Question

Write three equivalent ratios for each. Explain how you found each ratio.d) 4/9 : 1 1/3

Answer 1

4/3 : 4

4 : 12

16/3 : 16

Step-by-step explanation:

First, we need to transform the mixed number 1 1/3 into a fraction using the following equation:

`\begin{gathered} A(b)/(c)=(A* c+b)/(c) \\ 1(1)/(3)=(1*3+1)/(3)=(3+1)/(3)=(4)/(3) \end{gathered}`

Therefore the ratio is now 4/9 : 4/3

So, to find equivalent ratios, we can multiply both numbers by a constant value, for example, 3, 9, and 12.

Then, the equivalent ratios are:

Multiplying by 3:

`\begin{gathered} (4)/(9)*3\colon(4)/(3)*3 \\ (4*3)/(9)\colon(4*3)/(3) \\ (4)/(3)\colon4 \end{gathered}`

Multiplying by 9:

`\begin{gathered} (4)/(9)*9\colon(4)/(3)_{}*9 \\ (4*9)/(9)\colon(4*9)/(3) \\ 4\colon12 \end{gathered}`

Multiplying by 12:

`\begin{gathered} (4)/(9)*12\colon(4)/(3)*12 \\ (4*12)/(9)\colon(4*12)/(3) \\ (16)/(3)\colon16 \end{gathered}`

Therefore, the tree equivalent ratios are:

4/3 : 4

4 : 12

16/3 : 16