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Adding and Subtracting Fractions

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Adding and subtracting fractions is just as easy. It's the same idea once you have the same denominator, you can just add or subtract the numerators, keeping the denominator the same.

Adding Fractions

Example-1

Lissa has
2
8
of a pack of Chocolate and Jaycee has
4
8
of the same pack. How much of the pack do they have altogether?

Since the denominators are the same, we can just add 2 + 4 to get 6.

So,
2
8
+
4
8
=
6
8
The kids have
6
8
of the pack altogether.

Careful don't add the denominators by accident!

A quick way to check yourself is to make sure the denominator of your answer is the same as the denominators of the two fractions you add or subtract.

Subtracting Fractions

Subtracting fractions is just like adding them.

Example-2

 
9
6
-
4
6
=
???

We have the same denominator, so we can subtract 9 - 4 to get 5.

 
9
6
-
4
6
=
5
6
 
The answer
5
6

Remember, when the denominators aren't the same, we just find the least common denominator following the steps we learned earlier.

Example-3

Kenny painted
1
3
of a fence on Monday and
2
5
of the same fence on Tuesday. On which day did he paint more of the fence? How much of the fence did he paint altogether?

This question is asking us to compare and then add two fractions.

List out multiples and look for the first one that's the same for both numbers.

3: 3, 6, 9, 12, 15

5: 5, 10, 15, 20

Then convert each fraction with same denominator.

 
1 x 5
3 x 5
=
5
15
 
 
 
2 x 3
5 x 3
=
6
15
 
So, Kenny painted
5
15
of the fence on Monday and
6
15
on Tuesday.

Now, to compare the fractions, we just compare 5 and 6.

6 is bigger.

So, Kenny painted more of the fence on Tuesday.

 

Finally, we add the two fractions to see how much he painted on both days.

5 + 6 = 11, and remember to keep the denominator the same.

 
5
15
+
6
16
=
11
15
 
Hence, Kenny painted
11
15
of the fence over the two days!
Summary

Intro to Fractions

  • Fractions represent parts of whole numbers
  • Numerator (number on top) represents how many parts of the whole you have
  • Denominator (number on the bottom) represents how many equal parts the whole is divided into.
  • Least Common Denominator: To perform some operations on fractions, you'll need to make sure their denominator is the same. Follow these three steps:
  • List out the multiples of each denominator
  • Find the smallest multiple the two denominators have in common; this is the least common denominator.
  • Convert each fraction so it has this denominator by multiplying the numerator and the denominator by the same number.

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