Download Subtracting Fractions

Exercise 32
Fractions Subtraction
At the end of this exercise you will:
• Learn about vulgar fractions
• Learn about Improper fractions
• Be able to subtract two fractions
• Be able to subtract three fractions
Answers on page 5, of this exercise.
Page 1 of 5
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Subtracting 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 called ‘Common Fractions’ or Vulgar Fractions,
those bigger than one, are called ‘Improper Fractions’.
How to Subtract ⅔ from ⅝ (⅔ - ⅝)
Leaving a couple of lines in under the sum.
Draw a line under the sum, like this.
Put a minus 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 3 and 8 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.
⅔-⅝
Right, back to the sum.
We now put the 24 under the line
Now, how many times, does 3 go into 24 (8)
We multiple the 2 by 8 (16) and put it on the line.
Now, how many times does 8, go into 24 (3).
We multiple the 5 by 3 (15) and put it on the line.
x8
24
16 - 15
24
x3
16 - 15 = 1
24
24
(Take 15 away from 16 you get 1 hence, you get one twenty-fourth).
Tip: We only subtract the numbers on the top line, never the bottom
line.
Page 2 of 5
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Subtracting Fractions
Cont. from page 2.
⅔-⅝
x8
x3
16 - 15 = 1
24
24
This is how we obtain the number to go on the top line.
From the fraction ⅔ - ⅝, the bottom line numbers are 3 and 8.
The 3 goes into the 24, eight times, so we multiple 2 by 8, to get 16.
And the 8 goes into 24, three times, so we multiple 5 by the 3, to get 15.
(Don’t forget to use the multiplication table in Exercise 12, page 4.)
Subtracting Two Decimal numbers
¾-½=
5/9 - 1/3 =
7/8 - ¼ =
5/6 - 1/3 =
5/6 - ½ =
2/4 - 3/8 =
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 =
3/16 - 1/10 =
Page 3 of 5
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Subtracting Three Decimal numbers
8/9 - 1/3 -1/6 =
5/6 – 1/12 - 1/4 =
4/5 - 1/15 - 1/3 =
6/7 - 1/3 - 5/21 =
3/4 - 1/2 - 1/6 =
18/20 - 1/5 - 3/10 =
7/8 – 5/16 – ¼
9/10 – ½ - 3/15
Now for something harder: Combined adding and subtraction
Don’t forget to look at the answers if you need too.
3/6 + 2/3 – 5/6 =
x1
x2
7/8 + 1/3 – 1/6 =
x1
3+4- 5
6
=7–5=2=1
6
6 3
18/20 + 3/5 – 7/8 =
8/9 + 1/3 – 5/7 =
Page 4 of 5
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Answers
Page 3: Subtracting Two Decimal numbers
¾-½
5/9 - 1/3
7/8 - ¼
x1 x2
x1 x3
x1 x2
3–2=1
4
4
5–3=2
9
9
7–2= 5
8
8
5/6 - 1/3
5/6 - ½
2/4 - 3/8
x1 x2
x1 x3
x2 x1
5 – 2 =3 = 1
6
6 2
5–3=2=1
6
6 3
4–3=1
8
8
2/3 - 3/5
4/5 - 3/8
2/3 - 1/3
x5
x8
x1 x1
x3
x5
10 – 9 = 1
15 15
32 – 15 = 17
40
40
2–1=1
3
3
3/7 - 1/5
4/9 - 1/3
3/16 - 1/10
x5 x7
x1 x3
x5
15 – 7 = 8
35 35
4–3=1
9
9
15 – 8 = 7
80
80
7/8 - 4/9
9/10 - 2/5
3/5 - 1/3
x9
x1 x2
x3 x5
9–2=7
10
10
9–5=4
15
15
x8
63 – 32 = 31
72
72
x8
Page 4: Subtracting Three Decimal numbers
8/9 - 1/3 -1/6
5/6 – 1/12 - ¼
4/5 - 1/15 - 1/3
x2
x2
x3
x6
x3
x1 x3
x1 x5
16 – 6 – 3 = 7
18
18
10 – 1 – 3 = 6 = 1
12
12 2
12 – 1 – 5 = 6
15
15
6/7 - 1/3 - 5/21
3/4 - 1/2 - 1/6
18/20 - 1/5 - 3/10
x3
x3 x3 x2
x1 x 4 x2
18 – 7 – 5 = 6
21
21
9–6–2=1
6
6
18 – 4 – 6 = 8 = 2
20
20 5
7/8 – 5/16 – ¼
9/10 – ½ - 3/15
x7 x1
x2 x1 x4
x3
14 – 5 – 4 = 5
16
16
27 – 15 – 6 = 6 = 2 = 1
30
30 10 5
x 15 x 2
Page 4: Combined adding and subtraction
3/6 + 2/3 – 5/6
x1
7/8 + 1/3 – 1/6
x2 x1
x3 x8x4
3 + 4 –5 = 2 = 1
6
6 3
21 + 8 – 4 = 25 = 1
24
24
24
18/20 + 3/5 – 7/8
8/9 + 1/3 – 5/7
x2
x 8
x5
x7
36 + 24 – 35 = 25 = 5
40
40
x 21
x 9
56 + 21 – 45 = 32
8
63
Page 5 of 5
63
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