizes pairs of numbers that follow the same rule. Every row uses the same unit rate.

How It Works

If 1 pound of fudge costs $4.25, then 2 pounds cost $4.25 + $4.25 = $8.50. A ratio table tracks all of these amounts in one organized place.

Pounds of Fudge	1	?	?	?
Cost	$4.25	?	?	?

The unit rate ($4.25 per pound) is our starting point. Let's fill in the rest!

👨‍🏫 Building the Table: Step by Step

We start with what we know: 1 pound = $4.25. Then we use multiplication to find more rows.

Pounds	1	2	5	10
Cost	$4.25	$8.50	$21.25	$42.50

Strategy: Pick friendly numbers first — ×2, ×5, ×10 are easy to compute mentally. We'll use these as building blocks!

👨‍🏫 Smart Strategies: ×2, ×5, ×10

✌️Double It (×2)

$4.25 × 2

$4.25 + $4.25

= $8.50

🖐️Five Groups (×5)

$4.25 × 5

Half of ×10:

$42.50 ÷ 2

= $21.25

🔟Ten Groups (×10)

$4.25 × 10

Move decimal 1 place right:

= $42.50

These three benchmarks — ×2, ×5, ×10 — are your power tools. You can combine them to find ANY amount!

👨‍🏫 Combining Rows: Finding 19 Pounds

Here's the magic of ratio tables: you can add rows together to make new amounts!

Pounds	1	2	5	9	10	19
Cost	$4.25	$8.50	$21.25	$38.25	$42.50	$80.75

Strategy: 19 = 10 + 9, and 9 = 5 + 4, and 4 = 2 + 2. So: $42.50 + $21.25 + $8.50 + $8.50 = $80.75

Or even simpler: 19 = 20 − 1, so $85.00 − $4.25 = $80.75

📓 Write This Down

Write this in your notebook!

Key Terms

Ratio Table

Unit Rate

Combine Rows

Notes

Ratio Table Strategies:
1. Start with the unit rate (cost for 1).
2. Build benchmarks: ×2, ×5, ×10.
3. Combine rows by adding: if you know the cost for 10 and 9, you can find 19 by adding those costs.
4. You can also subtract: 20 − 1 = 19, so cost of 20 minus cost of 1 = cost of 19.

Example: $4.25 × 19 → $85.00 − $4.25 = $80.75

✅ Quick Check

If 1 item costs $3.50 and you know that 10 items cost $35.00...

How would you use the ratio table to find the cost of 12 items?

12 = 10 + 2, so: $35.00 + $7.00 = $42.00

You already know ×10 ($35) and ×2 ($7). Just add them!

🔄 Bridge: Two Powerful Ideas

What We Just Learned

We can use ratio tables and smart strategies (×2, ×5, ×10, combine rows) to multiply decimals.

→

What's Coming Next

Fractions and decimals are equivalent — and that connection makes multiplication even easier!

👨‍🏫 Finding 14 of 20

What does "14 of 20" actually mean? It means: divide 20 into 4 equal groups.

20 dots split into 4 equal groups of 5

14 × 20 = 20 ÷ 4 = 5

👨‍🏫 Now Try 0.25 × 20

We know that 14 = 0.25 (just like one quarter = $0.25). So what happens when we compute 0.25 × 20?

0.25 × 20 = 5

Wait — Same Answer!

14 × 20 = 5 and 0.25 × 20 = 5

That's because 14 and 0.25 are equivalent. They're the same number written two different ways!

⭐ The Big Connection

Multiplying by 0.25

is the same thing as

Finding 14 of that number

is the same thing as

Dividing by 4

Three ways to say the exact same thing. Pick whichever is easiest for the problem!

👨‍🏫 Scaling Up: 25 × 20

If we already know that 0.25 × 20 = 5, can we use that to find 25 × 20?

0.25 × 20 = 5

25 is 100 times bigger than 0.25

25 × 20 = 5 × 100 = 500

The pattern: If you know a decimal product, you can scale it up. Since 25 = 0.25 × 100, the product is also 100 times bigger: 5 × 100 = 500.

👨‍🏫 Putting It Together: 14 of 21

This one doesn't divide evenly! But we can break it apart using what we already know.

