Question

A painter has 5 1/3 gallons of paint. It takes 4 5/9 gallons for a family room. It's estimated that it will take 6 5/9 gallons to paint the living room. How much more paint does he need to buy?

someone help please​

Answer 1

Answer: The mixed number 5 7/9

We can write the mixed number as 5 & 7/9 to better separate the whole part (5) from the fractional part (7/9)

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Step-by-step explanation:

Use this formula

`a (b)/(c) = (a*c + b)/(c)`

to convert from a mixed number to an improper fraction.

Here are the steps in converting 5 & 1/3

`a (b)/(c) = (a*c+b)/(c)\\\\5 (1)/(3) = (5*3+1)/(3)\\\\5 (1)/(3) = (16)/(3)\\\\`

Through similar steps you should also have

`4 (5)/(9) = (41)/(9)\\\\6 (5)/(9) = (59)/(9)\\\\`

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Let's add the amounts needed for the family room and the living room.

`(41)/(9)+(59)/(9)\\\\(41+59)/(9)\\\\(100)/(9)\\\\`

Subtract off the amount the painter already has

`(100)/(9) - (16)/(3)\\\\(100)/(9) - (3*16)/(3*3)\\\\(100)/(9) - (48)/(9)\\\\(100-48)/(9)\\\\(52)/(9)\\\\`

This improper fraction is the number of gallons of paint that's missing, i.e. the amount the painter needs to buy.

Converting it to a mixed number gets us:

`(52)/(9)=(45+7)/(9)\\\\(52)/(9)=(45)/(9)+(7)/(9)\\\\(52)/(9)=5+(7)/(9)\\\\(52)/(9)=5(7)/(9)\\\\`

Note that 52/9 leads to a quotient of 5 and a remainder of 7. The 5 and 7 match with 5 & 7/9

The painter needs to buy 5 full gallons, plus another 7/9 of a gallon. Or we can state it as him needing 5 & 7/9 gallons of paint.