An equivalent fraction to 5/16 is
a. 5/32
b. 10/32
c.1/2
d. 10/16
The Correct Answer and Explanation is :
The correct answer is b. 10/32.
Explanation:
To find an equivalent fraction, we need to understand that equivalent fractions are different fractions that represent the same value or proportion of a whole. To create an equivalent fraction, you can multiply or divide the numerator (the top number) and the denominator (the bottom number) by the same non-zero number.
Let’s take the fraction ( \frac{5}{16} ) as our starting point. We can find an equivalent fraction by multiplying both the numerator and the denominator by the same number.
For example, if we multiply both the numerator and the denominator of ( \frac{5}{16} ) by 2:
[
\frac{5 \times 2}{16 \times 2} = \frac{10}{32}
]
Thus, ( \frac{10}{32} ) is an equivalent fraction to ( \frac{5}{16} ).
Now, let’s analyze the other options provided:
- a. ( \frac{5}{32} ): This fraction has a numerator smaller than that of ( \frac{5}{16} ), and while it has the same numerator, the denominator has changed, which reduces the overall value of the fraction. Therefore, it is not equivalent to ( \frac{5}{16} ).
- c. ( \frac{1}{2} ): To compare this with ( \frac{5}{16} ), we can convert ( \frac{1}{2} ) to a fraction with a denominator of 16. ( \frac{1}{2} = \frac{8}{16} ). Since ( \frac{8}{16} ) is not equal to ( \frac{5}{16} ), this option is also not equivalent.
- d. ( \frac{10}{16} ): While the numerator is correct, the denominator has changed, resulting in a larger fraction, which represents a different value. This fraction simplifies to ( \frac{5}{8} ), clearly not equivalent to ( \frac{5}{16} ).
In conclusion, the only correct equivalent fraction among the options given is b. ( \frac{10}{32} ), confirming that equivalent fractions maintain the same value even if their appearance differs.