21 = 20 + 1

14 of 20

= 5

+

14 of 1

= 0.25

14 × 21 = 5 + 0.25 = 5.25

This is the same "combine rows" strategy from our ratio table!

📓 Write This Down

Write this in your notebook!

Key Terms

Equivalent

14 = 0.25

÷ 4

Notes

The Fraction-Decimal Connection:
Multiplying by 0.25 = finding ¼ = dividing by 4.
All three give the SAME answer!

Break-apart strategy:
¼ of 21 → split into ¼ of 20 + ¼ of 1
= 5 + 0.25 = 5.25

Scaling up: If 0.25 × 20 = 5, then 25 × 20 = 500 (×100)

✅ Quick Check

True or False?

Multiplying a number by 0.25 gives you the same result as dividing that number by 4.

👍 Thumbs up if TRUE 👎 Thumbs down if FALSE

TRUE!

0.25 = 14, so multiplying by 0.25 IS dividing by 4.

🔄 Your Turn Together

What We Learned

Ratio table strategies (×2, ×5, ×10, combine) and the fraction-decimal connection (14 = 0.25).

→

Now Let's Practice

Callie is starting a bracelet business. Let's help her figure out costs, revenue, and profit using ratio tables!

👥 Callie's Beaded Bracelets: Cost

Each bracelet costs $2.25 to make

The unit rate is $2.25 per bracelet. Fill in the ratio table using your strategies!

Bracelets	1	2	4	5	10	19	20
Cost	$2.25	$4.50	$9.00	$11.25	$22.50	$42.75	$45.00

Hint: Try ×2, then double for ×4. Use ×10 and ×5. How would you find 19?

👥 Callie's Revenue: $3.50 Each

How much money comes IN from selling bracelets

Callie sells each beaded bracelet for $3.50. Let's build the revenue ratio table!

Bracelets	1	2	5	8	10	20
Revenue	$3.50	$7.00	$17.50	$28.00	$35.00	$70.00

💬 Turn & Talk

🤔Discuss with a Partner

If Callie makes and sells 10 beaded bracelets, she spends $22.50 on supplies and earns $35.00 in revenue. How much profit does she make? Is the bracelet business worth it?

Sentence starter: "Callie's profit on 10 bracelets is ___ because ___. I think this is / isn't worth it because ___."

$35.00 − $22.50 = $12.50 profit

That's $1.25 profit per bracelet!

👥 Woven Bracelets: $1.20 Each

A cheaper option — but is it better?

Woven bracelets cost only $1.20 each to make. Fill in this ratio table — notice the trickier numbers!

Woven	1	5	10	15	50	99	100
Cost	$1.20	$6.00	$12.00	$18.00	$60.00	$118.80	$120.00

Hint: 99 = 100 − 1. Can you use subtraction?

👥 Compare: Cost vs. Revenue

Which bracelet is the better business?

Beaded (10 bracelets)

Cost to make 10: $22.50 Revenue from selling 10: $35.00
Profit: $12.50 ($1.25 each)

Woven (10 bracelets)

Cost to make 10: $12.00 If she sells woven for $2.00 each: $20.00
Profit: $8.00 ($0.80 each)

💡 Click buttons to highlight, or use J/K keys to select

👥 Fraction-Decimal Practice

Use what you know about ¼ = 0.25

1️⃣14 of 40

40 ÷ 4 = ?

10

2️⃣0.25 × 40

Same as 14 of 40!

10

3️⃣14 of 32

32 ÷ 4 = ?

8

4️⃣14 of 33

Break it: ¼ of 32 + ¼ of 1

8.25

8 + 0.25 = 8.25

📓 Write This Down

Write this in your notebook!

Key Terms

Benchmarks

Break Apart

Profit

Notes

Ratio Table Steps:
1. Write the unit rate.
2. Pick benchmark amounts (×2, ×5, ×10).
3. Combine or subtract to find tricky amounts.

Fraction-Decimal Shortcut:
¼ of a number = 0.25 × that number = number ÷ 4.
If it doesn't divide evenly, break it apart!
Example: ¼ of 33 = ¼ of 32 + ¼ of 1 = 8 + 0.25 = 8.25

🔄 Time to Fly Solo

You've got the tools. Now use them!

