How to subtract mixed fractions?

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David Shabazi Profile
David Shabazi answered

Convert them into improper fraction form, make sure both fractions have the same common denominators, then subtract the numerator and put that number over the denominator, and that will be your answer. For example:

(3 + 3/7) - (2 + 6/11) = ?

Step 1: Convert both mixed fractions into improper fractions. Let's say that 3 + 3/7 is a seperate equation and we needed to add these two numbers together. We would then have to make "3" have a denominator of 7 because when you are adding whole numbers to fractions, you must make the whole number have the same denominator as the fraction, and then add the numerators.

So 3 is the same thing as 3/1, because anything with a denominator of 1 simply means you are dividing that number by 1, which will give the same number. 3 divided by 1 is 3. So now that we have 3/1, we need to think: "What number to we need to multiply to the denominator in order to make it 7?" Well, 1 multiplied by 7 gives us 7. So we need to multiply 7 to the denominator in order to make it have common denominators with the fraction (3/7). But, as a rule of fractions, you have to multiply the numerator by the same number that you're multiplying the denominator with. So you do the following:

(3 * 7)/(1 * 7) = 21/7

I multiplied 7 to both the denominator and numerator and got 21/7 as my answer. Now we have both numbers in fraction form, and we can add them together.

(21/7) + (3/7) = 24/7

Do this same exact process for the second equation, (2 + 6/11), and you will get 28/11.

Now we have 24/7 - 28/11. We have to make the denominators of both fractions equal. So we need to think of a number that has both 7 and 11 as factors. 77 would be that number. So now we need to think, "What number do I multiply to the denominator in order to give 77?" For the first one, you multiply 11, and the second one, you multiply 7. So here:

(24 * 11)/(7 * 11) - (28 * 7)/(11 * 7) = 264/77 - 196/77 = 68/77 <-- This would be your answer.

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