To multiply by 25: divide the number by 4, then multiply by 100.
Example: 25 × 36 → 36 ÷ 4 = 9 → 9 × 100 = 900
Why: 25 = 14 of 100
Benchmark Fractions & Mental Multiplication
Use what you know about fractions to multiply by 25, 50, and 75 — in your head!
📚
Subject
Math
⏱️
Duration
45 min
🎯
Standard
5.NBT.B.5
📋 Standards & Objectives
📜Standards
5.NBT.B.5Fluently multiply multi-digit whole numbers using the standard algorithm.
5.NF.B.4Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
5.NF.B.5Interpret multiplication as scaling (resizing) — understand what happens when you multiply by a fraction less than 1.
🎯SWBAT
- Find a unit fraction of a whole number (e.g., 14 of 36)
- Recognize that 25 = 14 of 100, 50 = 12 of 100, and 75 = 34 of 100
- Use benchmark fractions as a mental math strategy to multiply by 25, 50, and 75
- Explain why the strategy works using fraction reasoning
📖 Key Vocabulary
📝Benchmark Fraction
A common fraction that is easy to work with and useful as a reference point: 14, 12, 34
The three benchmark fractions we use most often: 14 = 25 out of 100, 12 = 50 out of 100, 34 = 75 out of 100.
Knowing benchmark fractions helps us estimate and calculate quickly — they're our mental math power tools!
📝Mental Math
Solving math problems in your head using strategies and number sense — no pencil needed!
Instead of stacking 25 x 36 and doing long multiplication, we can use mental math: think "14 of 36 is 9, so 25 x 36 = 900."
Mental math doesn't mean you memorized the answer — it means you found a smart shortcut to figure it out in your head.
📝Fraction of a Number
Finding a fractional part of a whole number by dividing. "14 of 36" means 36 ÷ 4.
Fraction of a number: 14 of 36 → 36 ÷ 4 = 9
Fraction of a number: 34 of 84 → 84 ÷ 4 = 21, then 21 × 3 = 63
📝Product
The answer you get when you multiply two numbers together.
The product of 25 × 36 is 900.
Today we'll find products using fraction shortcuts instead of the standard algorithm.
🚀 Can You Solve This... In Your Head?
No pencil. No paper. Just your brain.
50
×
12
=
?
Think about it...
If you know that half of 12 is 6... can you use that to figure out 50 × 12?
Today you'll learn the trick behind this — and it works for 25 and 75 too!
🔗 The Secret Connection
Fractions and 100 are best friends
These three numbers are hiding fractions!
25
= 25100 = 14 of 100
50
= 50100 = 12 of 100
75
= 75100 = 34 of 100
So when you multiply a number by 25, 50, or 75... you can think of it as finding a benchmark fraction of that number, then multiplying by 100!
💬 Turn & Talk
🤔Discuss with a Partner
If 25 is 14 of 100... why does finding 14 of a number and then multiplying by 100 give you the same answer as multiplying by 25?
Sentence starter: "I think it works because ___"
👨🏫 Strategy #1: Multiply by 25
25 = 14 of 100
The Rule
To multiply any number by 25:
Step 1: Find 14 of the number (divide by 4)
Step 2: Multiply the result by 100
Why? Because 25 × 4 = 100. So 25 = 1004
👨🏫 I Do: 25 × 36
Watch me solve this with the fraction strategy
25
×
36
=
?
1
Think: 25 is 14 of 100. So find 14 of 36.
2
Fraction of a number: 36 ÷ 4 = 9
3
Multiply by 100: 9 × 100 = 900
25
×
36
=
900
🧩 See It: 14 of 36
Why does 36 ÷ 4 = 9?
36 split into 4 equal groups:
9
Group 1
9
Group 2
9
Group 3
9
Group 4
14 of 36 = 9 → so 25 × 36 = 9 × 100 = 900
👨🏫 I Do: 25 × 48
Another example — same strategy
25
×
48
=
?
1
Think: 14 of 48 → 48 ÷ 4 = 12
2
Multiply by 100: 12 × 100 = 1,200
25
×
48
=
1,200
✅ Quick Check
What is 14 of 20?
Hold up your answer on your fingers!
14 of 20 = 5 → so 25 × 20 = 5 × 100 = 500
📓 Write This Down: ×25 Rule
Write this in your notebook!
Key Word
× 25 Rule
In Your Notebook
👨🏫 Strategy #2: Multiply by 50
50 = 12 of 100
The Rule
To multiply any number by 50:
Step 1: Find 12 of the number (divide by 2)
Step 2: Multiply the result by 100
Why? Because 50 × 2 = 100. So 50 = 1002
👨🏫 I Do: 50 × 46
The easiest one — just halve it!
50
×
46
=
?
1
Think: 12 of 46 → 46 ÷ 2 = 23
2
Multiply by 100: 23 × 100 = 2,300
50
×
46
=
2,300
✅ Quick Check
50 × 18 = ?
👍 Thumbs up when you have it!
12 of 18 = 9 → 9 × 100 = 900
🔄 What About 75?
This one has an extra step — but you've got this!
You've learned that 25 = 14 and 50 = 12. Now the big one:
75 = 34 of 100
This means: divide by 4, then multiply by 3, then multiply by 100.
