Simplify $\frac{4}{16}$ to lowest terms and find an equivalent fraction that has a denominator of 32.
A. $\frac{1}{4}, \frac{8}{32}$
B. $\frac{1}{4}, \frac{4}{32}$
C. $\frac{2}{8}, \frac{4}{32}$
D. $\frac{2}{8}, \frac{8}{32}$
Answer (2)
The fraction 16 4 simplifies to 4 1 . An equivalent fraction with a denominator of 32 is 32 8 . Therefore, the correct answer is option A: 4 1 , 32 8 .
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Simplify the fraction 16 4 by dividing both numerator and denominator by their greatest common divisor, which is 4, resulting in 4 1 .
Find an equivalent fraction to 4 1 with a denominator of 32 by multiplying both numerator and denominator by 8.
This gives us 4 × 8 1 × 8 = 32 8 .
The simplified fraction is 4 1 and the equivalent fraction is 32 8 , so the answer is 4 1 , 32 8 .
Explanation
Understanding the problem We are asked to simplify the fraction 16 4 to its lowest terms and find an equivalent fraction with a denominator of 32.
Simplifying the fraction To simplify 16 4 , we need to find the greatest common divisor (GCD) of 4 and 16. The GCD of 4 and 16 is 4. We divide both the numerator and the denominator by 4: 16 4 = 16 ÷ 4 4 ÷ 4 = 4 1 .
Finding the equivalent fraction Now we need to find an equivalent fraction to 4 1 with a denominator of 32. To do this, we need to find a number that we can multiply the denominator 4 by to get 32. Since 4 × 8 = 32 , we multiply both the numerator and the denominator of 4 1 by 8: 4 1 = 4 × 8 1 × 8 = 32 8 .
Final Answer Therefore, the simplified fraction is 4 1 and the equivalent fraction with a denominator of 32 is 32 8 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Simplifying fractions and finding equivalent fractions helps us to understand proportions and make calculations easier. For example, if you have a recipe that calls for 16 4 of a cup of flour, you can simplify this to 4 1 of a cup. If you need to double the recipe, you can easily find the equivalent fraction with a denominator of 32, which is 32 8 or 4 1 × 2 = 4 2 = 32 16 .
