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Basic Arithmetic
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Basic Arithmetic

lesson introduction

Basic Arithmetic

Addition, subtraction, multiplication and division are called operations. We can use them to manipulate numbers.

1

These symbols will be familiar to you. How else can we describe them? They are _________

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2

The four operations are:

Addition ++ Subtraction - Multiplication ×\times Division ÷\div

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3

Starting with addition, what is 17+817+8?

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What if you have 170170 and you add 2727?

Let's work it out step by step ➡️

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2

First break 2727 into easier numbers

2727 is made up of 22 tens and 77 units

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3

Add 2020 onto 170170

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Now add 77 to 190190

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5

So in total...

170+27=197170+27=197

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1

Addition is commutative.

The order of the numbers doesn't matter.

2

What is 14+714+7?

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3

We've seen that 14+7=2114+7=21. Let's change the order of our sum, what is 7+147+14?

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4

We have shown that 14+7=7+1414+7=7+14.

This is true for all additions.

What is 87+11587+115? Remember, if it makes it easier you can work out 115+87115+87 as addition is commutative.

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1

Sometimes it's easier to add more than we need

then subtract the difference.

2

What about 143+48143+48?

Let's work it out step by step ➡️

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3

4848 is two less than 5050

So 4848 becomes 50250-2

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4

Add 5050 to 143143

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5

Now subtract 22 from 193193

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6

The final answer is 191191

Nice! 👍

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What is 122+79122+79?

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1

What is the opposite of addition?

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2

Subtraction has similar strategies to addition

We can also use the words take away or minus for subtraction.

3

Take care with subtraction, unlike addition it is not commutative.

The order of the numbers matters 146=814-6=8 but 614=86-14=-8.

4

What about 18672186 - 72?

Let's work it out step by step ➡️

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5

Let's break 7272 into smaller parts

7272 = 77 tens and 22 units

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6

Subtract 77 tens from 186186

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7

Now subtract 22 units from 116116

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8

The final answer is 114114

Great work! 👍

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Calculate 18753187 - 53

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What is 20379203-79?

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Multiplication uses our knowledge of times tables. What is 8×48\times 4?

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Let's try a harder multiplication: 17×817 \times 8

1

We can split this into two multiplications

Let's work it out step by step ➡️

2

Break 1717 into smaller parts 17=10+717=10+7.

We can then work out 10×810\times 8 and add it to 7×87\times 8.

3

First, work out 10×810 \times 8

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Now work out 7×87 \times 8

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5

Finally, add them together

80+56=13680 + 56 = 136

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The final answer is 136136

Nice!

Like addition, multiplication is commutative. What does this mean?

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What is 7×237\times 23? Remember that you can change the order of the numbers if it makes it easier.

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What is the opposite of multiplication?

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For example: 18÷318 \div 3

1

1818 can be split into groups of 3s3's

We use our knowledge of the times tables, in this case6×3=186 \times 3 = 18

2

So six groups of three go into 1818 or:

18÷3=618 \div 3 = 6

Work out 45÷945 \div 9

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Which multiplication fact can be used to work out 72÷1272 \div 12?

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Like subtraction, division is not commutative. The order of the numbers matter. 8÷4=28\div 4=2 but 4÷8=0.54\div 8=0.5.

1

Summary! The four operations are:

Addition ++ Subtraction - Multiplication ×\times Division ÷\div

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2

Strategies for addition include:

Splitting a number 170+27=170+20+7170+27=170+20+7 Adding on more 143+48=143+502143+48=143+50-2

3

Strategies for subtraction include:

Splitting a number 18753=187503187-53=187-50-3 Taking away more 35749=35750+1357-49=357-50+1

4

Strategies for multiplication include:

Splitting a number 34×9=30×9+4×934\times 9=30\times 9+4\times 9

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Strategies for division include:

Use knowledge of times tables 84÷7=1284\div 7=12 as 7×12=847\times 12=84.

6

Addition and multiplication are commutative

The order of the numbers doesn't matter 115+80=80+115115+80=80+115

15×3=3×1515\times 3=3\times 15

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Subtraction and division are not commutative

The order of the numbers does matter 102=810-2=8 but 210=82-10=-8

40÷10=440\div 10=4 but 10÷40=1410\div 40=\dfrac{1}{4}