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If we think about a right angled triangle, it is the same as one half of a square or rectangle. This is because if we join two right angled triangles at their diagonal sides, we make a square or rectangle.

Now, in order to work out the area of a square or rectangle, we simply multiply the length and the width together.

However, we now have the area of a square or rectangle, when we actually need the area of the right angled triangle. To work out the area of the roght angled triangle, we must simply halve the area that we have worked out. This is because we have made the square or rectangle by putting 2 right angled triangles together. As there are 2 of them, we must simply divide the whole area by 2 in order to find the area of one right angled triangle.

This is why we say that in order to work out the area of a right angled triangle we simply do:

Length x Width and then divide the answer by 2

The most common way of doing this is called a bubble search (this may not be the technical name, but it's the one I was taught). The method is as follows:

Start by writing the number at the top of your page. Now find 2 numbers which multiply to that number (e.g. starting with 100, I might find 2 and 50). Draw lines down from 100 to the numbers 2 and 50. Check whether or not these numbers are primes (e.g. check whether 2 and 50 are primes - 2 is, 50 isn't). If you have found a prime number, draw a bubble around it. Now do the same process for 50. I find the factors 2 and 25. 2 is prime, 25 isn't. I draw a bubble around 2 and start again from 25. I find the numbers 5 and 5. both are prime so I bubble both.

Now that I've circled both numbers, my search is complete: the prime factors are the numbers in bubbles.

Note that, if neither number is prime, you have to apply the method to both numbers. Because of this, it's often best to find a prime number for one of the 2 numbers.

Some tricks to make this easier are:

If the number is even, use 2 as one of your factors.

If the number ends with a 5 or a 0, use 5 as one of your factors.

If the digits of the number add up to a multiple of 3, use 3 as one of your factors.

Start by multiplying the two numbers as though they didn't have a decimal point (e.g. 2.7*3.6 becomes 27*36 = 972). Now add up how many decimal places were in the original two numbers (e.g. 2.7 and 3.6 have 2 decimal places, 3.45 and 9.2 have 3 decimal places) and give your answer that number of decimal places (e.g. since 2.7 and 3.6 have 2 decimal places, 2.7*3.6 will have 2 decimal places. Calculate 27*36 = 972, then give it 2 decimal places to get 2.7*3.6 = 9.72).

Remember that, in this situation, zeroes should be counted as decimal places. For example: 1.02*4.05. Calculate 102*405 = 41,310. Now notice that 1.02 and 4.05 have 4 decimal places. Therefore, give 41,310 4 decimal places to find that 1.02*4.05 = 4.1310.

Step by step this is layed out as:

1) Multiply without decimal points.

2) Count the number of decimal places in the 2 numbers you're multiplying.

3) Give your answer to part (1) the number of decimal places from part (2).

Both are different ways to represent an amount of something. Fractions show how much of a whole item there is for example 2/10 2 parts out of a total of 10. On the other hand, a ratio describes one amount relative to another, for example 1:3 meaning 1 part of one amount corresponds to 3 parts of another amount, a good way to think about this is when making squash, you take an amount of squash, such as 10ml and add another amount of water, for example 100ml, the ratio would be 10:100, which can be simplified as 1:10, since there is 10 times more water as squash.

Answered by Alice C.

Studies Genetics at Cardiff

ok. Well think about a square. What times what creates the area of a square? Yes the bottom one and side on. So which do you think will be useful to know to find the area of a rectangle? Yes the same! So the area of this shape is 4x9 and what is that? Yes it is 36! So the answer is 36cm^3

Answered by Charlotte W.

Studies History and Innovation at Bristol

There are 5 steps you can follow to make this sort of problem easier to handle:

1) Line up all of the values in a column with the decimal points under each other

2) Ensure each value is the same length by filling in zeros

3) Ignore the decimal points and look at the values as if they were all whole numbers

4) Arrange in order of size

5) Put the decimal points and zeros at the front, back in

This would look like:

1-2) 0.45

1.09

0.30

0.08

3) 45

109

30

8

4) 8

30

45

109

5) 0.08

0.30

0.45

1.09

Step 5 shows the correct answer in ascending order from the smallest value at the top to the largest value at the bottom.

Answered by Aneesh S.

Studies Medicine MBBS BSc at University College London

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