Decimals & Percents · Percent of a number · 6.5

Find the whole.

If you know a percent and the part it represents, divide to find the whole. 15% of a number is 12 → the number is 12 ÷ 0.15 = 80. Dividing undoes the “percent of”.

01 / THE IDEA

See it work.

Watch the method

Find the whole

15% is 12 → 12 ÷ 0.15 = 80.

1 / 2
15% of ?=1215\% \text{ of } ? = 12
1

Set up the relation

15% of the whole is 12.

0.15×?=120.15 \times ? = 12
2

Divide to undo

Divide the part by the decimal.

12÷0.15=8012 \div 0.15 = 80
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a decimal, e.g. 0.75.

streak 0
best 0
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— / WHY IT WORKS

The idea underneath.

Undo with division

Since percent × whole = part, the whole = part ÷ percent (as a decimal).

Why it works

12 ÷ 0.15 = 80.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

50% of a number is 90. What is the number?

1

Set up the relation

50% of the whole is 90. 0.5 × ? = 90

2

Divide to undo

Divide the part by the decimal. 90 ÷ 0.5 = 180

EX 2medium

25% of a number is 35. What is the number?

1

Set up the relation

25% of the whole is 35. 0.25 × ? = 35

2

Divide to undo

Divide the part by the decimal. 35 ÷ 0.25 = 140

EX 3hard

20% of a number is 20. What is the number?

1

Set up the relation

20% of the whole is 20. 0.2 × ? = 20

2

Divide to undo

Divide the part by the decimal. 20 ÷ 0.2 = 100

04 / COMMON TRAPS

Where students slip.

Trap

Multiplying instead of dividing.

Fix

To undo “× 0.15”, divide by 0.15.

Trap

Using the part as the whole.

Fix

The part is smaller; work back to the whole.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

20% of a number is 20. What is the number?

Need a hint?
  • Write percent × whole = part.
  • Divide the part by the decimal.
C2

20% of a number is 6. What is the number?

Need a hint?
  • Write percent × whole = part.
  • Divide the part by the decimal.
C3

50% of a number is 30. What is the number?

Need a hint?
  • Write percent × whole = part.
  • Divide the part by the decimal.
C4

25% of a number is 32.5. What is the number?

Need a hint?
  • Write percent × whole = part.
  • Divide the part by the decimal.
Apply

Apply (4)

A1

20% of a number is 32. What is the number?

Need a hint?
  • Write percent × whole = part.
  • Divide the part by the decimal.
A2

20% of a number is 32. What is the number?

Need a hint?
  • Write percent × whole = part.
  • Divide the part by the decimal.
A3

25% of a number is 45. What is the number?

Need a hint?
  • Write percent × whole = part.
  • Divide the part by the decimal.
A4

10% of a number is 14. What is the number?

Need a hint?
  • Write percent × whole = part.
  • Divide the part by the decimal.
Extension

Extension (4)

E1

50% of a number is 50. What is the number?

Need a hint?
  • Write percent × whole = part.
  • Divide the part by the decimal.
E2

20% of a number is 20. What is the number?

Need a hint?
  • Write percent × whole = part.
  • Divide the part by the decimal.
E3

25% of a number is 50. What is the number?

Need a hint?
  • Write percent × whole = part.
  • Divide the part by the decimal.
E4

10% of a number is 19. What is the number?

Need a hint?
  • Write percent × whole = part.
  • Divide the part by the decimal.