
Concept explainers
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To write: The equivalent fractions of
Answer to Problem 1PCT
The equivalent fractions of
Explanation of Solution
Procedure used:
“Step 1: Find the least common denominator of the fractions.
Step 2: Rewrite each fraction with the least common denominator”.
Property used:
“If a, b, and c are whole numbers, then
Calculation:
The given fractions are
Recall that, the least common denominator is the least common multiple of the denominators.
Step 1: Find the least common denominator of the fractions.
The denominators of the fractions are 8 and 20.
Obtain the least common multiple of 8 and 20.
The number 8 can be written as the product of 2, 2, and 2.
Therefore, the prime factorization of 8 is
The number 20 can be written as the product of 2. 2, and 5.
Therefore, the prime factorization of 20 is
Now align the common factors vertically and write down the common factors and then write down the remaining factors as follows.
Multiply the above listed factors.
Thus, the least common denominator is 40.
Step2: Write each fractions with the least common denominator.
The number 8 becomes 40 when multiplied with 5.
That is,
By the above property,
Thus, the equivalent fraction of
The number 20 becomes 40 when multiplied by 2.
That is,
By the above property,
Thus, the equivalent fraction of
Therefore, the equivalent fractions of
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