Grade 6 Mathematics · Unit 4: Understand and Use PercentagesStandard 6.AT.4

Lesson 4.2Relate Fractions, Decimals, and Percentages

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can write equivalent fractions, decimals, and percents for the same value.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
PercentSpanish: Porcentaje A way to compare a number to 100, shown with the % sign. 45% = 45 out of 100
DecimalSpanish: Decimal A number with a dot, like 0.5, that shows a part less than one. 0.45 = 45 hundredths
EquivalentSpanish: Equivalente Having the same value, just written a different way. 3/4 = 0.75 = 75%
BenchmarkSpanish: Referencia A familiar number you use to guess, like 50% or 1/2. 50% = one half
DiscountSpanish: Descuento Money taken off the first price to make it cheaper. $40 shirt at 25% off: discount = $10
HundredthsSpanish: Centésimos The second place after the decimal point; parts out of 100. 0.09 = 9 hundredths

How it worksWorked examplewriting one value three ways

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A survey found 7 out of 20 students walk to school. Write that as a fraction, a decimal, and a percent.

  1. Write the fraction, part over whole: 7/20
  2. Twenty times five makes one hundred, so multiply both terms by five.
  3. That gives thirty-five hundredths, written as the decimal 0.35
  4. Hundredths read straight across into percent form: 0.35 is 35%

Answer: 7/20, 0.35, and 35% all name the very same amount.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

In the same survey, 9 out of 25 students ride the bus. Write it as a fraction, a decimal, and a percent.

  1. Fraction, part over whole: /
  2. Twenty-five times makes one hundred, so multiply both terms.
  3. Hundredths written as a decimal: 0.
  4. Percent form: %
Answer:the bus riders as a fraction, decimal, and percent

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • / is the same value as written as a decimal.
  • To change a decimal into a percent I .
  • % means out of every hundred.
  • I know these three forms are equivalent because .

Word bank percentdecimalfractionequivalenthundredthsdenominatornumeratorsimplest formbenchmarkscalewholepart

Watch outA common mistake

A common mistake in Relate Fractions, Decimals, and Percents is treating the numerator and denominator as the percent's digits — turning 3/5 into "35%" by just reading the 3 and the 5. Percent means out of 100, so the fix is to build an equivalent fraction with denominator 100: 5 × 20 = 100, so multiply the top by 20 too — 3/5 = 60/100 = 60%. A second version of this mistake is scaling only ONE part of the fraction (writing 3/5 = 3/100 or 60/5). Whatever you multiply the denominator by, you must multiply the numerator by the same number. When a denominator will not reach 100 evenly (8, 3, 7), divide the numerator by the denominator instead and then multiply by 100.

Grade 6 Mathematics · Unit 4: Understand and Use PercentagesStandard 6.AT.4

Lesson 4.2Relate Fractions, Decimals, and Percentages

Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can write equivalent fractions, decimals, and percents for the same value.

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Sort these values — which are greater than 50% and which are less than 50%?

    Groups: Greater than 50% Less than 50%
    • 3/4
    • 0.8
    • 65%
    • 7/10
    • 1/3
    • 0.25
    • 40%
    • 2/5

    Hint 50% is the same as 1/2 or 0.5 — that is your comparison line for every card.

Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Convert 3/5 to a percent.

    1. A35%
    2. B53%
    3. C60%
    4. D65%

    Hint Percent means out of 100. What do you multiply the denominator 5 by to get 100?

    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.
  2. 3Circle the letter of the best answer. Show how you know.

    Convert 7/20 to a percent.

    1. A14%
    2. B20%
    3. C35%
    4. D70%

    Hint The denominator 20 is friendly: 20 × 5 = 100, and percents are always 'out of 100'.

    Rewrite each fraction
    Work it out
    Simplify
    1. 1Same size piecesCommon denominator first.
    2. 2OperateOnly then add or subtract.
    3. 3SimplifyDivide out common factors.
  3. 4Circle the letter of the best answer. Show how you know.

    Which decimal is equivalent to 45%?

    1. A0.045
    2. B0.45
    3. C4.5
    4. D45.0

    Hint Percent means 'out of 100', so 45% is the fraction 45/100.

    0%50%100%
    Work
    1. 1Whole100% is what number?
    2. 2Find 10%Divide by 10.
    3. 3BuildAdd or multiply to the percent.
    4. 4CheckIs it under or over the whole?
  4. 5Circle the letter of the best answer. Show how you know.

    What fraction is equal to 0.75?

    1. A3/4
    2. B3/5
    3. C7/5
    4. D7/10

    Hint 0.75 is read 'seventy-five hundredths' — the place value tells you the denominator.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Convert 3/5 to a percent3/5
    2. 2Read the digits as the percentThe numerator is 3 and the denominator is 5, so the student writes 35%.
    3. 3Final answer3/5 = 35%

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint Do the digits 3 and 5 tell you how many parts out of 100?

    Correct work
    Correct answer:

Explain your thinkingWhat number did you multiply by to turn each denominator into 100, and how did that fraction out of 100 give you the percent?

Sentence starter I multiplied the top and bottom of ___ by ___ to get ___/100, so the percent is ___%.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 4: Understand and Use PercentagesStandard 6.AT.4

Lesson 4.2Relate Fractions, Decimals, and Percentages

Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can write equivalent fractions, decimals, and percents for the same value.

Part 1Understand the ideamodels and meaning
  1. 1Mark and label each value on the number line.

    Place each value on the number line: A = 3/8, B = 0.6, C = 85%

    00.10.20.30.40.50.60.70.80.91
    Show your thinking
  2. 2Complete the table. Show how you found each value.

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

    FractionEquivalent fraction out of 100DecimalPercent
    2/5
    0.125
    90%
    5/8
    Show your work
  3. 3Write the name of the correct group on each line.

    Order these values from least to greatest by sorting them into the correct position.

    Groups: 1st (Smallest) 2nd 3rd 4th 5th (Largest)
    • 1/5
    • 0.35
    • 2/5
    • 55%
    • 3/4
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A game shows your score as 7/8 complete. What percent is that?

    1. A75%
    2. B78%
    3. C87.5%
    4. D88%
    Rewrite each fraction
    Work it out
    Simplify
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Convert 5/8 to a percent5/8
    2. 2Divide the bottom by the top8 ÷ 5 = 1.6
    3. 3Multiply by 1001.6 × 100 = 160%
    4. 4Final answer5/8 = 160%

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingWhat number did you multiply by to turn each denominator into 100, and how did that fraction out of 100 give you the percent?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 4: Understand and Use PercentagesStandard 6.AT.4

Lesson 4.2Relate Fractions, Decimals, and Percentages

ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can write equivalent fractions, decimals, and percents for the same value.

Part 1Understand the ideamodels and meaning
  1. 1Mark and label each value on the number line.

    Place 1/3, 0.4, and 38% on the number line. Which is greatest?

    00.10.20.30.40.50.60.70.80.91
    Show your thinking
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the Conversion Error

    1. 1Convert 2/3 to a percent2/3
    2. 2Divide numerator by denominator2 ÷ 3 = 0.67
    3. 3Move decimal two places0.67 → 67%
    4. 4Final answer2/3 = 67%

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    A student says 3/8 is greater than 40% because 3 and 8 are bigger numbers than 4 and 0. Is the student correct? Convert both values to the same form and explain.

    Write your answer

Explain your thinkingWhat number did you multiply by to turn each denominator into 100, and how did that fraction out of 100 give you the percent?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help