Dividing a Unit Fraction by a Whole Number
Dividing a Unit Fraction by a Whole Number is a Grade 5 math skill from Illustrative Mathematics Chapter 3 (Multiplying and Dividing Fractions) that teaches the procedure (1/b) ÷ c = (1/b) × (1/c) = 1/(b × c). Dividing by a whole number means multiplying by its reciprocal. This connects the inverse operations of multiplication and division and shows why dividing a fraction by a whole number produces a fraction with a larger denominator.
Key Concepts
Property To divide a unit fraction by a whole number, you multiply the unit fraction by the reciprocal of the whole number. The reciprocal of a whole number $c$ is $\frac{1}{c}$. $$\frac{1}{b} \div c = \frac{1}{b} \times \frac{1}{c} = \frac{1}{b \times c}$$.
Examples $\frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$ $\frac{1}{5} \div 4 = \frac{1}{5} \times \frac{1}{4} = \frac{1}{20}$ $\frac{1}{8} \div 2 = \frac{1}{8} \times \frac{1}{2} = \frac{1}{16}$.
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 procedure for this is to change the division problem into a multiplication problem by using the reciprocal of the whole number. This method connects division and multiplication, showing they are inverse operations.
Common Questions
What is the procedure for dividing a unit fraction by a whole number?
Multiply the unit fraction by the reciprocal of the whole number: (1/b) ÷ c = (1/b) × (1/c) = 1/(b × c). For example, (1/2) ÷ 3 = (1/2) × (1/3) = 1/6.
What is the reciprocal of a whole number?
The reciprocal of whole number c is 1/c. To divide by c, you multiply by 1/c. For example, dividing by 3 is the same as multiplying by 1/3. This is because 3 × (1/3) = 1.
What chapter covers dividing a unit fraction by a whole number 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.
What are examples of dividing a unit fraction by a whole number?
(1/2) ÷ 3 = 1/6. (1/5) ÷ 4 = 1/20. (1/8) ÷ 2 = 1/16. Each time, the denominator grows because you are splitting the fraction into more equal parts.
Why does the denominator get larger when dividing a unit fraction by a whole number?
Dividing splits the fraction into more equal parts. More parts means each part is smaller, which requires a larger denominator to represent the smaller size. Multiplying the original denominator by the whole number gives the new denominator.