Dividing a fraction by a whole number is like splitting a piece of a pie into even smaller pieces. Imagine you have half a pizza ($ \frac{1}{2} $) and you want to share it equally among 3 friends. Each friend would get a portion of that half. To find out how much, you divide the fraction ($ \frac{1}{2} $) by the whole number (3). This is the same as multiplying the fraction by the reciprocal of the whole number (which is $ \frac{1}{3} $). So, $ \frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6} $. Each friend gets $ \frac{1}{6} $ of the whole pizza.
When dividing fractions by whole numbers, remember to treat the whole number as a fraction with a denominator of 1. Then, multiply the fraction by the reciprocal of the whole number. Simplify if needed!
Match the terms with their definitions:
| Term | Definition |
|---|---|
| 1. Fraction | A. The number below the fraction bar in a fraction. |
| 2. Numerator | B. To find a common factor and reduce the fraction. |
| 3. Denominator | C. A number that represents part of a whole. |
| 4. Reciprocal | D. The number above the fraction bar in a fraction. |
| 5. Simplify | E. Flipping the numerator and denominator of a fraction. |
Complete the following sentences with the correct words:
When dividing a fraction by a whole number, we multiply the fraction by the _______ of the whole number. The _______ is the top number of a fraction, and the _______ is the bottom number. To _______ a fraction, we find a common factor to reduce both numerator and denominator. Dividing by a whole number is the same as multiplying by a fraction with 1 as the _______.
Sarah has $ \frac{3}{4} $ of a cake left over from her birthday party. She wants to divide the remaining cake equally among 5 of her friends. What fraction of the whole cake will each friend receive? Explain your reasoning.
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