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week

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Practice questions

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Percentage increase and decrease powerpoint

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Percentage increase and decrease powerpoint

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Conversions and percentages

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How to understand power

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Order of Operation

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Operations

"Operations" mean things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation.

But, when you see something like...

... what part should you calculate first?

Start at the left and go to the right?
Or go from right to left?
Warning: Calculate them in the wrong order, and you can get a wrong answer !
So, long ago people agreed to follow rules when doing calculations, and they are:

Order of Operations

Do things in Brackets First

Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract

Multiply or Divide before you Add or Subtract

Otherwise just go left to right

How Do I Remember It All ... ? BODMAS !

Divide and Multiply rank equally (and go left to right).

Add and Subtract rank equally (and go left to right)

So do it this way:

After you have done "B" and "O", just go from left to right doing any "D" or "M" as you find them.

Then go from left to right doing any "A" or "S" as you find them.

Note: the only strange name is "Orders". You may prefer GEMS ( Grouping, Exponents, Multiply or Divide, Add or Subtract). Or in the US where they say "Parentheses" instead of Brackets, so it is " PEMDAS".

Examples

Example: How do you work out 3 + 6 × 2 ?

Multiplication before A ddition:

Example: How do you work out (3 + 6) × 2 ?

B rackets first:

Example: How do you work out 12 / 6 × 3 / 2 ?

Multiplication and D ivision rank equally, so just go left to right:

A practical example:

Example: Sam threw a ball straight up at 20 meters per second, how far did it go in 2 seconds?

Sam uses this special formula that includes gravity:

height = velocity × time − (1/2) × 9.8 × time ²

Sam puts in the velocity of 20 meters per second and time of 2 seconds:

height = 20 × 2 − (1/2) × 9.8 × 2 ²

Now for the calculations!
The ball reaches 20.4 meters after 2 seconds
Exponents of Exponents ...

What about this example?

Exponents are special: they go top-down (do the exponent at the top first). So we calculate this way:
And finally, what about the example from the beginning?
295, 1565, 1571, 296, 1567, 380, 1569, 3852, 3853, 382

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Learn how to calculate things in the correct order. Calculate them in the wrong order, and you can get a wrong answer!

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Revise the lesson if you need to see it again.

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Week 1 Homework Sheet

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Week 2

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Week 3 Homework Sheet

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Practice task sheet