Learn on PengiEureka Math, Grade 4Chapter 24: Fraction Addition and Subtraction

Lesson 2: Use visual models to add and subtract two fractions with the same units, including subtracting from one whole.

In this Grade 4 Eureka Math lesson from Chapter 24, students use visual models such as tape diagrams and number bonds to add and subtract two fractions with the same units, including subtracting a fraction from one whole. Students practice recognizing equivalent fractions, decomposing mixed numbers, and writing related addition and subtraction sentences using like-denominator fractions. The lesson builds toward fluency with fraction operations through hands-on drawing activities and guided concept development.

Section 1

Model Subtracting a Fraction from One on a Number Line

Property

To subtract a fraction from one whole, first rename 1 as a fraction with the same denominator as the fraction being subtracted.
Then, subtract the numerators.

1−ab=bb−ab=b−ab1 - \frac{a}{b} = \frac{b}{b} - \frac{a}{b} = \frac{b-a}{b}

Examples

Section 2

Subtracting a Fraction from a Mixed Number

Property

To subtract a fraction from a mixed number like 1ac−bc1 \frac{a}{c} - \frac{b}{c} (where bc>ac\frac{b}{c} > \frac{a}{c}), you can use two methods:

  1. Subtract from the Total: Convert the mixed number to an improper fraction and then subtract.
1ac−bc=c+ac−bc=c+a−bc1 \frac{a}{c} - \frac{b}{c} = \frac{c+a}{c} - \frac{b}{c} = \frac{c+a-b}{c}
  1. Take from 1: Decompose the mixed number, subtract the fraction from the whole number part, and add the fractional part back.
1ac−bc=(1−bc)+ac=(cc−bc)+ac1 \frac{a}{c} - \frac{b}{c} = (1 - \frac{b}{c}) + \frac{a}{c} = (\frac{c}{c} - \frac{b}{c}) + \frac{a}{c}

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Model Subtracting a Fraction from One on a Number Line

Property

To subtract a fraction from one whole, first rename 1 as a fraction with the same denominator as the fraction being subtracted.
Then, subtract the numerators.

1−ab=bb−ab=b−ab1 - \frac{a}{b} = \frac{b}{b} - \frac{a}{b} = \frac{b-a}{b}

Examples

Section 2

Subtracting a Fraction from a Mixed Number

Property

To subtract a fraction from a mixed number like 1ac−bc1 \frac{a}{c} - \frac{b}{c} (where bc>ac\frac{b}{c} > \frac{a}{c}), you can use two methods:

  1. Subtract from the Total: Convert the mixed number to an improper fraction and then subtract.
1ac−bc=c+ac−bc=c+a−bc1 \frac{a}{c} - \frac{b}{c} = \frac{c+a}{c} - \frac{b}{c} = \frac{c+a-b}{c}
  1. Take from 1: Decompose the mixed number, subtract the fraction from the whole number part, and add the fractional part back.
1ac−bc=(1−bc)+ac=(cc−bc)+ac1 \frac{a}{c} - \frac{b}{c} = (1 - \frac{b}{c}) + \frac{a}{c} = (\frac{c}{c} - \frac{b}{c}) + \frac{a}{c}