Question

directions: prove whether each set of fractions are equivalent or not equivalent by multiplying or dividing by a common factor of change each other and circle equivalent or not equivalent. show your work.
a) 1/2 and 10/18
a. equivalent
b. not equivalent
b) 24/36 and 20/42
a. equivalent
b. not equivalent
c) 12/15 and 22/35
a. equivalent
b. not equivalent
d) 7/8 and 5/6
a. equivalent
b. not equivalent

1. find the quotient of ÷ and 2/3

Explanation:

Step1: Simplify the first - pair of fractions

For $\frac{1}{2}$ and $\frac{10}{18}$, simplify $\frac{10}{18}=\frac{10\div2}{18\div2}=\frac{5}{9}$. Since $\frac{1}{2}
eq\frac{5}{9}$, they are not equivalent.

Step2: Simplify the second - pair of fractions

For $\frac{14}{21}$ and $\frac{28}{42}$, simplify $\frac{14}{21}=\frac{14\div7}{21\div7}=\frac{2}{3}$, and $\frac{28}{42}=\frac{28\div14}{42\div14}=\frac{2}{3}$. Since $\frac{14}{21}=\frac{28}{42}$, they are equivalent.

Step3: Simplify the third - pair of fractions

For $\frac{12}{15}$ and $\frac{22}{35}$, simplify $\frac{12}{15}=\frac{12\div3}{15\div3}=\frac{4}{5}$, and $\frac{22}{35}$ is already in simplest form. Since $\frac{4}{5}
eq\frac{22}{35}$, they are not equivalent.

Step4: Simplify the fourth - pair of fractions

For $\frac{7}{8}$ and $\frac{5}{6}$, find a common denominator. The common denominator of 8 and 6 is 24. $\frac{7}{8}=\frac{7\times3}{8\times3}=\frac{21}{24}$, $\frac{5}{6}=\frac{5\times4}{6\times4}=\frac{20}{24}$. Since $\frac{21}{24}
eq\frac{20}{24}$, they are not equivalent.

Answer:

A. b. Not Equivalent
B. a. Equivalent
C. b. Not Equivalent
D. b. Not Equivalent