Subtracting Fractions Get ready to become an expert at subtracting fractions & mixed numbers!

Subtracting with the same denominator. Subtracting fractions that have the same denominator is simple. You subtract the numerators and write the difference over the common denominator. If your answer is an improper fraction, re-write it as a mixed number.

Example: 5 6 1 6 - 2 3 4 6 = Solve on your own. Click for the answer!

Subtracting fractions with different denominators. Subtracting fractions with different denominators is impossible. In order for fractions to be subtracted from one another, they must have the same number of parts. The denominator represents the number of parts. Therefore, you must find a common denominator.

Why? You have a 5/6 of a pizza left. You eat 1/4 of the pizza that is remaining. How much of leftover pizza remains now? A common denominator is necessary so that each piece of pizza is the same size and can be added with the others. What is a common denominator for 6 and 4? - = 12

To subtract fractions: What are the steps? To subtract fractions: Find a common denominator if there isn’t one already. Convert each of your fractions into an equivalent fraction using the common denominator. Subtract the numerators. Write the difference as the numerator in your answer. The denominator will be your common denominator. If your answer is an improper fraction, convert to a mixed number. Simplify if necessary.

What is the least common denominator? 3 5 4 7 Click for the answer! - 35

How do you re-write the fractions using the common denominator? 3 5 x 7 21 35 Click for the answer! = x 7 4 7 35 20 x 5 = - x 5

Solve: Rewrite using the least common denominator, then solve on your own. Click for the answer! 3 5 4 7 - 21 35 20 35 1 35 - =

What is the least common denominator? 7 8 1 5 Click for the answer! - 40

Solve: Rewrite using the least common denominator, then solve on your own. Click for the answer! 7 8 1 5 - 35 40 8 40 27 40 - =

Solve: Rewrite using the least common denominator, then solve on your own. Click for the answer! 5 6 2 3 - 5 6 4 6 1 6 - =

When you subtract multi-digit numbers, do you subtract from: Right to left? Left to right?

Right to Left! For example: 485 123 You subtract 5-3 first! -

When we subtract mixed numbers, we do the same thing!

Subtract the fractions before the whole numbers Right to Left! Subtract the fractions before the whole numbers For example: 4 ¾ 1 ¼ 3 You subtract ¾ - ¼ first! - 2 4

But Why?

Click to move through the problem visually. We subtract the fractions before the whole numbers in order to determine if we need to borrow from the whole number. 2 3 1 4 Example: Click to move through the problem visually. 4 2 - 2 3 8 12 = 1 4 3 12 - - 5 12

We subtract the fractions before the whole numbers in order to determine if we need to borrow from the whole number. 2 3 1 4 Example: Click to move through the problem visually. 4 2 - You already figured out that - is 5 12 Next, subtract the whole numbers 4 – 2 = 2 2 3 1 4 5 12 5 12 5 12 2 + = 2

To subtract mixed numbers: What are the steps? To subtract mixed numbers: Find a common denominator if there isn’t one already. Convert each of your fractions into an equivalent fraction using the common denominator. Subtract the numerators. If you cannot subtract the numerators because the first numerator is smaller than the second, you need to borrow a whole from the first whole number and add it onto the first fraction. Write the difference as the numerator in your answer. The denominator will be your common denominator. If your answer is an improper fraction, convert to a mixed number. Simplify if necessary. Subtract the whole numbers. Combine with the fraction difference if necessary.

Solve: Rewrite using the least common denominator, then solve on your own. Click for the answer! 4 5 1 2 4 - 2 4 – 2 = 2 8 10 5 10 3 10 - = 3 10 3 10 2 + = 2

Solve: Rewrite using the least common denominator, then solve on your own. Click for the answer! 3 4 1 3 6 - 3 6 - 3 = 3 9 12 4 12 5 12 - = 5 12 5 12 3 + = 3

Solve: Rewrite using the least common denominator, then solve on your own. Click for the answer! 3 10 1 4 7 - 1 7 – 1 = 6 6 20 5 20 1 20 - = 1 20 1 20 6 + = 6

What If?

We can’t subtract 14 from 12… What if you re-write your fractions using a common denominator, and the first fraction is larger than the second? 4 7 x 3 12 21 2 = x 3 We can’t subtract 14 from 12… So now what? 2 3 21 14 x 7 1 = - x 7

Click to see the steps you take to solve a problem like this! You need to “borrow” a whole from the whole number part of the first mixed number. 1. Borrow 1 from the 2 in the form of a fraction. 4 7 x 3 21 12 21 33 21 1 2. To make it easy on you, write the fraction as the common denominator over the common denominator. 2 = = + x 3 3. Add your borrowed whole onto the fraction. 4. Now you can subtract! 2 3 21 14 x 7 5. Simplify if necessary. - 1 = x 7 19 21 Click to see the steps you take to solve a problem like this!

Solve on your own, then click to check your answer. You Try! Solve on your own, then click to check your answer. 1. Rewrite with a common denominator 1 2 x 2 4 2 4 6 4 2. Borrow 1 from the 4 in the form of a fraction. 3 5 = = + 3. To make it easy on you, write the fraction as the common denominator over the common denominator. x 2 4. Add your borrowed whole onto the fraction. 3 4 4 3 5. Now you can subtract! = - 2 3 4