Question

Darren bought some paint. He used 2 1/4 gallons painting his living room. After that, he had 3 5/6 gallons left. How much paint did he buy?

Answer 1

Explanation:

Let's pretend this was just whole numbers. So used 2 gallons and had 3 left. Hopefully it's clear you'd have started with 5. It's basically an algebra equation. If we say x is the starting amount then

x-2 = 3

x = 5. Let me know if that doesn't make sense. Now though we can plug in the actual values.

x - 2 1/4 = 3 5/6

x = 2 1/4 + 3 5/6

x = 5 1/4 + 5/6

Now, to add fractions you need to change the denominator. You need to know you can change fractions by multiplying the numerator and denominator by a number. so 1/2 can be 2/4 because 1*2 = 2 and 2*2 = 4. So on you can make it 3/6, 4/8 and on and on and on. This is what we want to use.

We have 1/4 and 5/6. Well, you could try increasing both one by one until you get the same denominator, but a way to do it in one step is to multiply one by the other's denominator. so 1/4 = (1*6)/(4*6) = 6/24 and similarly 5/6 = (5*4)/(6*4) = 20/24. So now we are adding 6/24 + 20/24 = 26/24 or 1 2/24 = 1 1/12. ANyway, now you are adding

5 1/4 + 5/6 = 5 + 1 1/12 = 6 1/12. There is a different way to add fractions, but it's a little more involved and this way always works so that's what I use.

Answer 2

Answer:
`6(1)/(12)\ gallons`

Explanation:

We can make the conversion from mixed numbers to improper fractions:

• Multiply the whole number part by the denominator of the fraction.
• Add the numerator of the fraction and the product obtained (This sum will be the new numerator).
• The denominator is the same.

Then:

`2(1)/(4)=((2*4)+1)/(4)=(9)/(4)\\\\3(5)/(6)=((6*3)+5)/(6)=(23)/(6)`

We need to add the fractions in order to calculate the amount of paint Darren bought. Since the denominators are differente, we must find the Least Common Denominator (LCD):

`4=2*2=2^2\\\\6=2*3\\\\\\LCD=2^2*3=12`

Then:

`(9)/(4)+(23)/(6)=(27+46)/(12)=(73)/(12)\ gallons`

To convert this improper fraction to a mixed number:

• When you divide 73 by 12 you get a quotient of 6. This will be the whole number.
• The remainder obtained is 1. This will be the numerator of the fraction.
• The denominator does not change.

Then:

`(73)/(12)\ gallons=6(1)/(12)\ gallons`