👨🏫 Strategy #3: Multiply by 75
75 = 34 of 100
The Rule
To multiply any number by 75:
Step 1: Find 14 of the number (divide by 4)
Step 2: Multiply that result by 3 (to get 34)
Step 3: Multiply by 100
👨🏫 I Do: 75 × 84
Three steps — watch closely
75
×
84
=
?
1
Find 14: 84 ÷ 4 = 21
2
Multiply by 3 (for 34): 21 × 3 = 63
3
Multiply by 100: 63 × 100 = 6,300
75
×
84
=
6,300
🧩 See It: 34 of 84
Three of the four groups
21
Group 1 ✓
21
Group 2 ✓
21
Group 3 ✓
21
Group 4 ✗
34 of 84 = 21 + 21 + 21 = 63 → 63 × 100 = 6,300
✅ Quick Check
34 of 40 = ?
Think: 14 of 40 first... then × 3!
40 ÷ 4 = 10 → 10 × 3 = 30 → so 75 × 40 = 30 × 100 = 3,000
📓 Write This Down: All 3 Rules
Write this in your notebook!
Key Words
× 25 Rule
× 50 Rule
× 75 Rule
In Your Notebook
× 25: ÷ 4, then × 100 (because 25 = 14 of 100)
× 50: ÷ 2, then × 100 (because 50 = 12 of 100)
× 75: ÷ 4, then × 3, then × 100 (because 75 = 34 of 100)
× 50: ÷ 2, then × 100 (because 50 = 12 of 100)
× 75: ÷ 4, then × 3, then × 100 (because 75 = 34 of 100)
🔄 Let's Practice Together
From watching → doing
You just learned 3 mental math strategies using benchmark fractions.
Now: I'll set up the problem. You solve it with your partner!
Step 1: Decide which benchmark fraction to use.
Step 2: Find the fraction of the number.
Step 3: Multiply by 100 for the product.
👥 We Do: 25 × 32
Solve this with your partner!
25
×
32
=
?
Which benchmark fraction is 25? What do you divide by?
25 = 14 → 32 ÷ 4 = 8 → 8 × 100 = 800
👥 We Do: 50 × 34
Talk through it with your partner
50
×
34
=
?
This one should be the easiest! Half of 34 is...
50 = 12 → 34 ÷ 2 = 17 → 17 × 100 = 1,700
👥 We Do: 75 × 16
The three-step one! You can do it.
75
×
16
=
?
Remember: 14 first... then × 3... then × 100.
75 = 34 → 16 ÷ 4 = 4 → 4 × 3 = 12 → 12 × 100 = 1,200
💬 Turn & Talk
🤔Discuss with a Partner
Which strategy do you think is hardest — × 25, × 50, or × 75? Why? Which is easiest?
Sentence starter: "I think ___ is the hardest because ___"
👥 We Do: 25 × 56
Can you do this one in your head?
25
×
56
=
?
Think quietly for 10 seconds... then share with your partner.
56 ÷ 4 = 14 → 14 × 100 = 1,400
🔄 Time to Fly Solo!
Use your mental math strategies
Your Toolkit
× 25
÷ 4, then × 100
× 50
÷ 2, then × 100
× 75
÷ 4, × 3, then × 100
🔍 You Try #1
25
×
44
=
?
Your Turn
- Which benchmark fraction is 25?
- Find that fraction of 44.
- Multiply by 100 for the product.
44 ÷ 4 = 11 → 11 × 100 = 1,100
🔍 You Try #2
50
×
66
=
?
Your Turn
- 50 is what benchmark fraction of 100?
- Find half of 66.
- Multiply by 100.
66 ÷ 2 = 33 → 33 × 100 = 3,300
🔍 You Try #3
75
×
24
=
?
Your Turn — 3 Steps!
- Find 14 of 24.
- Multiply that by 3 (to get 34).
- Multiply by 100.
24 ÷ 4 = 6 → 6 × 3 = 18 → 18 × 100 = 1,800
🏆 Challenge Round
This one takes a little more number sense!
75
×
52
=
?
Hint: 52 ÷ 4 = 13. Now what?
52 ÷ 4 = 13 → 13 × 3 = 39 → 39 × 100 = 3,900
📝 Anchor Chart: Benchmark Fraction Strategies
🟡× 25
25 = 14 of 100
÷ 4, then × 100
25 × 36 → 9 × 100 = 900
🔵× 50
50 = 12 of 100
÷ 2, then × 100
50 × 46 → 23 × 100 = 2,300
🟢× 75
75 = 34 of 100
÷ 4, × 3, then × 100
75 × 84 → 63 × 100 = 6,300
📓 Summary Note
Write 1 Sentence
In the bottom of your notebook page, write one sentence explaining what you learned today about using benchmark fractions to do mental math multiplication.
🎫 Exit Ticket
Show what you know!
1️⃣× 25
14 of 28 is ___, so 25 × 28 = ___
14 of 28 = 7, so 25 × 28 = 700
2️⃣× 75
34 of 40 is ___, so 75 × 40 = ___
34 of 40 = 30, so 75 × 40 = 3,000
🎉 Remember This?
From the beginning of class...
50
×
12
=
600
12 of 12 = 6 → 6 × 100 = 600
Now you know the trick — and the math behind it!