Learn on PengienVision, Mathematics, Grade 5Chapter 9: Apply Understanding of Division to Divide Fractions

Lesson 2: Fractions and Mixed Numbers as Quotients

In this Grade 5 lesson from enVision Mathematics Chapter 9, students learn how to express division quotients as fractions and mixed numbers, such as writing 4 ÷ 3 as 4/3 or 1⅓. The lesson uses real-world sharing problems to show how a whole number divided by another whole number can result in a fraction or mixed number rather than a whole number quotient. Students practice converting between division expressions, improper fractions, and mixed numbers across a range of problems.

Section 1

Expressing a Remainder as a Fraction

Property

When a division problem a÷ba \div b results in a whole number quotient qq and a remainder rr, the exact answer can be expressed as a mixed number:

a÷b=qrba \div b = q \frac{r}{b}

Examples

Section 2

Application: Solving Division Word Problems with Fractions

Property

To find the amount for a single share in an equal sharing situation, divide the total amount by the number of shares. The result can be expressed as a fraction or a mixed number.

Size of one share=Total amountNumber of shares \text{Size of one share} = \frac{\text{Total amount}}{\text{Number of shares}}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Expressing a Remainder as a Fraction

Property

When a division problem a÷ba \div b results in a whole number quotient qq and a remainder rr, the exact answer can be expressed as a mixed number:

a÷b=qrba \div b = q \frac{r}{b}

Examples

Section 2

Application: Solving Division Word Problems with Fractions

Property

To find the amount for a single share in an equal sharing situation, divide the total amount by the number of shares. The result can be expressed as a fraction or a mixed number.

Size of one share=Total amountNumber of shares \text{Size of one share} = \frac{\text{Total amount}}{\text{Number of shares}}

Examples