Learn on PengiEureka Math, Grade 5Chapter 17: Making Like Units Numerically

Lesson 4: Subtract fractions with unlike units using the strategy of creating equivalent fractions.

In this Grade 5 Eureka Math lesson from Chapter 17, students learn to subtract fractions with unlike denominators by generating equivalent fractions to create like units. The lesson covers subtracting both simple fractions and mixed numbers, such as 3/4 minus 3/10, by finding a common denominator before subtracting. Students build on prior fluency with like-unit fraction operations to apply this numerical strategy across a variety of problems.

Section 1

Subtracting a Fraction from a Whole Number

Property

To subtract a fraction from a whole number, first convert the whole number into an equivalent fraction with the same denominator as the fraction being subtracted.
For a whole number nn and a fraction ab\frac{a}{b}:

n−ab=n×bb−ab=nb−abn - \frac{a}{b} = \frac{n \times b}{b} - \frac{a}{b} = \frac{nb - a}{b}

Examples

Section 2

Subtracting Fractions with Unlike Denominators

Property

To subtract fractions with unlike denominators, find a common denominator and convert each fraction to an equivalent fraction with that denominator.
Then, subtract the numerators.

ab−cd=adbd−cbbd=ad−cbbd\frac{a}{b} - \frac{c}{d} = \frac{ad}{bd} - \frac{cb}{bd} = \frac{ad - cb}{bd}

Examples

Section 3

Regrouping to Subtract Mixed Numbers

Property

When subtracting mixed numbers, if the minuend's fraction is smaller than the subtrahend's fraction, you must regroup from the whole number.
To regroup WacW\frac{a}{c}, you borrow 1 from WW and convert it to a fraction cc\frac{c}{c}.

Wac=(W−1)+1+ac=(W−1)+cc+ac=(W−1)a+ccW\frac{a}{c} = (W-1) + 1 + \frac{a}{c} = (W-1) + \frac{c}{c} + \frac{a}{c} = (W-1)\frac{a+c}{c}

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Chapter 17: Making Like Units Numerically

  1. Lesson 1

    Lesson 1: Add fractions to and subtract fractions from whole numbers using equivalence and the number line as strategies.

    LearnPractice
  2. Lesson 2

    Lesson 2: Add fractions making like units numerically.

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  3. Lesson 3

    Lesson 3: Add fractions with sums greater than 2.

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  4. Lesson 4Current

    Lesson 4: Subtract fractions with unlike units using the strategy of creating equivalent fractions.

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  5. Lesson 5

    Lesson 5: Subtract fractions greater than or equal to 1.

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Lesson overview

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Section 1

Subtracting a Fraction from a Whole Number

Property

To subtract a fraction from a whole number, first convert the whole number into an equivalent fraction with the same denominator as the fraction being subtracted.
For a whole number nn and a fraction ab\frac{a}{b}:

n−ab=n×bb−ab=nb−abn - \frac{a}{b} = \frac{n \times b}{b} - \frac{a}{b} = \frac{nb - a}{b}

Examples

Section 2

Subtracting Fractions with Unlike Denominators

Property

To subtract fractions with unlike denominators, find a common denominator and convert each fraction to an equivalent fraction with that denominator.
Then, subtract the numerators.

ab−cd=adbd−cbbd=ad−cbbd\frac{a}{b} - \frac{c}{d} = \frac{ad}{bd} - \frac{cb}{bd} = \frac{ad - cb}{bd}

Examples

Section 3

Regrouping to Subtract Mixed Numbers

Property

When subtracting mixed numbers, if the minuend's fraction is smaller than the subtrahend's fraction, you must regroup from the whole number.
To regroup WacW\frac{a}{c}, you borrow 1 from WW and convert it to a fraction cc\frac{c}{c}.

Wac=(W−1)+1+ac=(W−1)+cc+ac=(W−1)a+ccW\frac{a}{c} = (W-1) + 1 + \frac{a}{c} = (W-1) + \frac{c}{c} + \frac{a}{c} = (W-1)\frac{a+c}{c}

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 17: Making Like Units Numerically

  1. Lesson 1

    Lesson 1: Add fractions to and subtract fractions from whole numbers using equivalence and the number line as strategies.

    LearnPractice
  2. Lesson 2

    Lesson 2: Add fractions making like units numerically.

    LearnPractice
  3. Lesson 3

    Lesson 3: Add fractions with sums greater than 2.

    LearnPractice
  4. Lesson 4Current

    Lesson 4: Subtract fractions with unlike units using the strategy of creating equivalent fractions.

    LearnPractice
  5. Lesson 5

    Lesson 5: Subtract fractions greater than or equal to 1.

    LearnPractice