my maths revision guide answers

My maths revison guide answers

Prime numbers

There are lots of ways to solve this. Here are two:

Solution 1

Start with the smallest prime number that divides into 24, in this case 2. 2 divides into all even numbers, so we can write 24 as:

24 = 2 x 12

Now think of the smallest prime number that divides into 12. Again we can use 2, and write the 12 as 2 x 6, to give.

24 = 2 x 2 x 6

6 also divides by 2 (6 = 2 x 3), so we have:

24 = 2 x 2 x 2 x 3

2, 2, 2 and 3 are all prime numbers, so we have our answer.

In short, we would write the solution as:

24 = 2 x 12

= 2 x 2 x 6

= 2 x 2 x 2 x 3

Solution 2

We can also use a factor tree:

 This shows us that 24 = 2 x 2 x 2 x 3

 Remember that we can write these factors in index form. 

 In this case  

 24 = 2 x 2 x 2 x 3, so

 24 = 2³ x 3               

36 = 2 x 2 x 3 x 3

or 2² x 3²

You might have shown this as

36 = 2 x 18

= 2 x 2 x 9

= 2 x 2 x 3 x 3

Factors

The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40.

Make sure that you got all of them. Do not forget 1 and 40.

Multiples

The first  {4} multiples of  {6} are  {6},~{12},~{18} and  {24}.

Remember that  {3} is the first multiple of  {3}.

5 times 3={15}, therefore the 5th  multiple of  {3} is  {15}.

Common Factors

24a + 16 = 8(3a + 2)

Therefore, the HCF of 24 and 16 is 8.

The factors of 20 are 1, 2, 4, 5, and 20.

The factors of 25 are 1, 5, and 25.

The common factors of 20 and 25 are 1 and 5.

Common Multiples

The multiples of 6 are 6, 12, 18, 24, 30, 36, 42…

The multiples of 10 are 10, 20, 30, 40, 50…

The LCM of 6 and 10 is 30.

BIDMAS

If you calculate the '4 + 2' part first you get:

4 + 2 × 3 = 6 × 3 = 18

If you calculate the '2 × 3' part first you get:

4 + 2 × 3 = 4 + 6 = 10

These are two very different answers, but only one is correct.

In BIDMAS, multiplication comes before addition, so multiply 2 by 3 first.

4 + 2 × 3 = 4 + 6 = 10, so this is the right answer

This sum has only addition and subtraction. So work them out from left to right.

9 - 4 + 3 = 5 + 3 = 8

Notice that if you didn't go…