Question
Add. Do not use a number line except as a check. \( -\frac{19}{28}+\frac{31}{42} \) \( -\frac{19}{28}+\frac{31}{42}=\square \) (Simplify your answer. Type an integer or a fragction.)
Ask by Johnson Knight. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( -\frac{19}{28} + \frac{31}{42} = \frac{5}{84} \)
Solution
To add –19/28 and 31/42 without using a number line, follow these steps:
1. Find the least common denominator (LCD) of 28 and 42. The prime factors are:
28 = 2² × 7
42 = 2 × 3 × 7
LCD = 2² × 3 × 7 = 84
2. Convert each fraction to an equivalent fraction with denominator 84:
- –19/28 = –(19 × 3)/(28 × 3) = –57/84
- 31/42 = (31 × 2)/(42 × 2) = 62/84
3. Add the fractions:
–57/84 + 62/84 = (–57 + 62)/84 = 5/84
Thus, the simplified answer is 5/84.
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Simplify this solution The Deep Dive
To add the two fractions, we first need a common denominator. The least common multiple of 28 and 42 is 84. We convert each fraction: \(-\frac{19}{28} = -\frac{19 \times 3}{28 \times 3} = -\frac{57}{84}\) \(\frac{31}{42} = \frac{31 \times 2}{42 \times 2} = \frac{62}{84}\) Now we can add them: \(-\frac{57}{84} + \frac{62}{84} = \frac{62 - 57}{84} = \frac{5}{84}\) Thus, \(-\frac{19}{28} + \frac{31}{42} = \frac{5}{84}\)
