Percents

6.B.1Percent of a quantity01/04

Percent of a quantity.

Step01of 04

Percent means "per hundred." 75% = 75/100 = 0.75. To find a percent OF a number, multiply.

percent of quantity = \frac{percent}{100} \times quantity

6.B.1 — Percent of a quantity.

Step 01 of 04

Percent means "per hundred." 75% = 75/100 = 0.75. To find a percent OF a number, multiply.

percent of quantity = \frac{percent}{100} \times quantity

Step 02 of 04

Worked examples.

25% of 80	→0.25 × 80 = 20
10% of 50	→0.10 × 50 = 5
150% of 60	→1.50 × 60 = 90

Step 03 of 04

Mental math shortcuts.

10% of X	→shift decimal one place left (10% of 240 = 24)
1% of X	→shift two places (1% of 240 = 2.4)
50% of X	→half (50% of 240 = 120)
25% of X	→quarter (25% of 240 = 60)

Step 04 of 04

Word problem. A shirt is $40 with 20% tax. How much tax?

0.20 \times 40 = $8 tax

Key insight

Percent OF means multiply. Convert percent to decimal (or fraction) first. Memorize the easy ones (10%, 25%, 50%) for quick mental math.

6.B.2 — Percent / fraction / decimal conversions.

Step 01 of 04

All three notations express the same kind of value. Converting among them is a key skill.

Step 02 of 04

Decimal ↔ Percent. Move the decimal point 2 places.

Decimal → percent	→shift right 2 (× 100)
Percent → decimal	→shift left 2 (÷ 100)
0.45	→45%
0.07	→7%
1.2	→120%
85%	→0.85

Step 03 of 04

Percent ↔ Fraction. Percent over 100, then simplify.

25%	→25/100 = 1/4
60%	→60/100 = 3/5
75%	→75/100 = 3/4
12.5%	→12.5/100 = 1/8

Step 04 of 04

Fraction → Percent. Either convert to a decimal first (divide), or build up to denominator 100.

3/4	→0.75 = 75%
7/10	→70%
1/8	→12.5%
2/3	→0.6666... ≈ 66.67%

Key insight

Decimal ↔ percent: shift 2 places. Percent ↔ fraction: percent / 100, simplify. Fraction → percent: divide top by bottom, multiply by 100.

6.B.3 — Find the whole given a percent.

Step 01 of 04

Reverse problem: you know the PART and the PERCENT; find the WHOLE.

whole = \frac{part}{percent (as decimal)}

Step 02 of 04

Worked example. 15 is 25% of what number?

whole = \frac{15}{0.25} = 60

Verify: 25% of 60 = 0.25 × 60 = 15 $✓$ .

Step 03 of 04

Equation form. "Part = percent × whole." Solve for the missing piece.

15 = 0.25 \times W \Rightarrow W = 15/0.25 = 60

Step 04 of 04

Word problem. A team won 9 games, which was 60% of their games. How many games total?

\frac{9}{0.60} = 15 games

Key insight

Three ways percent can come up: find part (multiply), find percent (divide part by whole), find whole (divide part by percent). Always identify which piece is missing.

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6.B.1 – 6.B.3 · CCSS 6.RP.A.3c · Full curriculum →