Neft Teacher · Learn It

Unit 4 · Standard 6.AT.4

Relate Fractions, Decimals, and Percentages

Lesson 4-2 · Learn It — how the math works

Why we're learning this

You're designing the scoring system for a new arcade game. Players earn points as fractions of the total possible score. The leaderboard shows scores as percentages, but the game engine uses decimals. You need to convert between all three forms to build the display! A player scored 3/4 of the total possible points. Write that score as a decimal and as a percent.

✱ Math Workbench

Learn It

How can one value be written as a fraction, a decimal, AND a percent?

Equivalent forms name the same value in different ways. Percent means "out of 100," so a fraction is already a percent once its denominator is 100.

Picture itSee what the math looks like before you read about it

Some middle school students are running a canned food drive. Their goal is to collect 100 cans each week for the local food pantry. So far this week, students have brought in 75 cans.
Where you see this in real lifeSome middle school students are running a canned food drive. Their goal is to collect 100 cans each week for the local food pantry. So far this week, students have brought in 75 cans.

Watch me solve itI do — read one step at a time

The problem looks like this
Double number line: 3 out of 4 is the same as 75 out of 100.Points scored375Points possible4100
  1. A player scored 3/4 of the points. means out of 100, so I want an fraction with 100 on the bottom.
  2. What do I multiply the denominator 4 by to get 100? 4 × 25 = 100, so my scale factor is 25.100? 4 × 25 = 100
  3. I have to multiply the top by that same 25: 3 × 25 = 75. So 3/4 = 75/100.3 × 25 = 75
  4. 75 out of 100 is 75%. And 75/100 as a is 0.75, because sit two places after the point.
  5. So 3/4 = 75/100 = 0.75 = 75%. All three name the same score.

Watch out — mistakes students make here

  • 45% is right, but 4/5 just reuses the digits 4 and 5 — 4/5 is 0.8. Forty-five hundredths is 45/100, which simplifies to 9/20.
  • Your fraction 9/20 is right — the percent is what slipped. Converting 0.45 to a percent moves the decimal two places right, not one.
  • Both parts slipped a place: 45/10 is 4.5, not 0.45, and 4.5% moves the point only one place. Write 0.45 as 45/100 and as 45%.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Let's change 1/5 into a fraction out of 100, then a and a .
  2. What do we multiply the denominator 5 by to get 100?
    Check this step
    (20)
  3. Now multiply the numerator by that same 20: 1 × 20 = ?1 × 20
    Check this step
    (20) So 1/5 = 20/100.
  4. 20 out of 100 is what ?
    Check this step
    (20%) And as a ? (0.2)

On your ownYou do — solve this one by yourself

Before you start, remember:

  • In the table, first build the fraction out of 100 — you find the number that turns the denominator into 100.
  • Then read the straight off the new numerator, and write the same value as a .
  • If the denominator will not scale to 100 evenly (like 8 or 3), divide the numerator by the denominator instead, then multiply by 100.

Solve: Complete each row. Build the fraction out of 100 first — that column hands you the .

FractionEquivalent fraction out of 100DecimalPercent
2/5
0.125
90%
5/8

Stuck? Open one hint at a time.

Hint 1

Each row gives you ONE form. Percent means out of 100, so try to rewrite each fraction with a denominator of 100.

Hint 2

Fraction → percent: scale to /100 when you can (2, 4, 5, 10, 20, 25, 50 all work). If the denominator will not reach 100 (8, 3, 7), divide instead and then multiply by 100.

Hint 3

Row 1: 5 × 20 = 100, so 2/5 = 40/100 = 40% = 0.4. Row with 5/8: 8 will not scale, so 5 ÷ 8 = 0.625 = 62.5%.

Check my answer
✅ Answers:
  • 2/5 → Equivalent fraction out of 100: 40/100
  • 2/5 → Decimal: 0.4
  • 2/5 → Percent: 40%
  • Row 2 → Fraction: 1/8
  • Row 2 → Equivalent fraction out of 100: 12.5/100
  • Row 2 → Percent: 12.5%
  • Row 3 → Fraction: 9/10
  • Row 3 → Equivalent fraction out of 100: 90/100
  • Row 3 → Decimal: 0.9
  • 5/8 → Equivalent fraction out of 100: 62.5/100
  • 5/8 → Decimal: 0.625
  • 5/8 → Percent: 62.5%
Percent means out of 100, so scale each fraction to a denominator of 100 when you can: 2/5 = 40/100 = 0.4 = 40%, and 90% = 90/100 = 0.9 = 9/10. When the denominator will not reach 100 with a whole number, divide instead: 1/8 = 0.125 = 12.5%, and 5/8 = 0.625 = 62.5%.

Turn & TalkSay it out loud with a partner

A player scored 3/4 of the points. The leaderboard shows and the game engine uses . What are three different ways to write the same score?

Try starting with:

  • The fraction ___ is the same as the decimal ___ and the percent ___.La fracción ___ es igual al decimal ___ y al porcentaje ___.
  • I can write the same value as a fraction, a ___, or a ___.Puedo escribir el mismo valor como fracción, ___ o ___.
Use these wordspercentdecimalequivalentbenchmark