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#### How to divide in a ratio

### Example:

Share `£300` in the ratio `2:3`.

We need to share the amount `£300` between two people so that for every `£2` the first person gets, the second gets `£3`.

- Share the amount into `5` equal parts.
- Give the first person `2` parts
- Give the second person `3` parts.

Working out:

`5` parts `=300`

`1` part `=300-:5=60`

`2` parts `=2xx 60 = 120`

`3` parts `=3xx60=180`

So the shares are `£120:£180`

#### How increase using a multiplier

##### What is the multiplier to increase an amount by `5%`?

How?

Start with the initial amount which is `100%`.

Add `5%` so the new amount is `100% +5% = 105%` of the starting amount.

Now `105% = 1.05` as a decimal so the new amount is `1.05` of the starting amount.

We say that `1.05` is the multiplier to increase an amount by `5%`

Example: Increase `£30` by `5%`. Using the multiplier, the increased amount will be `1.05 xx £30 = £31.50`.

##### How do you find the value of the multiplier?

1. Add the % increase to `100`

2. Divide by `100`

The decimal number is the value of the multiplier.

#### How decrease using a multiplier

##### What is the multiplier to decrease an amount by `5%`?

How?

Start with the initial amount which is `100%`.

Subtract `5%` so the new amount is `100% -5% = 95%` of the starting amount.

Now `95% = 0.95` as a decimal so the new amount is `0.95` of the starting amount.

We say that `0.95` is the multiplier to decrease an amount by `5%`

Example: Decrease `£30` by `5%`. Using the multiplier, the decreased amount will be `0.95 xx £30 = £28.50`.

##### How do you find the value of the multiplier when decreasing?

1. Subtract the % decrease from `100`

2. Divide by `100`

The decimal number is the value of the multiplier.

#### How to divide by a decimal

Example:

`15-:0.3`

The difficulty is that we don't know how to divide by decimals like we can divide by whole numbers.

Steps:

`15-:0.3` can be written as `15/0.3`.

This looks like a fraction and we can use the idea of equivalent fractions to change the denominator to a whole number:

`15/0.3 = \{15xx10\}/\{0.3xx10\} = 150/3 =50`

#### Circle Theorem - Angles in a cyclic quadrilateral

#### Circle Theorem 1-Angle at center

Move the points `A`, `B` or `C` and observe the values of the angles. What is the relationship between angles `O` and `C`?

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