GED Mathematical Reasoning
Percents & Percent Change
Percent means "out of one hundred." 25% is 25 out of 100, which is 25/100, which is 0.25. Every percent problem becomes easy the moment you turn the percent into a decimal by moving the dot two places left.
The words first
- percent
- a number out of one hundred
- of
- in a percent problem, the word "of" means multiply
- percent increase
- how much something grew, measured against what it started at
- original / base
- the number you started with — always the bottom of the fraction
The method
TURN THE PERCENT INTO A DECIMAL FIRST
25% → 0.25 8% → 0.08 140% → 1.40
(move the dot two places to the LEFT)
FINDING A PERCENT OF SOMETHING
25% of 80 = 0.25 × 80 = 20
PERCENT INCREASE OR DECREASE
amount it changed
percent = ———————————————————— × 100
the ORIGINAL amount
The original goes on the bottom. Always.
ADDING A PERCENT ON (tax, tip, markup) — one-step version
price + 8% tax = price × 1.08
price − 30% off = price × 0.70
Worked all the way through
The problem
A jacket was $80. Now it is $68. What percent did the price drop?
- Step 1 — Find how much it actually changed.80 − 68 = 12 dollars
- Step 2 — Ask what it changed FROM.It started at $80. That is the original, so 80 goes on the bottom.
- Step 3 — Build the fraction.12 / 80
- Step 4 — Divide.12 ÷ 80 = 0.15
- Step 5 — Turn the decimal back into a percent.0.15 → move the dot two places RIGHT → 15%
On the board
80 − 68 = 12
how much it changed
12 / 80
changed ÷ ORIGINAL
0.15
12 ÷ 80
15%
move the dot 2 right
Answer
15%
A second one, in a different form
A $50 shirt has 8% sales tax. What is the total?
8% → 0.08
percent to decimal, dot 2 left
50 × 0.08 = 4
the tax
50 + 4 = 54
price plus tax
or in one step: 50 × 1.08 = 54
Answer
$54
The usual mistake
Dividing percent change by the new number instead of the original. The word 'from' points to your denominator.
Check yourself
The classic trap: dividing by 68 instead of 80. Ask yourself "changed from what?" — that number is the bottom.
Practice it
Reading a worked example is not the same as doing one. score145 generates fresh Math questions on this and 17 other topics, scores them on the real 100–200 scale, and keeps every question you miss so it comes back. Try five questions free with no account; a plan opens the full practice tests $6.99 a month, 3 days free.
Try 5 questions free →