Solve Word Problems: Division of a Unit Fraction by a Whole Number
Solving Word Problems: Division of a Unit Fraction by a Whole Number is a Grade 5 math skill from Illustrative Mathematics Chapter 3 (Multiplying and Dividing Fractions) where students apply the formula (1/b) ÷ c = 1/(b × c) to real-world sharing situations. These problems describe splitting a fractional amount into equal groups, resulting in an even smaller unit fraction.
Key Concepts
Property A real world situation involving sharing or splitting a fractional amount ($\frac{1}{b}$) into a number of equal groups ($c$) can be solved using division. The equation is: $$\frac{1}{b} \div c = \frac{1}{b \times c}$$.
Examples There is $\frac{1}{2}$ of a pizza left. If 3 friends share it equally, what fraction of the whole pizza does each friend get? $$\frac{1}{2} \div 3 = \frac{1}{6}$$ A runner completes $\frac{1}{4}$ of a race in 5 minutes, running at a constant speed. What fraction of the total race distance does the runner complete each minute? $$\frac{1}{4} \div 5 = \frac{1}{20}$$.
Explanation These problems require you to divide a unit fraction by a whole number. To solve, identify the initial fractional amount and the number of equal groups it is being divided into. Dividing a unit fraction by a whole number results in a smaller unit fraction. This is because you are splitting an existing part into even smaller pieces.
Common Questions
How do you solve a word problem about dividing a unit fraction by a whole number?
Identify the unit fraction being split and the number of equal parts. Use the formula (1/b) ÷ c = 1/(b × c). For example, (1/2) of a pizza shared by 3 friends: (1/2) ÷ 3 = 1/6. Each friend gets 1/6 of the whole pizza.
What types of word problems involve dividing a unit fraction by a whole number?
Problems where a fractional portion is divided equally among several people or into equal sections. Examples: sharing leftover pizza, splitting a fraction of a race distance across equal time intervals.
What chapter covers unit fraction division word problems in Illustrative Mathematics Grade 5?
Solving word problems: division of a unit fraction by a whole number is covered in Chapter 3 of Illustrative Mathematics Grade 5, titled Multiplying and Dividing Fractions.
What is an example of a unit fraction division word problem?
A runner completes 1/4 of a race in 5 minutes at constant speed. What fraction of the race is covered each minute? (1/4) ÷ 5 = 1/20. The runner covers 1/20 of the race each minute.
Why is the result always a smaller unit fraction?
Dividing a unit fraction (already less than 1) by a whole number greater than 1 creates even smaller equal pieces. More divisions means a larger denominator and a smaller fraction.