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

Answer: $6\frac{1}{12}\ gallons$

Step-by-step 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:

$2\frac{1}{4}=\frac{(2*4)+1}{4}=\frac{9}{4}\\\\3\frac{5}{6}=\frac{(6*3)+5}{6}=\frac{23}{6}$

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:

$\frac{9}{4}+\frac{23}{6}=\frac{27+46}{12}=\frac{73}{12}\ gallons$

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:

$\frac{73}{12}\ gallons=6\frac{1}{12}\ gallons$

Answer 2

Answer:

Step-by-step 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.