Adding and Subtracting Fractions

Video 1

Video 2

Video 3

Adding and learning how to make the denominators the same

Adding and subtracting fractions is not hard at all, as shown in the videos. You have to make sure that the denominator is the same in each fraction, for you to add or subtract the fractions.
If they are not the same, then we must manipulate the fraction so that the fractions that need to be added or subtracted attain the same denominator. How do find the value of the denominator?
Firstly, you must attain a common multiple between the two denominators, this COMMON MULTIPLE WILL BE THE NEW DENOMINATOR THAT BOTH FRACTIONS WILL HAVE.
To make the denominators of both fractions equal the COMMON MULTIPLE, what we have to do is multiply EACH fraction by 1 so they achieve the same denominator. Once we attain two fractions with the same denominator, we can add or subtract the fractions.
You might be thinking HOW CAN WE MULTIPLY EACH FRACTION BY 1 TO GET THE SAME DENOMINATORS? ISN'T 1 MULTIPLIED BY ANY NUMBER, JUST GOING TO GIVE THE SAME NUMBER?
The answer to both of these questions is YES, however you will understand what we mean below.

Video 1 (Explanation of Question 2)


Question: 1/5 + 3/4
We need to find a common multiple between 5 and 4, this common multiple will be our new denominator, a common multiple between 5 and 4 is 20.
Lets focus on the first fraction: 1/5
To make the denominator equal 20 we must multiply the 5 by 4. Whatever we do to to one side of the fraction, we must do to the other.
So
(1x4)/(5x4) = 4/20
WE HAVE successfully made the denominator equal 20. We have not changed the value of the fraction, what we have really done is multiply 1/5 with 4/4.
1/5 x 4/4 = 1/5 x 1 = 1/5
4/4 = 4 divided by 4 = 1
So by multiplying the first fraction (1/5) with 4/4 we have not changed the value of the fraction, however have changed the denominator to 20.
Lets now focus on the second fraction: 3/4
To make the denominator equal 20 we must multiply 4 by 5. Whatever we do to one side of the fraction, we must do the other.
So
(3x5)/(4x5) = 15/20
WE HAVE successfully made the denominator equal 20. We have not changed the value of the fraction, what we have really done is multiply 3/4 with 5/5.
3/4 x 5/5 = 3/4 x 1 = 3/4
So by multiplying the second fraction (3/4) with 5/5 we have not changed the value of the fraction and changed the denominator to 20.
So now we can write
1/5 + 3/4 = 4/20 + 15/20 = 19/20
So now you should understand how we can manipulate fractions to attain the same denominator, so they can be added or subtracted.

Subtracting Fractions


If we were to find the value of 3/4 - 1/5,
Then we would make the denominators the same, as explained above.
3/4 - 1/5 = 15/20 - 4/20 = 11/20

Video 2 Explanation


Question 1: 4/7 - 1/7
As the denominator of both fractions is the same, we can simply perform the subtraction, as shown below.
4/7 - 1/7 = (4-1)/7 = 3/7
Question 2: 7/8 - 2/9
The denominators of the fraction are not the same. First lets find a common multiple between 8 and 9. One common multiple is 72, thus we need to make the denominators of both fractions equal 72.
To make the denominator of the first fraction equal 72, we must multiply the 8 with 9. Whatever we do to the bottom part of the fraction, we must do to the top part of the fraction. So we must multiply 7 with 9 as well, as shown below.
(7 x 9)/(8 x 9) = 7/8 x 9/9 = 63/72
To make the denominator of the second fraction equal 72, we must multiply the 9 with 8. Whatever we do to the bottom part of the fraction, we must do to the top part of the fraction. So we must multiply the 2 with 8 as well, as show below.
(2 x 8)/(9 x 8) = 2/9 x 8/8 = 16/72
So
7/8 - 2/9 = 63/72 - 16/72 = (63-16)/72 = 47/72

Improper Fractions (Adding and Subtraction)


An improper fraction is where the numerator (the top number of a fraction) is bigger than the denominator (the bottom number of the fraction). Examples of improper fractions are 15/6, 23/18, and 34/7.
Is 2/3 is an improper fraction?
NO. Why? 3 which is the denominator is bigger than the numerator so this is NOT an improper fraction.
Adding and subtracting improper fractions is DONE IN THE EXACT SAME WAY AS EXPLAINED ABOVE. You just have to make sure the improper fractions have the common denominator.

Video 3 Explanation


Question 1: Find the value of 7/5 + 5/2, as a decimal.
The denominator of the first fraction is 5 and the denominator of the second fraction is 2. Thus we need to find a common multiple between 5 and 2, one common multiple is 10. Thus, we need to make the denominator of both fractions equal 10.
To make the denominator of the first fraction equal 10, we must multiply the 5 with 2. Whatever we do to the bottom part of the fraction we must do to the top part of the fraction. So we must multiply 7 with 2 as well, as shown below.
(7 x 2)/(5 x 2) = 7/5 x 2/2 = 14/10
To make the denominator of the second fraction equal 10, we must multiply the 2 with 5. Whatever we do to the bottom part of the fraction we must do to the top part of the fraction. So we must multiply 5 with 5 as well, as shown below.
(5 x 5)/(2 x 5) = 5/2 x 5/5 = 25/10
So
7/5 + 5/2 = 14/10 + 25/10 = (25 + 14)/10 = 39/10 = 3.9
Question 2: Find the value of 6/4 - 8/3, leave the value as an improper fraction.
The denominator of the first fraction is 4 and the denominator of the second fraction is 3. Thus we need to find a common multiple between 4 and 3, one common multiple is 12. Thus, we need to make the denominator of both fractions equal 12.
To make the denominator of the first fraction equal 12, we must multiply the 4 with 3. Whatever we do to the bottom part of the fraction we must do to the top part of the fraction. So we must multiply 6 with 3 as well, as shown below.
(6 x 3)/(4 x 3) = 6/4 x 3/3 = 18/12
To make the denominator of the second fraction equal 12, we must multiply the 3 with 4. Whatever we do to the bottom part of the fraction we must do to the top part of the fraction. So we must multiply the 8 with 4 as well, as shown below.
(8 x 4)/(3 x 4) = 8/3 x 4/4 = 32/12
So
6/4 - 8/3 = 18/12 - 32/12 = (18-32)/12 = -14/12 = -7/6 (Simplified)