Learn on PengiPengi Math (Grade 4)Chapter 7: Fraction Operations

Lesson 3: Subtracting Mixed Numbers

In this Grade 4 lesson from Pengi Math Chapter 7, students learn multiple strategies for subtracting mixed numbers, including separating wholes and fractions, regrouping by decomposing a whole into fractional parts, and converting to improper fractions. They also apply the counting up strategy on a number line to find differences. Skills are reinforced through real-world subtraction problems involving mixed numbers.

Section 1

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}

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

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Chapter 7: Fraction Operations

  1. Lesson 1

    Lesson 1: Addition and Subtraction of Fractions with Like Denominators

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  2. Lesson 2

    Lesson 2: Adding Mixed Numbers

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  3. Lesson 3Current

    Lesson 3: Subtracting Mixed Numbers

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  4. Lesson 4

    Lesson 4: Multiplying Fractions by Whole Numbers and Applications

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Section 1

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}

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

Book overview

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

Continue this chapter

Chapter 7: Fraction Operations

  1. Lesson 1

    Lesson 1: Addition and Subtraction of Fractions with Like Denominators

    LearnPractice
  2. Lesson 2

    Lesson 2: Adding Mixed Numbers

    LearnPractice
  3. Lesson 3Current

    Lesson 3: Subtracting Mixed Numbers

    LearnPractice
  4. Lesson 4

    Lesson 4: Multiplying Fractions by Whole Numbers and Applications

    LearnPractice