FRACTIONS
Adding Fractions:
When you are adding fractions, you will need to find a common denominator. Once both fractions have the same denominator, simply add the numerators and LEAVE THE COMMON DENOMINATOR as is.
Ex: 1 3
2 + 5 = ?
Cd = 10 therefore 5 6 11
10 + 10 = 10
Subtracting Fractions:
When you are subtracting fractions, like above, you will need a common denominator. The only difference is that you will be SUBTRACTING the numerators. Again, leaving the COMMON denominator as is.
Ex: 3 1
4 - 3 = ?
Cd = 12 therefore 9 4 5
12 - 12 = 12
Multiplying Fractions:
When multiplying fractions, all you need to do is multiply across. à (both the numerators (tops) and the denominators (bottoms) must be multiplied)
Ex: 4 3 12
7 X 4 = 28
Dividing Fractions:
When dividing fractions, all you need to do is FLIP the 2nd fraction and change the divison (÷) to a multiplication (X). Once those two changes have been made, simply multiply across like we did above.
Ex: 5 2
7 ÷ 3 *Flip and change from (÷) to( X)
5 3 15
7 X 2 = 14
Improper Vs. Mixed Fractions:
15
14 = Divide the numerator BY the denominator…. In this case, 14 goes into 15, ONCE. How much is left? 15-14 = 1 *and the denominator (the bottom number NEVER changes)
= 1 1/4
Or the reverse…. Example: 2 3/8
Multiply 8 by 2… and add 3…. *keep the denominator the same….
= 19
8
Reducing Fractions:
When you have only one fraction in an equation, simply multiply the entire equation by the denominator. Reminder: When you multiply a fraction by its denominator, you do NOT multiply the numerator, it stays as is.
Ex: 1x + 2y = 5 (multiply the entire equation by 3)
3
You are left with the following: 1x + 6y = 15 which is the same as: x + 6y = 15
When you have multiple fractions in an equation, you will need a common denominator. Once all the denominators are equal, you can remove them from the equation. (Reminder, any number in a fraction, over 1, is itself.)
Ex: 1x + 3y = 4
3 4 1
Cd: 12 (which is the lowest number 3, 4 and 1 all divide into equally)
Therefore: 4x + 9y = 48
12 12 12
Again, now that all the denominators are the same, you can now remove them.
4x + 9y = 48
Adding Fractions:
When you are adding fractions, you will need to find a common denominator. Once both fractions have the same denominator, simply add the numerators and LEAVE THE COMMON DENOMINATOR as is.
Ex: 1 3
2 + 5 = ?
Cd = 10 therefore 5 6 11
10 + 10 = 10
Subtracting Fractions:
When you are subtracting fractions, like above, you will need a common denominator. The only difference is that you will be SUBTRACTING the numerators. Again, leaving the COMMON denominator as is.
Ex: 3 1
4 - 3 = ?
Cd = 12 therefore 9 4 5
12 - 12 = 12
Multiplying Fractions:
When multiplying fractions, all you need to do is multiply across. à (both the numerators (tops) and the denominators (bottoms) must be multiplied)
Ex: 4 3 12
7 X 4 = 28
Dividing Fractions:
When dividing fractions, all you need to do is FLIP the 2nd fraction and change the divison (÷) to a multiplication (X). Once those two changes have been made, simply multiply across like we did above.
Ex: 5 2
7 ÷ 3 *Flip and change from (÷) to( X)
5 3 15
7 X 2 = 14
Improper Vs. Mixed Fractions:
15
14 = Divide the numerator BY the denominator…. In this case, 14 goes into 15, ONCE. How much is left? 15-14 = 1 *and the denominator (the bottom number NEVER changes)
= 1 1/4
Or the reverse…. Example: 2 3/8
Multiply 8 by 2… and add 3…. *keep the denominator the same….
= 19
8
Reducing Fractions:
When you have only one fraction in an equation, simply multiply the entire equation by the denominator. Reminder: When you multiply a fraction by its denominator, you do NOT multiply the numerator, it stays as is.
Ex: 1x + 2y = 5 (multiply the entire equation by 3)
3
You are left with the following: 1x + 6y = 15 which is the same as: x + 6y = 15
When you have multiple fractions in an equation, you will need a common denominator. Once all the denominators are equal, you can remove them from the equation. (Reminder, any number in a fraction, over 1, is itself.)
Ex: 1x + 3y = 4
3 4 1
Cd: 12 (which is the lowest number 3, 4 and 1 all divide into equally)
Therefore: 4x + 9y = 48
12 12 12
Again, now that all the denominators are the same, you can now remove them.
4x + 9y = 48