Question

Which pair represents equivalent ratios?
A.2/3,95
B.5/8,15/21
C.3/12,6/18
D.4/10,12/30

Answer 1

Answer:

D

Step-by-step explanation:

We can test each pair making each ratio into its simplest form.

For A 2/3 is already in its simplest form and 9/15=3/5. they are not equivalent.

For B, 5/8 is already in its simplest form and 15/21=5/7. they are not equivalent.

For C, 3/12=1/4, and 6/18=1/3. They are not equivalent.

For D, 4/10=2/5, and 12/30=2/5. They are equivalent.

Answer 2

$\huge\text{Hey there!}$

$\huge\textbf{Let's see which ones are equivalent}\\\huge\textbf{to each other, shall we?}\\\\\\\huge\textbf{We will convert the given fractions to}\\\huge\textbf{decimals or make the fractions on the}\\\huge\textbf{right to easier to solve or comparing it}\\\huge\textbf{to the one on the left.}$

$\huge\textsf{Option A.}$

$\mathsf{\dfrac{2}{3}, \dfrac{9}{15}}$

$\mathsf{\dfrac{2}{3}}\\\\\mathsf{= 2\div3}\\\\\mathsf{= 0.66\overline{6}7}\\\\\\\mathsf{\dfrac{9}{15}}\\\\\mathsf{= \dfrac{9\div3}{15\div3}}\\\\\mathsf{= \dfrac{3}{5}}\\\\\\\\\mathsf{\dfrac{2}{3} \neq \dfrac{9}{15}}$

$\huge\textsf{Option B.}$

$\mathsf{\dfrac{5}{8}, \dfrac{15}{21}}$

$\mathsf{\dfrac{5}{8}}\\\\\mathsf{= 5\div8}\\\\\mathsf{= 0.625}\\\\\\\mathsf{\dfrac{15}{21}}\\\\\mathsf{= \dfrac{15\div3}{21\div3}}\\\\\mathsf{= \dfrac{5}{7}}\\\\\mathsf{\dfrac{5}{8}\neq \dfrac{15}{21}}$

$\huge\textsf{Option C.}$

$\mathsf{\dfrac{3}{12}.\dfrac{6}{18}}$

$\mathsf{\dfrac{3}{12}}\\\\\mathsf{= 3 \div 12}\\\\\mathsf{= 0.25}\\\\\\\\\mathsf{\dfrac{6}{18}}\\\\\\\mathsf{= \dfrac{6\div3}{18\div3}}\\\\\\\mathsf{= \dfrac{2}{6}}\\\\\\\mathsf{= \dfrac{2\div2}{6\div2}}\\\\\\\mathsf{= \dfrac{1}{3}}\\\\\\\mathsf{\dfrac{3}{12}\neq \dfrac{6}{18}}$

$\huge\textsf{Option D.}$

$\mathsf{\dfrac{4}{10}, \dfrac{12}{30}}$

$\mathsf{\dfrac{4}{10}}\\\\\mathsf{= 4\div10}\\\\\mathsf{= 0.40}\\\\\\\mathsf{\dfrac{6}{18}}\\\\\mathsf{= \dfrac{12\div3}{30\div3}}\\\\\mathsf{= \dfrac{4}{10}}\\\\\mathsf{= \dfrac{4}{10}}\\\\\mathsf{= \dfrac{4\div2}{10\div2}}\\\\\mathsf{= \dfrac{2}{5}}\\\\\mathsf{\dfrac{4}{10} = \dfrac{12}{20}}$

$\huge\text{Thus, your answer should be: \boxed{\mathsf{Option\ D. \dfrac{4}{10}, \dfrac{12}{30}}}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~$\frak{Amphitrite1040:)}$