Question
Analyze White a fracion equal to \( \frac{2}{3} \) that has a denominator of 12 . Then intiy a fraction equal to \( \frac{1}{4} \) that has a denominator of 12 . What is the sum of the thin fractions you made?
Ask by Best Lang. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The sum of the fractions is \( \frac{11}{12} \).
Solution
To write a fraction equal to 2/3 with a denominator of 12, we first determine the factor needed to change the denominator from 3 to 12. Since 3 × 4 = 12, multiply both the numerator and the denominator by 4:
2/3 = (2 × 4)/(3 × 4) = 8/12.
Next, to write a fraction equal to 1/4 with a denominator of 12, we find the factor needed to change 4 to 12. Since 4 × 3 = 12, multiply both the numerator and denominator by 3:
1/4 = (1 × 3)/(4 × 3) = 3/12.
Now, add the two fractions:
8/12 + 3/12 = (8 + 3)/12 = 11/12.
Thus, the sum of the fractions is 11/12.
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Simplify this solution The Deep Dive
To find a fraction equal to \( \frac{2}{3} \) with a denominator of 12, we can multiply both the numerator and the denominator of \( \frac{2}{3} \) by 4, yielding \( \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \). Next, to create a fraction equal to \( \frac{1}{4} \) with a denominator of 12, we multiply both the numerator and the denominator of \( \frac{1}{4} \) by 3, resulting in \( \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \). Now, adding \( \frac{8}{12} \) and \( \frac{3}{12} \) gives us: \[ \frac{8}{12} + \frac{3}{12} = \frac{11}{12} \] Thus, the sum of the two fractions is \( \frac{11}{12} \).
