my maths revision guide answers
- Created by: shweta1223
- Created on: 04-04-18 13:42
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…
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