Can you find a fraction that is equivalent to $\frac{6}{25}$ ? Which of the following terminating decimals is equivalent to this fraction?
0.20
0.22
0.24
none
Answer (1)
Find an equivalent fraction by multiplying the numerator and denominator by the same number: 25 6 = 25 × 4 6 × 4 = 100 24 .
Convert the fraction to a decimal: 25 6 = 0.24 .
Compare the decimal representation with the given options.
The equivalent terminating decimal is 0.24 .
Explanation
Problem Analysis We are given the fraction 25 6 and asked to find an equivalent fraction and a terminating decimal representation from the options 0.20, 0.22, 0.24, and none.
Finding an Equivalent Fraction To find an equivalent fraction, we can multiply both the numerator and the denominator of the given fraction by the same non-zero number. For example, multiplying both by 4, we get: 25 × 4 6 × 4 = 100 24 So, 100 24 is an equivalent fraction.
Converting to Decimal To convert the fraction 25 6 to a decimal, we can divide the numerator by the denominator: 25 6 = 0.24
Comparing with Options Comparing the decimal representation 0.24 with the given options, we find that 0.24 is one of the options.
Final Answer Therefore, the equivalent fraction we found is 100 24 , and the equivalent terminating decimal is 0.24.
Examples
Fractions and decimals are used in everyday life, such as when calculating discounts at a store. For example, if an item costs $25 and is 6/25 off, you would calculate 6/25 of $25 to find the discount amount. Converting 6/25 to a decimal (0.24) makes it easier to calculate the discount: 0.24 * $25 = $6. So the item is $6 off.
