Learn on PengiIllustrative Mathematics, Grade 5Chapter 3: Multiplying and Dividing Fractions

Lesson 10: Fraction Division Situations

In this Grade 5 lesson from Illustrative Mathematics Chapter 3, students apply their understanding of dividing a whole number by a unit fraction and a unit fraction by a whole number to write and solve real-world word problems. Using a card sort activity, students match situations to expressions such as 5 ÷ 1/4 and 1/4 ÷ 5, interpreting what each equation means in context. The lesson builds fluency with fraction division and addresses standards 5.NF.B.7 and 5.NF.B.7.c.

Section 1

Applying Partitive Division: Fraction ÷ Whole Number

Property

Partitive division with a fraction dividend and whole number divisor, ab÷c\frac{a}{b} \div c, answers the question: "If an amount ab\frac{a}{b} is split into cc equal groups, what is the size of one group?"

Examples

Section 2

Applying Quotative Division: Whole Number ÷ Unit Fraction

Property

Quotative division, or measurement division, answers the question "how many groups of a certain size are in a given amount?" When dividing a whole number by a unit fraction, we are finding how many fractional pieces fit into the whole.

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

Examples

  • How many 14\frac{1}{4}-cup servings are in 3 cups of sugar?
3÷14=3×4=12 servings3 \div \frac{1}{4} = 3 \times 4 = 12 \text{ servings}
  • A baker has 5 pounds of flour. How many 12\frac{1}{2}-pound bags can he make?
5÷12=5×2=10 bags5 \div \frac{1}{2} = 5 \times 2 = 10 \text{ bags}

Explanation

This skill applies division to real-world scenarios where you need to find out how many smaller, fractional units can be made from a larger whole amount. This is known as quotative or measurement division. For example, if you are dividing 2 pies into slices that are 16\frac{1}{6} of a pie each, you are asking how many groups of 16\frac{1}{6} are in 2. Dividing a whole number by a unit fraction results in a larger whole number, as you are finding the total number of fractional parts within the wholes.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Applying Partitive Division: Fraction ÷ Whole Number

Property

Partitive division with a fraction dividend and whole number divisor, ab÷c\frac{a}{b} \div c, answers the question: "If an amount ab\frac{a}{b} is split into cc equal groups, what is the size of one group?"

Examples

Section 2

Applying Quotative Division: Whole Number ÷ Unit Fraction

Property

Quotative division, or measurement division, answers the question "how many groups of a certain size are in a given amount?" When dividing a whole number by a unit fraction, we are finding how many fractional pieces fit into the whole.

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

Examples

  • How many 14\frac{1}{4}-cup servings are in 3 cups of sugar?
3÷14=3×4=12 servings3 \div \frac{1}{4} = 3 \times 4 = 12 \text{ servings}
  • A baker has 5 pounds of flour. How many 12\frac{1}{2}-pound bags can he make?
5÷12=5×2=10 bags5 \div \frac{1}{2} = 5 \times 2 = 10 \text{ bags}

Explanation

This skill applies division to real-world scenarios where you need to find out how many smaller, fractional units can be made from a larger whole amount. This is known as quotative or measurement division. For example, if you are dividing 2 pies into slices that are 16\frac{1}{6} of a pie each, you are asking how many groups of 16\frac{1}{6} are in 2. Dividing a whole number by a unit fraction results in a larger whole number, as you are finding the total number of fractional parts within the wholes.