Divide a Unit Fraction by a Whole Number
Divide a Unit Fraction by a Whole Number is a Grade 5 math skill from Illustrative Mathematics Chapter 3 (Multiplying and Dividing Fractions) where students learn the rule: (1/b) ÷ a = 1/(b × a). Dividing a unit fraction by a whole number splits an already small piece into even smaller equal parts, resulting in a fraction with a larger denominator. This procedural shortcut connects directly to visual models of partitioning.
Key Concepts
Property To divide a unit fraction by a whole number, multiply the denominator of the fraction by the whole number. $$\frac{1}{b} \div a = \frac{1}{b \times a}$$.
Examples $\frac{1}{2} \div 3 = \frac{1}{2 \times 3} = \frac{1}{6}$ $\frac{1}{4} \div 5 = \frac{1}{4 \times 5} = \frac{1}{20}$.
Explanation Dividing a unit fraction by a whole number means splitting an already small piece into even smaller, equal parts. For example, dividing $\frac{1}{2}$ by 3 is like cutting half a pizza into 3 equal slices. The resulting fraction has a larger denominator because the whole is now divided into more parts. This calculation provides a direct way to find the size of each smaller piece without drawing a model.
Common Questions
How do you divide a unit fraction by a whole number?
Multiply the denominator of the unit fraction by the whole number. The formula is (1/b) ÷ a = 1/(b × a). For example, (1/2) ÷ 3 = 1/(2 × 3) = 1/6.
What does dividing a unit fraction by a whole number mean?
It means splitting an already small fractional piece into even more equal parts. For example, dividing 1/2 by 3 is like cutting a half pizza into 3 equal slices, giving each person 1/6 of the whole pizza.
What chapter covers dividing unit fractions in Illustrative Mathematics Grade 5?
Dividing a unit fraction by a whole number is covered in Chapter 3 of Illustrative Mathematics Grade 5, titled Multiplying and Dividing Fractions.
Why does the denominator get larger when you divide a unit fraction by a whole number?
Because you are splitting the fraction into more parts. The whole is now divided into more equal pieces than before, so each piece represents a smaller fraction and the denominator increases accordingly.
What is the formula for dividing a unit fraction by a whole number?
The formula is (1/b) ÷ a = 1/(b × a). You simply multiply the denominator by the whole number. For example, (1/4) ÷ 5 = 1/20.