Learn on PengiEureka Math, Grade 5Chapter 25: Division of Fractions and Decimal Fractions

Lesson 1: Divide a whole number by a unit fraction.

In this Grade 5 Eureka Math lesson from Chapter 25, students learn to divide a whole number by a unit fraction using tape diagrams and area models to build conceptual understanding. Through hands-on problems, such as determining how many one-third or one-fourth pound bags can be made from a whole number of pounds, students discover the relationship between division by a unit fraction and multiplication by its reciprocal. The lesson connects prior knowledge of fraction and decimal operations to this new division concept.

Section 1

Whole Number ÷ Unit Fraction

Property

Dividing a whole number, aa, by a unit fraction, 1b\frac{1}{b}, is a way of asking: "How many groups of size 1b\frac{1}{b} are in aa?"
This can be modeled visually to find the total number of fractional parts.

Examples

Section 2

Connecting Division by a Unit Fraction to Multiplication

Property

We noticed in the previous visual models that dividing by a unit fraction (1b\frac{1}{b}) produces the same result as multiplying by the denominator (bb).
To solve a÷1ba \div \frac{1}{b}, you can ask: "aa is 1b\frac{1}{b} of what number?". The shortcut is to multiply the whole number by the denominator:

a÷1b=a×ba \div \frac{1}{b} = a \times b

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Whole Number ÷ Unit Fraction

Property

Dividing a whole number, aa, by a unit fraction, 1b\frac{1}{b}, is a way of asking: "How many groups of size 1b\frac{1}{b} are in aa?"
This can be modeled visually to find the total number of fractional parts.

Examples

Section 2

Connecting Division by a Unit Fraction to Multiplication

Property

We noticed in the previous visual models that dividing by a unit fraction (1b\frac{1}{b}) produces the same result as multiplying by the denominator (bb).
To solve a÷1ba \div \frac{1}{b}, you can ask: "aa is 1b\frac{1}{b} of what number?". The shortcut is to multiply the whole number by the denominator:

a÷1b=a×ba \div \frac{1}{b} = a \times b

Examples