Learn on PengiPengi Math (Grade 5)Chapter 5: Add & Subtract Fractions and Mixed Numbers

Lesson 5: Subtract Mixed Numbers with Unlike Denominators

In this Grade 5 Pengi Math lesson, students learn how to subtract mixed numbers with unlike denominators, including how to use regrouping when the fraction part of the minuend is smaller than the subtrahend. The lesson also covers solving multi-step word problems involving fractions and mixed numbers, and using estimation to check the reasonableness of solutions. This is part of Chapter 5, which focuses on adding and subtracting fractions and mixed numbers.

Section 1

Subtract Mixed Numbers with Unlike Denominators

Property

To subtract mixed numbers with unlike denominators, first find a common denominator for the fractional parts. Then, subtract the fractions, and subtract the whole numbers. Simplify the result if necessary.

Examples

  • 534−218=3585 \frac{3}{4} - 2 \frac{1}{8} = 3 \frac{5}{8}
534−218=53×24×2−218(Find common denominator: LCM of 4 and 8 is 8)=568−218=(5−2)+(68−18)(Subtract whole numbers and fractions separately)=3+58=358\begin{align*} 5\frac{3}{4} - 2\frac{1}{8} &= 5\frac{3\times2}{4\times2} - 2\frac{1}{8} \quad \text{(Find common denominator: LCM of 4 and 8 is 8)} \\ &= 5\frac{6}{8} - 2\frac{1}{8} \\ &= (5-2) + \left(\frac{6}{8}-\frac{1}{8}\right) \quad \text{(Subtract whole numbers and fractions separately)} \\ &= 3 + \frac{5}{8} \\ &= 3\frac{5}{8} \end{align*}
  • 423−135=31154\frac{2}{3} - 1\frac{3}{5} = 3\frac{1}{15}
423−135=42×53×5−13×35×3(Find common denominator: LCM of 3 and 5 is 15)=41015−1915=(4−1)+(1015−915)(Subtract whole numbers and fractions separately)=3+115=3115\begin{align*} 4\frac{2}{3} - 1\frac{3}{5} &= 4\frac{2\times5}{3\times5} - 1\frac{3\times3}{5\times3} \quad \text{(Find common denominator: LCM of 3 and 5 is 15)} \\ &= 4\frac{10}{15} - 1\frac{9}{15} \\ &= (4-1) + \left(\frac{10}{15}-\frac{9}{15}\right) \quad \text{(Subtract whole numbers and fractions separately)} \\ &= 3 + \frac{1}{15} \\ &= 3\frac{1}{15} \end{align*}

Explanation

This skill focuses on subtracting mixed numbers where the fraction in the first number is larger than the fraction in the second number, so no regrouping (or borrowing) is needed. The first step is to convert the fractions to have a common denominator. After that, you can subtract the fractional parts from each other and the whole numbers from each other to find the final answer.

Section 2

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

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Chapter 5: Add & Subtract Fractions and Mixed Numbers

  1. Lesson 1

    Lesson 1: Estimate Fraction Sums and Differences

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  2. Lesson 2

    Lesson 2: Finding Equivalent Fractions Using a Common Denominator

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  3. Lesson 3

    Lesson 3: Add & Subtract Fractions with Unlike Denominators

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  4. Lesson 4

    Lesson 4: Add Mixed Numbers with Unlike Denominators

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  5. Lesson 5Current

    Lesson 5: Subtract Mixed Numbers with Unlike Denominators

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  6. Lesson 6

    Lesson 6: Solve Multi-step Fraction Problems

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Lesson overview

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Section 1

Subtract Mixed Numbers with Unlike Denominators

Property

To subtract mixed numbers with unlike denominators, first find a common denominator for the fractional parts. Then, subtract the fractions, and subtract the whole numbers. Simplify the result if necessary.

Examples

  • 534−218=3585 \frac{3}{4} - 2 \frac{1}{8} = 3 \frac{5}{8}
534−218=53×24×2−218(Find common denominator: LCM of 4 and 8 is 8)=568−218=(5−2)+(68−18)(Subtract whole numbers and fractions separately)=3+58=358\begin{align*} 5\frac{3}{4} - 2\frac{1}{8} &= 5\frac{3\times2}{4\times2} - 2\frac{1}{8} \quad \text{(Find common denominator: LCM of 4 and 8 is 8)} \\ &= 5\frac{6}{8} - 2\frac{1}{8} \\ &= (5-2) + \left(\frac{6}{8}-\frac{1}{8}\right) \quad \text{(Subtract whole numbers and fractions separately)} \\ &= 3 + \frac{5}{8} \\ &= 3\frac{5}{8} \end{align*}
  • 423−135=31154\frac{2}{3} - 1\frac{3}{5} = 3\frac{1}{15}
423−135=42×53×5−13×35×3(Find common denominator: LCM of 3 and 5 is 15)=41015−1915=(4−1)+(1015−915)(Subtract whole numbers and fractions separately)=3+115=3115\begin{align*} 4\frac{2}{3} - 1\frac{3}{5} &= 4\frac{2\times5}{3\times5} - 1\frac{3\times3}{5\times3} \quad \text{(Find common denominator: LCM of 3 and 5 is 15)} \\ &= 4\frac{10}{15} - 1\frac{9}{15} \\ &= (4-1) + \left(\frac{10}{15}-\frac{9}{15}\right) \quad \text{(Subtract whole numbers and fractions separately)} \\ &= 3 + \frac{1}{15} \\ &= 3\frac{1}{15} \end{align*}

Explanation

This skill focuses on subtracting mixed numbers where the fraction in the first number is larger than the fraction in the second number, so no regrouping (or borrowing) is needed. The first step is to convert the fractions to have a common denominator. After that, you can subtract the fractional parts from each other and the whole numbers from each other to find the final answer.

Section 2

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 5: Add & Subtract Fractions and Mixed Numbers

  1. Lesson 1

    Lesson 1: Estimate Fraction Sums and Differences

    LearnPractice
  2. Lesson 2

    Lesson 2: Finding Equivalent Fractions Using a Common Denominator

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  3. Lesson 3

    Lesson 3: Add & Subtract Fractions with Unlike Denominators

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  4. Lesson 4

    Lesson 4: Add Mixed Numbers with Unlike Denominators

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  5. Lesson 5Current

    Lesson 5: Subtract Mixed Numbers with Unlike Denominators

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  6. Lesson 6

    Lesson 6: Solve Multi-step Fraction Problems

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