📚 Topic Summary
Multiplying a fraction by a whole number is like adding the fraction to itself a certain number of times. For example, multiplying $\frac{1}{4}$ by 3 is the same as adding $\frac{1}{4} + \frac{1}{4} + \frac{1}{4}$, which equals $\frac{3}{4}$. To multiply a fraction by a whole number, you simply multiply the numerator (the top number) of the fraction by the whole number, and keep the denominator (the bottom number) the same. If the resulting fraction is an improper fraction (where the numerator is greater than or equal to the denominator), you can convert it to a mixed number.
Let's say we want to multiply the fraction $\frac{a}{b}$ by the whole number $c$. The formula would be: $\frac{a}{b} \times c = \frac{a \times c}{b}$. Then simplify the result if needed!
🗂️ Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Numerator |
A. The number below the fraction bar. |
| 2. Denominator |
B. A fraction where the numerator is greater than or equal to the denominator. |
| 3. Proper Fraction |
C. The number above the fraction bar. |
| 4. Improper Fraction |
D. A whole number and a fraction combined. |
| 5. Mixed Number |
E. A fraction where the numerator is less than the denominator. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph with the correct words:
To multiply a fraction by a whole number, multiply the ______ by the whole number, keeping the ______ the same. For example, to multiply $\frac{2}{5}$ by 3, you multiply 2 by 3 to get 6, so the answer is $\frac{6}{5}$. This is an ______ fraction, and it can be converted to a ______ number which is $1\frac{1}{5}$.
🤔 Part C: Critical Thinking
Explain in your own words why multiplying a fraction by a whole number increases the value of the fraction (unless the whole number is 0 or 1). Give an example to support your explanation.