Question

Proportions A proportion is a statement that to ratios or rates are equal. It can be given as a sentence in words, but most often a proportion is an algebraic equation The arithmetic equation 3 5 3 X 35 = 105 21 35 is a proportion because its cross products are equal. and 5 x 21 = 105 Proportions are solved by using this cross-product rule Example #2 Example #1: 4 = 9 Y 36 72 1.5 12 y

Answer 1

in Example #2,
`\( y = 0.25 \)` or
`\( (1)/(4) \)` when rounded to the nearest hundredth.

in Example #1,
`\( y = 16 \)`.

Here are the detailed steps to solve the proportions for
`\( y \)`:

Example #1:

The proportion is given by:

`\[ (4)/(9) = (y)/(36) \]`

To solve for
`\( y \)`, cross-multiply to get:

`\[ 4 * 36 = 9 * y \]`

`\[ 144 = 9y \]`

Now, divide both sides by 9 to isolate
`\( y \)`:

`\[ y = (144)/(9) \]`

`\[ y = 16 \]`

So, in Example #1,
`\( y = 16 \)`.

**Example #2:**

The proportion is given by:

`\[ (72)/(1.5) = (12)/(y) \]`

To solve for
`\( y \)`, cross-multiply to get:

`\[ 72 * y = 12 * 1.5 \]`

`\[ 72y = 18 \]`

Now, divide both sides by 72 to isolate
`\( y \)`:

`\[ y = (18)/(72) \]`

`\[ y = 0.25 \]`

So, in Example #2,
`\( y = 0.25 \)` or
`\( (1)/(4) \)` when rounded to the nearest hundredth.

Answer 2

We have the following:

example #1

`\begin{gathered} (4)/(9)=(y)/(36) \\ 9\cdot y=4\cdot36 \\ y=(4\cdot36)/(9) \\ y=16 \end{gathered}`

example #2

`\begin{gathered} (72)/(1.5)=(12)/(y) \\ 72\cdot y=12\cdot1.5 \\ y=(12\cdot1.5)/(72) \\ y=0.25 \end{gathered}`