Learn on PengienVision, Mathematics, Grade 5Chapter 7: Use Equivalent Fractions to Add and Subtract Fractions

Lesson 10: Subtract Mixed Numbers

In Grade 5 math, this lesson from enVision Mathematics Chapter 7 teaches students how to subtract mixed numbers by finding common denominators, renaming fractions when the fractional part being subtracted is greater, and regrouping whole numbers as fractions when necessary. Students practice multi-step subtraction involving unlike denominators, such as converting fourths and thirds into twelfths before subtracting. Real-world problems involving measurements and weights help reinforce when and how to apply these skills.

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

Procedure: Subtracting Mixed Numbers with Regrouping

Property

To subtract mixed numbers when the top fraction is smaller than the bottom fraction:

  1. Regroup: Take one from the whole number part of the first mixed number. Add that one to its fraction part by converting it to a fraction with the common denominator (e.g., 1=nn1 = \frac{n}{n}).
  2. Subtract Fractions: Subtract the fraction parts.
  3. Subtract Whole Numbers: Subtract the whole number parts.
  4. Simplify: Write the final answer in simplest form.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

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

Procedure: Subtracting Mixed Numbers with Regrouping

Property

To subtract mixed numbers when the top fraction is smaller than the bottom fraction:

  1. Regroup: Take one from the whole number part of the first mixed number. Add that one to its fraction part by converting it to a fraction with the common denominator (e.g., 1=nn1 = \frac{n}{n}).
  2. Subtract Fractions: Subtract the fraction parts.
  3. Subtract Whole Numbers: Subtract the whole number parts.
  4. Simplify: Write the final answer in simplest form.

Examples