Question
Use the common-numerator and common-denominator rules to compute these divisions, expressing each answer in lowest terms. \( \begin{array}{ll}\text { (a) } \frac{12}{7} \div \frac{11}{7} & \text { (b) } \frac{7}{9} \div \frac{7}{8} \\ \text { (a) } \frac{12}{7} \div \frac{11}{7}=\square \text { (Type an integer or a simplified fraction.) }\end{array} \)
Ask by Hardy Johnston. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) 12/11
(b) 8/9
Solution
To perform these divisions, we can use the following rules:
• Common-Denominator Rule: When dividing fractions with the same denominator,
(a/b) ÷ (c/b) = a/c.
• Common-Numerator Rule: When dividing fractions with the same numerator,
(a/b) ÷ (a/d) = d/b.
Now, apply the rules to each problem:
(a) For 12/7 ÷ 11/7, the fractions have the same denominator (7). Use the common-denominator rule:
12/7 ÷ 11/7 = 12/11.
(b) For 7/9 ÷ 7/8, the fractions have the same numerator (7). Use the common-numerator rule:
7/9 ÷ 7/8 = 8/9.
Both answers are in lowest terms.
Thus, the answers are:
(a) 12/11 (b) 8/9.
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Simplify this solution Bonus Knowledge
To solve \( \frac{12}{7} \div \frac{11}{7} \), we use the common-numerator rule. Since both fractions share the same denominator, we can simplify the division by focusing on the numerators: \[ \frac{12}{7} \div \frac{11}{7} = \frac{12}{11} \] Now, \( \frac{12}{11} \) is already in its lowest terms since 12 and 11 have no common factors. Now let's tackle \( \frac{7}{9} \div \frac{7}{8} \). Again, since both fractions have the same numerator, we use the common-numerator rule: \[ \frac{7}{9} \div \frac{7}{8} = \frac{8}{9} \] Here, \( \frac{8}{9} \) is also already in its lowest terms. So, the answers are: (a) \( \frac{12}{11} \); (b) \( \frac{8}{9} \).
