Learn on PengienVision, Mathematics, Grade 4Chapter 10: Extend Multiplication Concepts to Fractions

Lesson 1: Fractions as Multiples of Unit Fractions

Property.

Section 1

Decomposing a Fraction into a Sum of Unit Fractions

Property

A fraction ab\frac{a}{b} can be expressed as the sum of its unit fractions, 1b\frac{1}{b}, added 'a' times.
This can also be written as the product of the numerator 'a' and the unit fraction 1b\frac{1}{b}.

ab=1b+1b+⋯+1b⏟a times=a×1b\frac{a}{b} = \underbrace{\frac{1}{b} + \frac{1}{b} + \dots + \frac{1}{b}}_{\text{a times}} = a \times \frac{1}{b}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Decomposing a Fraction into a Sum of Unit Fractions

Property

A fraction ab\frac{a}{b} can be expressed as the sum of its unit fractions, 1b\frac{1}{b}, added 'a' times.
This can also be written as the product of the numerator 'a' and the unit fraction 1b\frac{1}{b}.

ab=1b+1b+⋯+1b⏟a times=a×1b\frac{a}{b} = \underbrace{\frac{1}{b} + \frac{1}{b} + \dots + \frac{1}{b}}_{\text{a times}} = a \times \frac{1}{b}

Examples