An equivalent fraction for $5 / 16$ is
Select one:
a. 5/32
b. $10 / 32$
c. $1 / 2$
d. $10 / 16$
Answer (1)
Check each option to see if it is equivalent to 16 5 โ .
Simplify 32 10 โ by dividing both numerator and denominator by 2: 32 10 โ = 16 5 โ .
Conclude that the equivalent fraction is 32 10 โ โ .
Explanation
Understanding Equivalent Fractions We need to find which of the given fractions is equivalent to 16 5 โ . A fraction is equivalent to another if it represents the same value, which means we can obtain one from the other by multiplying or dividing both the numerator and the denominator by the same non-zero number.
Checking Each Option Let's examine each option:
a. 32 5 โ : This fraction has the same numerator as the original fraction, but the denominator is different. If we multiply the numerator and denominator of 16 5 โ by the same number, we won't get 32 5 โ . So, it's not equivalent.
b. 32 10 โ : We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2. 32 รท 2 10 รท 2 โ = 16 5 โ . So, this fraction is equivalent to 16 5 โ .
c. 2 1 โ : This fraction is a simple fraction. If we want to check if 2 1 โ is equivalent to 16 5 โ , we can cross-multiply: 1 ร 16 = 16 and 2 ร 5 = 10 . Since 16 ๎ = 10 , the fractions are not equivalent.
d. 16 10 โ : This fraction has the same numerator as the equivalent fraction we found in option b, but the denominator is different. If we simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2. 16 รท 2 10 รท 2 โ = 8 5 โ . So, this fraction is not equivalent to 16 5 โ .
Final Answer Therefore, the equivalent fraction for 16 5 โ is 32 10 โ .
Examples
Equivalent fractions are useful in everyday situations, such as when you're cooking and need to adjust the quantities of ingredients in a recipe. For example, if a recipe calls for 16 5 โ of a cup of flour, but your measuring cups only have markings for fractions with a denominator of 32, you can use the equivalent fraction 32 10 โ of a cup to measure the correct amount. This ensures that your recipe turns out as expected, even when you need to work with different units or measuring tools.
