Decimals & Percents · Percent in the real world · 7.4

Change mastery.

Mixed practice: find the percent of an increase or a decrease, and watch the direction. From 80 to 60 is a decrease of 20 over 80 = 25%. The base is always the original.

01 / THE IDEA

See it work.

Watch the method

Percent change mastery

80 → 60: 20 ÷ 80 = 25% decrease.

1 / 2
80→6080 \to 60
1

Find the change

From 80 to 60 is a decrease of 20.

60−8060 - 80
2

Over the original

Divide the change by the original, then ×100.

=25%= 25\%
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.

Both directions

Increase or decrease, the formula is the same: change ÷ original × 100. The sign/direction comes from new vs old.

Why it works

20 less out of 80 is 25%.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

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

1

Find the change

From 50 to 37.5 is a decrease of 12.5. 37.5 - 50

2

Over the original

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

EX 2medium

A value changes from 80 to 72. By what percent?

1

Find the change

From 80 to 72 is a decrease of 8. 72 - 80

2

Over the original

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

EX 3hard

A value changes from 80 to 64. By what percent?

1

Find the change

From 80 to 64 is a decrease of 16. 64 - 80

2

Over the original

Divide the change by the original, then ×100. = 20%

04 / COMMON TRAPS

Where students slip.

Trap

Using the new value as the base.

Fix

The base is the original.

Trap

Reporting the wrong direction.

Fix

Down is a decrease, up an increase.

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 20 to 10. By what percent?

Need a hint?
  • Change ÷ original × 100.
  • State increase or decrease.
C2

A value changes from 70 to 56. By what percent?

Need a hint?
  • Change ÷ original × 100.
  • State increase or decrease.
C3

A value changes from 20 to 10. By what percent?

Need a hint?
  • Change ÷ original × 100.
  • State increase or decrease.
C4

A value changes from 50 to 45. By what percent?

Need a hint?
  • Change ÷ original × 100.
  • State increase or decrease.
Apply

Apply (4)

A1

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

Need a hint?
  • Change ÷ original × 100.
  • State increase or decrease.
A2

A value changes from 70 to 35. By what percent?

Need a hint?
  • Change ÷ original × 100.
  • State increase or decrease.
A3

A value changes from 100 to 125. By what percent?

Need a hint?
  • Change ÷ original × 100.
  • State increase or decrease.
A4

A value changes from 40 to 32. By what percent?

Need a hint?
  • Change ÷ original × 100.
  • State increase or decrease.
Extension

Extension (4)

E1

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

Need a hint?
  • Change ÷ original × 100.
  • State increase or decrease.
E2

A value changes from 100 to 125. By what percent?

Need a hint?
  • Change ÷ original × 100.
  • State increase or decrease.
E3

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

Need a hint?
  • Change ÷ original × 100.
  • State increase or decrease.
E4

A value changes from 60 to 48. By what percent?

Need a hint?
  • Change ÷ original × 100.
  • State increase or decrease.