You know how to:

1. Build a ratio table from a unit rate

2. Use benchmarks (×2, ×5, ×10) and combine rows

3. Connect fractions and decimals (14 = 0.25 = ÷4)

4. Break apart tricky numbers

🔍 You Try: Build a Ratio Table

Your Turn

A food truck sells tacos for $3.75 each. Build a ratio table to find the cost of 14 tacos.

In your notebook, draw a ratio table with the unit rate ($3.75 for 1 taco).
Fill in benchmarks: ×2, ×5, ×10.
Use your benchmarks to find the cost of 14 tacos. Show your strategy!

14 = 10 + 4, and 4 = 2 + 2

$37.50 + $7.50 + $7.50 = $52.50

🔍 You Try: Work Backwards

Challenge: Reverse It

A baker spends $5.50 per batch of cookies. She spent a total of $82.50. How many batches did she make?

Build a ratio table starting with 1 batch = $5.50.
Fill in benchmarks until you reach or get close to $82.50.
How many batches make $82.50? Write your answer.

10 batches = $55.00 | 5 batches = $27.50

$55.00 + $27.50 = $82.50 → 10 + 5 = 15 batches

🔍 You Try: Fraction-Decimal Connection

1️⃣Find 14 of 48

Think: 48 ÷ 4 = ?

12

2️⃣Find 0.25 × 48

Same as #1 — verify!

12

3️⃣Find 14 of 50

Break apart: ¼ of 48 + ¼ of 2

12.5

12 + 0.5 = 12.5

4️⃣Find 25 × 48

Scale up: 0.25 × 48 × 100

1,200

12 × 100 = 1,200

🔍 You Try: Real-World Problem

Soccer Cleats Fund

Callie needs $65.00 for soccer cleats. She can sell beaded bracelets for $3.50 each and they cost $2.25 each to make (profit = $1.25 each).

Build a profit ratio table — profit per bracelet is $1.25.
Use your table to find: how many bracelets does Callie need to sell to earn at least $65?
What is the total cost of supplies for that many bracelets?

10 bracelets = $12.50 profit | 50 bracelets = $62.50 profit

52 bracelets = $62.50 + $2.50 = $65.00 → 52 bracelets

Supply cost: 52 × $2.25 = $117.00

⭐ Challenge: Stretch Problem

For early finishers — push your thinking!

The Fudge Shop Returns

Remember: fudge costs $4.25 per pound to make. A customer orders enough fudge to spend exactly $429.25.

Build a ratio table to figure out how many pounds of fudge that is.
Hint: start with ×100 ($425.00). How close is that to $429.25?
Write the number of pounds AND explain your strategy.

100 lbs = $425.00 | 1 lb = $4.25 | $429.25 − $425.00 = $4.25

That's exactly 1 more pound! → 101 pounds

📝 Key Takeaways

📊Ratio Tables

Start with the unit rate, build benchmarks (×2, ×5, ×10), then combine or subtract rows to find any amount.

🔗Fraction = Decimal

Multiplying by 0.25 is the same as finding 14 of a number, which is the same as dividing by 4.

🧩Break Apart

When a number doesn't divide evenly, split it into a friendly part and what's left: ¼ of 21 = ¼ of 20 + ¼ of 1.

🚀Scale Up

If you know 0.25 × 20 = 5, then 25 × 20 = 500. A decimal product can be scaled by powers of 10.

📓 Summary Note

Write 1 Sentence

In the bottom of your notebook page, write one sentence explaining what you learned today about multiplying with decimals and using ratio tables. Try to include at least one vocabulary word!

🎫 Exit Ticket

Show what you know!

1️⃣Ratio Table

Pencils cost $0.75 each. Use a ratio table to find the cost of 12 pencils.

10 pencils = $7.50 | 2 pencils = $1.50

$7.50 + $1.50 = $9.00

2️⃣Fraction-Decimal

Find 14 of 30. Show your strategy.

¼ of 28 = 7 | ¼ of 2 = 0.5

7 + 0.5 = 7.5

Or: 30 ÷ 4 = 7.5