816 Math Blog

Hey Everyone! Last fraction post here and I'm gonna show you how to add, subtract, multiply and divide fractions! Let's start with adding!

Here's an example: 2/4 + 1/4
Since the denominators are the same, all you have to do is add the numerators together.
2 + 1 is 3 so... 3/4!

What if the denominators weren't the same?? :O! Well it's still easy! :) Just MAKE the denominators the same!
For example: 2/4 + 2/8
Now, how do you make the denominators of 4 and 8 the same? Divide 8 by 2! 8 divided by 2 is 4, which is the same as the other denominator. And whatever you do to one side, you do to the other. Now you have to divide the numerator by 2 'cuz you did it to the bottom. The numerator is 2 so 2 divided by 2 is 1. The fraction is 1/4!
2/4 + 1/4 = 3/4 ...hard? I think not!

Subtracting Fractions isn't very hard neither. I'll give you one example with the same denominators and another with different denominators.
Example 1: 4/10 - 2/10
Just subtract the numerators since denominators are the same. 4 - 2 = 2. 2/10 is the answer.

Example 2: 4/10 - 6/30
The denominators are 10 and 30. Divide 30 by 3 to equal 10, an equal denominator to 10! Whatever you do down there, you do up there, too. Divide 6 by 3 to get 2. The equation is 4/10 - 2/10 = 2/10

Multiplying Fractions gets a bit complicated, but not if you know what you're doing.
Example 1: 2/3 x 4/5
The first step is to multiply the numerators. 2 x 4 equals 8. Then multiply the denominators. 3 x 5 equals 15. Your fraction is 8/15! EEEEAASSYYY!!....if you know how to do it :)

Example 2: 2 1/2 x 1/2
Woah! That's hard, eh? NOT! Do you know what an improper fraction is? It's a fraction that has a greater numerator than denominator, meaning its total value is more than 1 whole. All you need to do is convert 2 1/2 into an improper fraction, then use the 2 steps from example 1! To convert a mixed number into an improper fraction, multiply your wholes (2) by your denominator (2) and then add it to your numerator (1). 2 x 2 = 4 + 1 =5. Then use the same denominator. 5/2 is the fraction so you're multiplying 5/2 by 1/2. Multiply Numerators (5 x 1 = 5) and denominators (2 x 2 = 4) to get the fraction 5/4. That's your answer!

Everything is easy so far, right? Well, how do you think dividing will be? EASY! I'll teach you on the way!
Example 1: 9/10 ÷ 3/4

The reciprocal is just a way to find the answer easier. The question is 9/10 ÷ 3/4. Take 3/4 and multiply it by its "opposite". 3/4 x 4/3 is 1 whole. Whatever you do down there, you do up there. Now you multiply 9/10 by 4/3 because you did it to the bottom fraction. Your answer is shown above. Just simplify the improper fraction into a mixed number.

Example 2: Mixed Numbers!
3 1/2 ÷ 7
First, convert your mixed number!
Whole x denominator + numerator...
3 x 2 = 6 + 1 = 7
7/2 is your fraction.
You also have to convert the 7. Let's use the denominator of 2! 7 x 2 is 14. 14/2 is 7 wholes!
7/2 ÷ 14/2 ...use the reciprocal now!


Dividing fractions isn't so bad...

Now let's get to word problems :)

#1: It takes 2 1/4 scoops of flour to make one cake. How many cakes do 15 scoops make?
Let's draw pictures!



As you can see by the indicated colors, 15 scoops of flour can make 6 cakes and 2/3 of a cake.

#2:
One day in Winnipeg with 10 1/2 hours of daylight, it was sunny for 1/3 of that time. For how many hours was it sunny that day?
Convert 10 1/2 into improper to make it easier...
10 x denominator (2) + numerator (1).
10 x 2 = 20 + 1 = 21
21/2 is equal to 10 1/2.
We're trying to find 1/3, so just divide it by 3 if you can, and take 1 piece because you have 1 thirds.

3 1/2 hours of that sunlight were sunny on that day in Winnipeg, out of 10 1/2 hours.

Oh! Before I go, remember to always simplify your fractions if possible, and to always have simple sentence answers to any word problem! Cya guys later!!