Adding and Subtracting Fractions

Question 1:

First of all, we have to look at the denominators and see what 4 and 8 both go into. We can do this by multiplying 4 by 8 which is 32. Maybe some people would choose to use 32 as the next denominator, but using 8 is much easier since 4 and 8 both go into 8.

Then, we make another set of fractions, but with the denominator of 8. First we look at the denominators. How many times does 4 have to be counted to go into 8? 2. How many times does 8 have to be counted to go to 8? 1.

What we do to the bottom, we do to the top. So since 4 was multiplied by 2, then the numerator (3) has to be multiplied by 2. And since 8 was multiplied by 1, then the numerator (1) has to be multiplied by one. 3 x 2? 6. 1 x 1? 1.

The last thing we have to do is subtract the numerators. So 6 take away one is 5. The denominator stays the same, so the overall answer is 5 over 8!

Question 2:

First of all, we have to look at the denominators and see what 2 and 7 both go into. So we multiply both of them to see what number they both fit in. 2 multiplied by 7 results as 14.

Then we make another set of fractions but with the denominator of 14. We look at the denominators first. What does 2 have to be multiplied by to get to 14? 7. What does 7 have to be multiplied by to get to 14? 2.

What we have to do to the bottom, we have to do to the top! So since 2 was multiplied by 7, the numerator (1) has to be multiplied by 7. And since 7 was multiplied by 2, the numerator (2) has to be multiplied by 2.. too!

So now we take away the old fractions, and use the new one! All we have to do is add the numerators together. 7 + 4 results as 11, and the denominator stays the same.

Question 3:

Now we are dealing with mixed fractions. First, we put the whole numbers 20 and 4 out of the way.

Now it looks like a normal subtraction fraction question. Now we have to find out what 3 and 10 both go into. So 3 X 10 = 30.

Then we make a set a fractions that have a denominator of 30. First, we look at the denominators. How many times does 3 have to be multiplied by to get to 30? 10. How many times does 10 have to be multiplied to get to 30?3.

Now, we have to multiply the top fraction numerators by the number that their denominators were multiplied by. So 1 multiplied by 10 is 10, and 3 multiplied by 3 is 9.

Then we take away the old fractions and use the new ones. We have to subtract numerator 9 from numerator 10.The answer to that is 1. And of course, we keep the denominator the same.

Then we bring back the whole numbers and we just use simple subtraction.

Now, we just combine the whole number 16 and the fraction 1 over 30. So the answer to question 3 is 16 and 1 thirtieths!

Multiplying Fractions

Question 1:

Now we are dealing with multiplying fractions. It's not that hard once you get it.

To answer a multiplying fraction question, all you have to do is multiply the numerator to the other, and the same goes to the denominators.

So 3 multiplied by 2 makes 6. 4 multiplied by 5 is 20. So that makes 6 over 20. Then we just simplify by finding a number 6 and 20 both go into, like 2. So 6 divided by 2 is 3, and 20 divided by 2 is 10.

Question 2:

Now we are going to start multiplying mixed fractions.

Since these fractions are mixed, we can turn them into improper fractions. We can do this by going denominator multiplied by whole number plus numerator.

Now with the improper fractions, the multiplication question looks like this.

Then we multiply 5 by 11, and 2 by 10. Which results as 55 twentieths.

We then simplify the improper fraction, then turn it back into a mixed fraction.

So then the answer to this mixed fraction multiplication question is 2 and 7 fourths!

Dividing Fractions

Question 1:

Now it's onto dividing fractions!

To divide fractions, we can use a ratio table to help us. The paint cans and the room labels are just there to help us.. Like we have 4 fifths of a paint can the filled up 2 sevenths of the room. What we're supposed to do in this ratio table is to make 2 sevenths into a whole number. So what we do first is divide the numerator by 2, so that makes 1 seventh. Then we multiply one by 7, which makes 7 sevenths, a whole number. If we did those on one side, we have to do it to the other. So divide the numerator by 2, so that makes 2 fifths.Then we multiply 2 by 7, which makes 14 fifths.

Then we change the 14 fifths into a mixed fraction. How many 5's are in 14? 2. So 2 becomes the whole number. How much do you have to add to 2 groups of 5 to get to 14? 4. So 4 becomes the numerator. The denominator stays the same as 5.

So the answer to this fraction division question is 2 and 4 fifths!

Question 2:

Here is a fraction division question with a mixed number and a whole number.

Then we turn 8 and 1 third into an improper fraction. We make the whole number 7 a fraction by making it a numerator and making the denominator 1.

So this is what the division question looks like now.

To help us with this question, we'll use something that's a fraction over fraction. 25 fifths is the numerator, and 7 over 1 is the denominator. To make 7 over 1 completely whole, we'll use something called a reciprocal. We multiply 7 over 1 by 1 over 7 which results as 1. Then we multiply 25 thirds by 1 over 7 which equals 25 over 21.

We then turn 25 over 21 into an improper fraction. 21 goes into 25 once, and we have to add 4 more to get to 25.

So the answer to this division question is 1 and 4 twenty-fifths!

Word Problem #2 :

Word Problem #3 :

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