Adding and subtracting fractions
Whenever a fraction is added or subtracted, all the fractions being added or subtracted must have the same denominators. This is called Lowest common denominator.
To find the LCD of two fractions e.g
2/3 + 3/5. The first step is to multiply the two denominators. 5*3 = 15. From this, we know that the L.C.D cannot be higher than 15, but it could be lower. How do you check this???? By finding the multiples of both denominators
3= 3, 6, 9, 12, 15
5= 5, 10, 15
From this, we know that their lowest common multiples that both numbers have is 15. Therefore 15 in the L.C.D.
In this case, we change the denominator of both fractions to 15.
Note: Whatever you do to the denominator, you do to the numerator too. We know the L.C.D is 15
2/3 *5 + 3/5 * 3 What numbers must be multiplied to their denominators to get 15?
The first fraction is 5, and the second is 3. Therefore we multiply both the denominators and numerators with these numbers.
The result is 10/15 and 9/15. Now we can easily add up the fractions,by adding the two numerators,divided by the L.C.D.
10/15 + 9/15 = 19/15 or 14/5 (Mixed fractions, which means whole number is bigger than 1).
Note: when the fractions are changed, the values remain the same, only the numbers change so that both fractions have the same denominators, because we still multiply the numerator and the denominator by the same value.
2/3 = 10/5 *(5) and 3/5 = 9/15 * (3)
To find the LCD of two fractions e.g
2/3 + 3/5. The first step is to multiply the two denominators. 5*3 = 15. From this, we know that the L.C.D cannot be higher than 15, but it could be lower. How do you check this???? By finding the multiples of both denominators
3= 3, 6, 9, 12, 15
5= 5, 10, 15
From this, we know that their lowest common multiples that both numbers have is 15. Therefore 15 in the L.C.D.
In this case, we change the denominator of both fractions to 15.
Note: Whatever you do to the denominator, you do to the numerator too. We know the L.C.D is 15
2/3 *5 + 3/5 * 3 What numbers must be multiplied to their denominators to get 15?
The first fraction is 5, and the second is 3. Therefore we multiply both the denominators and numerators with these numbers.
The result is 10/15 and 9/15. Now we can easily add up the fractions,by adding the two numerators,divided by the L.C.D.
10/15 + 9/15 = 19/15 or 14/5 (Mixed fractions, which means whole number is bigger than 1).
Note: when the fractions are changed, the values remain the same, only the numbers change so that both fractions have the same denominators, because we still multiply the numerator and the denominator by the same value.
2/3 = 10/5 *(5) and 3/5 = 9/15 * (3)
Examples
Start by inserting the correct number
3/4 = (9)/12 *3 2/8 = 6/(24) *3
4/5 = (12)/15 *3 3/4 = 15/ (20) *5
1/3 = (4)/12 *4 2/7 = 4/ ( 14) *2
Adding and Subtracting Fractions
3/10 + 5/8 3/4 - 2/5
7/10 + 2/10 7/8 - 6/8
1/3 + 3/10 2/4 - 1/3
1) 3/10 + 5/8. Find LCD 10 * 8 = 80. But since its the lowest multiple, 40 is a multiple of both 8 and 5
Multiples of 5= 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
8= 8, 16, 24, 32, 40, 48, 56, 64
Multiply both the numerator and denominator of 3/10 by (4) and 5/8 by (5)
12/40 + 25/40 = 37/40
2) 7/10 + 2/10 ( L.C.D = 10, because they already share the same denominator)
7/10 + 2/10 = 9/10
3) 1/3 + 3/10. LCD= 10* 3 = 30.
Multiply the numerator and denominator of 1/3 by(10) and 3/10 by (3)
10/30 + 9/30 = 19/30
Subtraction follows the same process as the addition, the only difference is that you subtract the numerator after finding the L.C.D
4) 3/4 - 2/5. L.C.D (5*4 = 20)
Multiply both the numerator and denominator of 3/4 by (5) and 2/5 by (4)
10/20 + 8/20 = 18/20 or 9/10 when simplified in lowest term.
5) 7/8 - 6/8 (L.C.D = 8)
7/8 - 6/8 = 1/8
6) 2/4-1/3 L.C.D (4*3 = 12)
Multiply both the numerator and denominator of 2/4 by (3) and 1/3 by (4)
6/12 - 4/12 = 2/12 or 1/6 when simplified in lowest term
3/4 = (9)/12 *3 2/8 = 6/(24) *3
4/5 = (12)/15 *3 3/4 = 15/ (20) *5
1/3 = (4)/12 *4 2/7 = 4/ ( 14) *2
Adding and Subtracting Fractions
3/10 + 5/8 3/4 - 2/5
7/10 + 2/10 7/8 - 6/8
1/3 + 3/10 2/4 - 1/3
1) 3/10 + 5/8. Find LCD 10 * 8 = 80. But since its the lowest multiple, 40 is a multiple of both 8 and 5
Multiples of 5= 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
8= 8, 16, 24, 32, 40, 48, 56, 64
Multiply both the numerator and denominator of 3/10 by (4) and 5/8 by (5)
12/40 + 25/40 = 37/40
2) 7/10 + 2/10 ( L.C.D = 10, because they already share the same denominator)
7/10 + 2/10 = 9/10
3) 1/3 + 3/10. LCD= 10* 3 = 30.
Multiply the numerator and denominator of 1/3 by(10) and 3/10 by (3)
10/30 + 9/30 = 19/30
Subtraction follows the same process as the addition, the only difference is that you subtract the numerator after finding the L.C.D
4) 3/4 - 2/5. L.C.D (5*4 = 20)
Multiply both the numerator and denominator of 3/4 by (5) and 2/5 by (4)
10/20 + 8/20 = 18/20 or 9/10 when simplified in lowest term.
5) 7/8 - 6/8 (L.C.D = 8)
7/8 - 6/8 = 1/8
6) 2/4-1/3 L.C.D (4*3 = 12)
Multiply both the numerator and denominator of 2/4 by (3) and 1/3 by (4)
6/12 - 4/12 = 2/12 or 1/6 when simplified in lowest term
Exercise
1) 1/2 = ( )/4 = ( )/6 = ( )/8 = ( )/ 10 = ( )/12
2) 1/5 = ( )/10 = ( )/15 = ( )/20 = ( )/25 = ( )/30
3) 2/4 = 15/ ( )
4) 1/3 = 3/( ) = 9/( )= ( )/81
5) 15/6 = ( )/2
ADDING AND SUBTRACTING
1) 1/6 + 4/6
2) 2/10 + 5/10
3) 7/10 + 3/5
4) 11/100- 6/100
5) 9/10- 1/2
6) 1/2 - 7/25
7) 3 - 1/4
8) 3/4 + 1/8 - 1/6
9) 1/3 - 5/6 + 1/6
10) 4/9 - 6/7
2) 1/5 = ( )/10 = ( )/15 = ( )/20 = ( )/25 = ( )/30
3) 2/4 = 15/ ( )
4) 1/3 = 3/( ) = 9/( )= ( )/81
5) 15/6 = ( )/2
ADDING AND SUBTRACTING
1) 1/6 + 4/6
2) 2/10 + 5/10
3) 7/10 + 3/5
4) 11/100- 6/100
5) 9/10- 1/2
6) 1/2 - 7/25
7) 3 - 1/4
8) 3/4 + 1/8 - 1/6
9) 1/3 - 5/6 + 1/6
10) 4/9 - 6/7