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.
Answer: [tex]6\frac{1}{12}\ gallons[/tex]
Step-by-step explanation:
We can make the conversion from mixed numbers to improper fractions:
Then:
[tex]2\frac{1}{4}=\frac{(2*4)+1}{4}=\frac{9}{4}\\\\3\frac{5}{6}=\frac{(6*3)+5}{6}=\frac{23}{6}[/tex]
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):
[tex]4=2*2=2^2\\\\6=2*3\\\\\\LCD=2^2*3=12[/tex]
Then:
[tex]\frac{9}{4}+\frac{23}{6}=\frac{27+46}{12}=\frac{73}{12}\ gallons[/tex]
To convert this improper fraction to a mixed number:
Then:
[tex]\frac{73}{12}\ gallons=6\frac{1}{12}\ gallons[/tex]
