**Number**

Prime Factors

HCF & LCM

Indices

Start by making a factor tree - find two things that multiply together to give the number. Keep going until you find a prime number. Circle it!

You can use your prime factor trees to find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of two numbers.

2 = 2 x 2 x 2 x 2

Fractions

To multiply fractions, just multiply the tops together, and then multiply the bottoms together.

Rounding

Anything to 4, I ignore.

5 or above, I round it up.

Percentages

To find one number as a % of another:

Keep going until you run out of new numbers!

1092 = 2 x 2 x 3 x 7 x 13

Ratio

You can simplify ratios in the same way as fractions.

Find a number that both/all parts divide by, and divide by it!

Proportion

A typical proportion question is about recipes

You will be shown a recipe for a certain number of people, and asked to figure out how much of each ingredient you would need for a different number of people.

36 = 2 x 2 x 3 x 3

16 = 2 x 2 x 2 x 2

For each prime factor, you need to check if it belongs to both numbers. If so, put it in the middle. If not, put it in the rest of the circle.

There are still all four factors inside the 16 circle, some in the green section, some in the middle.

To get the HCF, multiply together any numbers in the middle.

To get the LCM, multiply together ALL the numbers you can see in the diagram.

HCF = 2 x 2 =

4

LCM =

2 x 2 x 2 x 2 x 3 x 3 =

144

4

3 x 3 = 3

Multiply: You add the powers.

4

5

9

The main number stays the same.

4

4

= 4

8

2

6

Divide: you subtract the powers.

( 5 )

4

3

= 5

12

Brackets: you multiply the powers

5

6

3

4

x

=

5 x 3

6 x 4

15

24

=

5

8

Both of these

divide by 3

=

For dividing, just flip the second fraction upside down, and multiply them!

(You don't need to do anything else, that's the answer.)

To add or subtract fractions, the bottom of each must be the same.

Find a common denominator - you can just multiply the two denominators together if you can't see an obvious number that both go into.

Work out what you need to multiply each fraction by to get the common denominator on the bottom.

Once you have the same number on the bottom of each fraction, you just add/subtract the tops and leave the bottom unchanged.

0, 1, 2, 3, 4

5, 6, 7, 8, 9

Ignore

Round up

For s.f.

(significant figures)

, start on the left.

Work your way along until you hit a number that's not 0.

That's your first s.f.

(Don't skip any more 0's after this!)

To find a fraction of an amount

Divide by the bottom, then multiply by the top

2

3

x (of)

**33**

33 divided by 3 = 11

11 times 2 = 22

**=**

22

22

Eg - there are 48 cars, 13 are blue. What % of the cars are blue?

Do 13 divided by 48 (this gives you the answer as a decimal)

= 0.27....

To turn it into a %, multiply it by 100.

= 27%

Divide the number by the total, then multiply by 100.

% increase and decrease

INCREASE:

Start with 100%. Add on the % increase.

DECREASE:

Start with 100%. Take off the % decrease.

Divide by 100. Multiply your amount by this number.

eg - Increase £240 by 20%

100% + 20% = 120%

Divide by 100 = 1.20

£240 x 1.20 = £288

To share something in a ratio:

- add together the parts of the ratio

- divide the full amount by that answer

- Multiply each part of the ratio by

the new answer

Check your amounts add up to the total!!

Share £200 in the ratio 2:3

2+3 = 5

£200 divided by 5 = £40

2:3 multiplied by £40 = £80 : £120

80+120 = 200

Trial and Improvement

We do this by trying halfway between them (7.75) to see which is nearest to the answer.

7.75 x 7.75 = 60.0625

Because this is ABOVE the answer we want, our answer must have been closer to

7.7

Anything to the power of 0 equals 1.

Standard Index Form