Question

Lily is making 3 1/5 batches of paint and it takes 2 3/4 of acetone for one batch. How much acetone is needed.

Answer 1

`(44)/(5) \text{ or } 8(4)/(5) \text{ acetone is needed }`

Solution:

Given that,

Lily is making
`3(1)/(5)` batches of paint

It takes
`2(3)/(4)` of acetone for one batch

Let us first convert the mixed fraction to improper fraction

Multiply the whole number part by the fraction's denominator

Add that to the numerator

Then write the result on top of the denominator

`3(1)/(5) = (3 * 5 + 1)/(5) = (16)/(5)\\\\2(3)/(4) = (2 * 4 + 3)/(4) = (11)/(4)`

Therefore,

`\text{Batches of paint} = (16)/(5)\\\\\text{Acetone for one batch } = (11)/(4)`

To find the acetone needed for 16/5 batches, multiply it with acetone for one batch

`\text{Acetone needed } = \text{Batches of paint}} * \text{acetone needed for 1 batch}}`

`\text{Acetone needed} = (16)/(5) * (11)/(4) = (44)/(5)\\\\\text{Acetone needed} = (44)/(5) = 8(4)/(5)`

`\text{Thus } (44)/(5) \text{ or } 8(4)/(5) \text{ acetone is needed }`