Exercise 31
Adding Fractions
At the end of this exercise you will:
• Learn about vulgar fractions
• Learn about Improper fractions
• Be able to add two fractions together
• Be able to add three fractions together
Answers on pages 5 and 6, of this exercise.
Page 1 of 6
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Adding Fractions
Fractions are just like decimals, they are parts of a whole number and they look like
this ⅝.
There are two parts to every fraction.
There’s the
, which is the top bit of the fraction
And there’s the
, which is the bit on the bottom, it shows how
many bits are needed to make a whole one, i.e. ⅝, the 8, means that if you have 8
bits, then that will make a whole one. At the moment there is only 5 bits, so we call it
five eights, of what ever it is (a cake). The top number we always read as a proper
number. By the way, when we say the number on the bottom, we add a ‘ths’ sound to
it.
Fractions smaller than one are known as ‘Common Fractions’ or ‘Proper
Fractions’ or ‘Vulgar Fractions’.
Fractions bigger than one, are called ‘Improper Fractions’.
How to add ⅝ to ⅔ (⅝ + ⅔)
Leaving a couple of lines in under the sum.
Draw a line under the sum, like this.
Put a plus sign on the line, as well.
+
Next we have to find the LCD (Lowest Common Denominator),
Don’t worry, all that means is the smallest number that the two
bottom numbers will go into.
In this case the lowest number that both 8 and 3 will go into, is 24 (3
x 8 =24). You don’t always have to multiple the two bottom numbers
together, if you had 6 and 2, then 6 would be the LCD, as 2 goes into
6 and 6 goes into its self, once.
Right, back to the sum.
5+2
8 3
We now put the 24 under the line
+
24
Now, how many times, does 8 go into 24 (3)
We multiple the 5 by 3 (15) and put it on the line.
Now, how many times does 3 goes into 24 (8).
We multiple the 2 by 8 (16) and put it on the line.
x3
15 + 16
24
x8
15 + 16 = 31
24
24
Take 24 away from 31, you get 7.
7
24
Tip: We only add the numbers on the top line, never the bottom line.
hence, your answer =
Page 2 of 6
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Adding Fractions
Cont. from page 2.
⅝+⅔
x3
x8
15 + 16 = 31 =
24
24
7
24
This is how we obtain the number to go on the top line.
From the fraction ⅝ + ⅔, the bottom line numbers are 8 and 3.
The 8 goes into the 24, three times, so we multiple 3 by 5, to get 15.
And the 3 goes into 24, eight times, so we multiple 2 by the 8, to get 16.
(Don’t forget to use the multiplication table in Exercise 12, page 4.)
Adding Two Decimal numbers
One has been done for you.
¾+½
5/9 + 1/3
7/8 + ¼
1/3 + 5/6
½ + 5/6
2/4 + 3/8
x
3
x1
1
3+5=8= 2= 1
6
6
6
3
3
2/3 + 3/5
4/5 + 3/8
2/3 + 1/3
7/8 + 4/9
9/10 + 2/5
3/5 + 1/3
3/7 + 1/5
4/9 + 1/3
1/10 + 3/16
Page 3 of 6
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Adding Three Fractions
5/9 + 1/3 +1/6 =
5/6 + ¾ + 7/12 =
4/5 + 3/15 + 2/3 =
3/7 + 1/3 + 11/21 =
1/2 + 5/6 + 1/3 =
5/6 + 2/4 + 3/8 =
2/3 + 9/10 + 2/5 =
7/8 + 4/9 + 17/24 =
13/45 + 2/3 + 7/9 =
8/18 + 2/9 + 5/6 =
24/56 + 5/7 + 3/8 =
9/27 + 5/3 + 2/9 =
32/27 + 15/9 + 1/3 =
7/3 + 5/4 + 3/5 =
Page 4 of 6
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Answers
Page 3:
¾+½
x1
x2
5/9 + 1/3
7/8 + ¼
x1
x1
x3
x2
5 + 3=8
9
9
7 + 2=9
8
8
1/3 + 5/6
½ + 5/6
2/4 + 3/8
x2
x3
3 + 2= 5 = 1 ¼
4
4
x1
x1
x2
3 + 5=8=
6
6
2/3 + 3/5
4/5 + 3/8
2/3 + 1/3
x5
x8
x1
x3
2= 1
6
6
x1
2 + 5 = 7= 1
6
6
6
4 + 3=7
8
8
x5
x1
10 + 9 = 19 = 4
15
15 15
32 + 15 = 47 = 7
40
40
40
2 + 1=3=1
3
3
7/8 + 4/9
9/10 + 2/5
3/5 + 1/3
x9
x1
x3
x8
x2
x5
63 + 32 = 95 = 23
72
72
72
9 + 4 = 13 = 3
10
10 10
9 + 5 = 14
15
15
3/7 + 1/5
x5
x7
15 + 7 = 22
35
35
4/9 + 1/3
x1 x3
4 + 3=7
9
9
1/10 + 3/16
x8 x5
8 + 15 = 23
80
80
4/5 + 3/11
x 11 x 5
44 + 15 = 59 = 4
55
55 55
7/8 + 3/16
x2
x1
14 + 3 = 17 =
16
16
2/3 + 5/12
x4 x1
8 + 5 = 13 = 1
12
12
12
1
16
Page 4:
5/9 + 1/3 +1/6
5/6 + ¾ + 7/12
4/5 + 3/15 + 2/3
x2
x2
x3
x6
x3
x3
x1
x1
x5
10 + 6 + 3 = 19 = 1
18
18
18
10 + 9 + 7 = 26 = 1
12
12
3
3/7 + 1/3 + 11/21
1/2 + 5/6 + 1/3
5/6 + 2/4 + 3/8
x3
x3 x1 x2
x4
9 + 7 + 11 = 27 = 2
21
21
7
3 + 5 + 2 = 10 = 2
6
6
3
20 + 12 + 9 = 41 = 17
24
24
24
2/3 + 9/10 + 2/5
7/8 + 4/9 + 17/24
13/45 + 2/3 + 7/9
x 10
x9
x1
x7 x1
x3
x6
20 + 27 + 12 = 59 = 29
30
30 30
x8 x3
63 + 32 + 51 = 146
72
72
=2 1
36 (Two & one thirty-sixth)
Page 5 of 6
12 + 3 + 10 = 25 = 2
15
15
5
x6 x3
x 15
x5
13 + 30 + 35 = 78 = 11
45
45
15
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Answers
8/18 + 2/9 + 5/6
24/56 + 5/7 + 3/8
9/27 + 5/3 + 2/9
x1 x2
x1
x1 x9 x3
x3
8 + 4 + 15 = 27 = 1
18
18
2
x8
x7
24 + 40 + 21 = 85 = 29
56
56
56
9 + 40 + 6 = 55 = 2 1
27
27
27
(Two & one twenty-sevenths)
32/27 + 15/9 + 1/3
7/3 + 5/4 + 3/5
x1
x 20
x3
x9
32 + 45 + 9 = 86 =3 5
27
27
27
(Three & five twenty-sevenths)
x 15
x 12
140 + 75 + 36 = 251
60
60
= 4 11 (Four & eleven sixths )
60
Page 6 of 6
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