Write equivalent fractions for 3/7 and 1/3 using 21 as a common denominator
The correct answer and explanation is:
Correct Answer:
- The equivalent fraction for 3/7 with 21 as the common denominator is 9/21
- The equivalent fraction for 1/3 with 21 as the common denominator is 7/21
Explanation (300 words):
To write equivalent fractions using a common denominator, the goal is to make the denominators of the fractions the same. In this case, the desired common denominator is 21. A fraction can be rewritten in equivalent form by multiplying both the numerator and the denominator by the same number. This process does not change the value of the fraction but represents it in a different form that is more convenient for operations like addition or comparison.
Start with the fraction 3/7. To convert it to an equivalent fraction with 21 as the denominator, determine what number 7 must be multiplied by to become 21. Since
7 × 3 = 21,
multiply both the numerator and denominator of 3/7 by 3:
3 × 3 = 9
7 × 3 = 21
So, 3/7 = 9/21
Next, convert 1/3 to an equivalent fraction with a denominator of 21. Since
3 × 7 = 21,
multiply both the numerator and denominator of 1/3 by 7:
1 × 7 = 7
3 × 7 = 21
So, 1/3 = 7/21
Having a common denominator is especially useful when adding or subtracting fractions. For example, once 3/7 and 1/3 are rewritten as 9/21 and 7/21, they can be added directly:
9/21 + 7/21 = 16/21
Using a common denominator also allows easy comparison. Since both fractions are out of 21 parts, one can see that 9/21 is greater than 7/21. Therefore, the process of finding equivalent fractions with a shared denominator is a foundational skill in working with fractions efficiently in arithmetic.