Decimals & Percents · Percent in the real world · 7.1

Increase & decrease.

Percent change compares the change to the original: (new − old) ÷ old × 100. From 50 to 65 is a change of 15 over 50 = 30% increase. A drop is a decrease.

01 / THE IDEA

See it work.

Watch the method

Percent increase & decrease

50 → 65: 15 ÷ 50 = 30% increase.

1 / 2
50→6550 \to 65
1

Find the change

From 50 to 65 is an increase of 15.

65−5065 - 50
2

Over the original

Divide the change by the original, then ×100.

=30%= 30\%
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a percent, e.g. 25%.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Change over original

Always divide the change by the ORIGINAL amount, not the new one, then ×100.

Why it works

15 more out of 50 is 30%.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

A value changes from 50 to 75. By what percent?

1

Find the change

From 50 to 75 is an increase of 25. 75 - 50

2

Over the original

Divide the change by the original, then ×100. = 50%

EX 2medium

A value changes from 100 to 110. By what percent?

1

Find the change

From 100 to 110 is an increase of 10. 110 - 100

2

Over the original

Divide the change by the original, then ×100. = 10%

EX 3hard

A value changes from 30 to 22.5. By what percent?

1

Find the change

From 30 to 22.5 is a decrease of 7.5. 22.5 - 30

2

Over the original

Divide the change by the original, then ×100. = 25%

04 / COMMON TRAPS

Where students slip.

Trap

Dividing by the new value.

Fix

Divide the change by the ORIGINAL.

Trap

Confusing increase with decrease.

Fix

New > old is an increase; new < old a decrease.

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

A value changes from 40 to 50. By what percent?

Need a hint?
  • Find the change (new − old).
  • Divide by the original, ×100.
C2

A value changes from 50 to 37.5. By what percent?

Need a hint?
  • Find the change (new − old).
  • Divide by the original, ×100.
C3

A value changes from 30 to 22.5. By what percent?

Need a hint?
  • Find the change (new − old).
  • Divide by the original, ×100.
C4

A value changes from 30 to 22.5. By what percent?

Need a hint?
  • Find the change (new − old).
  • Divide by the original, ×100.
Apply

Apply (4)

A1

A value changes from 30 to 15. By what percent?

Need a hint?
  • Find the change (new − old).
  • Divide by the original, ×100.
A2

A value changes from 70 to 63. By what percent?

Need a hint?
  • Find the change (new − old).
  • Divide by the original, ×100.
A3

A value changes from 30 to 33. By what percent?

Need a hint?
  • Find the change (new − old).
  • Divide by the original, ×100.
A4

A value changes from 80 to 100. By what percent?

Need a hint?
  • Find the change (new − old).
  • Divide by the original, ×100.
Extension

Extension (4)

E1

A value changes from 90 to 135. By what percent?

Need a hint?
  • Find the change (new − old).
  • Divide by the original, ×100.
E2

A value changes from 60 to 30. By what percent?

Need a hint?
  • Find the change (new − old).
  • Divide by the original, ×100.
E3

A value changes from 80 to 120. By what percent?

Need a hint?
  • Find the change (new − old).
  • Divide by the original, ×100.
E4

A value changes from 70 to 84. By what percent?

Need a hint?
  • Find the change (new − old).
  • Divide by the original, ×100.