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Introduction | Adding | Subtracting | Multiplying | Dividing | BODMAS
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Introduction
These four rules of number are Add, Subtract, Multiply and Divide.
The symbols are +, –, x, and ÷.
Other words that are sometimes used for these operations include:
- Add: sum, total, plus
- Subtract: difference, minus, take away
- Multiply: product, times
- Divide: share, quotient
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Adding
Adding, for example 156 + 378
Always set the sum down with the figures under one another in columns, as below.
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Subtracting
Subtracting, for example 734 – 589
71 31 4
- 5 8 9
1 4 5
We say that we cannot take 9 from 4 so we borrow a ten from the next column and take 9 from 14, leaving 5.
Having borrowed from the 3, it must now be reduced to 2.
So 8 must be taken from 2.
Again, we borrow and take 8 from 12.
In the last column we take 5 from 6.
Therefore, 734 – 589 = 145.
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Multiplying
Short multiplication: For example 75 x 4
Set this down as:
75
x 4
300
4 x 5 is 20 so we put down the 0 and carry the 2.
Next, 4 x 7 is 28, add on the 2, giving 30.
Long multiplication: For example 45 x 32
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46
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x 32
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92
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(46 x 2) |
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1380
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(46 x 30) Note: Put down the 0 and multiply by 3 |
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1472
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Dividing
Short division: For example 56 ÷ 2 =
We say 2 goes into 5 and the answer is 2 remainder 1.
This 1 is put in the 6 column as a 10, giving 16.
Again, we say 2 goes into 16, 8 times, giving the answer 28.
Long division: For example 7682 ÷ 14 =
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70 |
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68
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64
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42
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42
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14 x 5 = 70 so 14 goes into 76, 5 times remainder 6.
We bring down the 8 to make 68.
Again 14 goes into 68, 4 times remainder 4, because 14 x 4 = 64.
We bring down the 2 to make 42.
Now 14 goes into 42, 3 times, because 14 x 3 = 42 , no remainder.
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BODMAS
B O D M A S tells us the order in which to do things when simplifying an expression.
B stands for brackets
O for order
D for division
M for multiply
A for add
S for subtract
For example, work out 5 + 3 x 2 = 5 + 6 = 11.
We must do the x before the +
( 5 + 3 ) x 2 = 8 x 2 = 16.
In this case we must do the brackets before the x
12 – 6 ÷ 2 = 9.
Here we do the division before the subtract.
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