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

D

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{(2)/(3), (9)/(15)}`

`\mathsf{(2)/(3)}\\\\\mathsf{= 2/3}\\\\\mathsf{= 0.66\overline{6}7}\\\\\\\mathsf{(9)/(15)}\\\\\mathsf{= (9/3)/(15/3)}\\\\\mathsf{= (3)/(5)}\\\\\\\\\mathsf{(2)/(3) \\eq (9)/(15)}`

`\huge\textsf{Option B.}`

`\mathsf{(5)/(8), (15)/(21)}`

`\mathsf{(5)/(8)}\\\\\mathsf{= 5/8}\\\\\mathsf{= 0.625}\\\\\\\mathsf{(15)/(21)}\\\\\mathsf{= (15/3)/(21/3)}\\\\\mathsf{= (5)/(7)}\\\\\mathsf{(5)/(8)\\eq (15)/(21)}`

`\huge\textsf{Option C.}`

`\mathsf{(3)/(12).(6)/(18)}`

`\mathsf{(3)/(12)}\\\\\mathsf{= 3 / 12}\\\\\mathsf{= 0.25}\\\\\\\\\mathsf{(6)/(18)}\\\\\\\mathsf{= (6/3)/(18/3)}\\\\\\\mathsf{= (2)/(6)}\\\\\\\mathsf{= (2/2)/(6/2)}\\\\\\\mathsf{= (1)/(3)}\\\\\\\mathsf{(3)/(12)\\eq (6)/(18)}`

`\huge\textsf{Option D.}`

`\mathsf{(4)/(10), (12)/(30)}`

`\mathsf{(4)/(10)}\\\\\mathsf{= 4/10}\\\\\mathsf{= 0.40}\\\\\\\mathsf{(6)/(18)}\\\\\mathsf{= (12/3)/(30/3)}\\\\\mathsf{= (4)/(10)}\\\\\mathsf{= (4)/(10)}\\\\\mathsf{= (4/2)/(10/2)}\\\\\mathsf{= (2)/(5)}\\\\\mathsf{(4)/(10) = (12)/(20)}`

`\huge\text{Thus, your answer should be: \boxed{\mathsf{Option\ D. (4)/(10), (12)/(30)}}}\huge\checkmark`

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