Solve Word Problems: Division of a Whole Number by a Unit Fraction
Solving Word Problems: Division of a Whole Number by a Unit Fraction is a Grade 5 math skill from Illustrative Mathematics Chapter 3 (Multiplying and Dividing Fractions) where students recognize situations asking how many fractional pieces fit into a whole, and solve using c ÷ (1/b) = c × b. Real-world contexts include baking, relay races, and measuring, helping students connect division by fractions to everyday problem-solving.
Key Concepts
Property Dividing a whole number $c$ by a unit fraction $\frac{1}{b}$ is equivalent to multiplying the whole number by the denominator $b$. This answers the question: "How many pieces of size $\frac{1}{b}$ fit into $c$ wholes?" $$c \div \frac{1}{b} = c \times b$$.
Examples A baker has 4 pounds of flour. If each cake recipe requires $\frac{1}{3}$ of a pound of flour, how many cakes can the baker make? $$4 \div \frac{1}{3} = 4 \times 3 = 12 \text{ cakes}$$ A relay race is 5 miles long. If each runner runs for $\frac{1}{2}$ of a mile, how many runners are needed for the race? $$5 \div \frac{1}{2} = 5 \times 2 = 10 \text{ runners}$$.
Explanation This skill involves situations where you need to find out how many fractional parts fit into a whole number. For example, if you have 2 pizzas and you want to know how many $\frac{1}{4}$ pizza slices there are, you are solving $2 \div \frac{1}{4}$. Since each whole pizza has 4 quarter slices, 2 pizzas would have $2 \times 4 = 8$ slices. Dividing a whole number by a unit fraction is the same as multiplying the whole number by the denominator of the fraction.
Common Questions
How do you solve a word problem about dividing a whole number by a unit fraction?
Identify the total amount and the fractional piece size. Set up the division c ÷ (1/b) and solve by multiplying c × b. For example, a baker with 4 pounds of flour using 1/3 lb per cake: 4 ÷ (1/3) = 4 × 3 = 12 cakes.
What type of real-world situations involve dividing a whole number by a unit fraction?
Situations like: how many 1/2-mile legs in a 5-mile race, how many 1/4-cup servings in 3 cups, or how many 1/3-pound portions from 4 pounds. These all ask how many fractional pieces fit into a whole amount.
What chapter covers division word problems with unit fractions in Illustrative Mathematics Grade 5?
Solving word problems: division of a whole number by a unit fraction is covered in Chapter 3 of Illustrative Mathematics Grade 5, titled Multiplying and Dividing Fractions.
What is the formula for dividing a whole number by a unit fraction?
c ÷ (1/b) = c × b. For example, 5 ÷ (1/2) = 5 × 2 = 10 runners. Dividing by a unit fraction asks how many such pieces fit in the whole, which equals the whole number times the denominator.
How do you recognize that a word problem requires division by a unit fraction?
Look for phrases like "how many pieces of size 1/x are in," "how many portions fit in," or "divided equally into 1/x-sized groups." These signal that you need to divide by a unit fraction.