Relate Fractions, Decimals, and Percentages

Convert among fractions, decimals, and percents to show equivalent representations.

6.AT.A.3c · Understand & Use Percentages
Level
Guided practice with vocabulary support

🟠 Level 0 — Extra Support

Sentence starters: “First, I…” · “The answer is… because…” · “I know this because…”
W

Warm-Up

2 questions
Warm-Up 1
Which decimal is equivalent to 1/2?
Vocabulary: Equivalent means equal in value. To convert a fraction to a decimal, divide the numerator by the denominator: 1 ÷ 2 = ?
✓Correct! 1 ÷ 2 = 0.5, so 1/2 = 0.5.
✗Divide 1 by 2: 1 ÷ 2 = 0.5. The answer is C.
Warm-Up 2
True or false: 0.25 and 25% represent the same value.
Hint: To convert a decimal to a percent, multiply by 100. 0.25 × 100 = 25. So 0.25 = 25%.
✓Correct! 0.25 = 25/100 = 25%. They are equivalent.
✗0.25 × 100 = 25, so 0.25 = 25%. The statement is true.
P

Practice

5 questions
Practice 1
Convert 3/4 to a percent.
Strategy: First make an equivalent fraction with 100 as the denominator. 3/4 = ?/100. Since 4 × 25 = 100, multiply the numerator by 25 too: 3 × 25 = 75. So 3/4 = 75/100 = 75%.
Show your conversion steps:

Sentence frame: "3/4 = ___/100 because 4 × ___ = 100 and 3 × ___ = ___. So 3/4 = ___%."

✓Correct! 3/4 = 75/100 = 75%.
✗3/4: multiply top and bottom by 25 to get 75/100 = 75% (answer C).
Practice 2
Write 0.6 as a percent.
How to convert: Multiply the decimal by 100 to get the percent. 0.6 × 100 = ?
0.6 = %
Explain your work:

Sentence frame: "To convert a decimal to a percent, I multiply by ___. 0.6 × 100 = ___, so 0.6 = ___%."

✓Correct! 0.6 × 100 = 60, so 0.6 = 60%.
✗Multiply by 100: 0.6 × 100 = 60%.
Practice 3
Match each fraction to its equivalent percent.
Strategy: Convert each fraction to a denominator of 100, or divide numerator by denominator and multiply by 100.
50%
20%
10%
25%
1/2 =
1/4 =
1/5 =
1/10 =
✓All correct! 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/10 = 10%.
✗Some matches are incorrect. Remember: 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/10 = 10%.
Practice 4
Complete the table by filling in the missing values.
Conversions: Fraction to decimal: divide. Decimal to percent: multiply by 100. Percent to decimal: divide by 100.
a. 2/5 = 0.4 = %
b. 3/10 = = 30%
c. ___ = 0.05 = %

Sentence frame: "I know ___ = ___ = ___% because they are all equivalent forms of the same value."

✓All correct! 2/5 = 0.4 = 40%, 3/10 = 0.3 = 30%, 1/20 = 0.05 = 5%.
✗Check your conversions: 2/5 = 40%, 3/10 = 0.3, and 0.05 = 5%.
Practice 5
Aisha says 1/3 = 30% because 3 × 30 = 90 and that is close to 100. Is she correct?
Check it: To convert 1/3 to a percent, divide 1 ÷ 3 = 0.333... and then multiply by 100 = 33.3...%. Is that the same as 30%?
Explain Aisha's error:

Sentence frame: "1/3 does not equal 30% because 1 ÷ 3 = ___, and ___ × 100 = ___%, not 30%."

✓Correct! 1 ÷ 3 = 0.333..., so 1/3 ≈ 33.3%, not 30%.
✗1 ÷ 3 = 0.333... which is about 33.3%, not 30%. The answer is B.
★

Challenge

1 question
Challenge
Order these values from least to greatest: 0.45,   3/8,   42%
Strategy: Convert everything to the same form. Try decimals: 0.45 stays. 3/8 = 3 ÷ 8 = 0.375. 42% = 0.42. Now compare: 0.375, 0.42, 0.45.
Show your conversion work:

Sentence frame: "I converted to decimals: 3/8 = ___, 42% = ___, and 0.45 stays. In order: ___, ___, ___."

✓Correct! 3/8 = 0.375, 42% = 0.42, and 0.45. Least to greatest: 3/8, 42%, 0.45.
✗Convert to decimals: 3/8 = 0.375, 42% = 0.42, 0.45. Order: 3/8, 42%, 0.45 (answer B).