1. Whole Numbers (Miscellaneous) Multiples Factors Squares and cubes BODMAS Rounding whole numbers Significant figure Approximation Negative numbers

2. Multiples of a number A multiple of a number is any in the number’s times table. 18 is a multiple of 6 because 18 = 3x6 If buns come in packs of 6 in a shop can we buy 18? YES QUESTIONS Find five multiples of 6. Find five multiples of 15. Do they have any multiples in common?

3. Lowest common multiple Numbers can have various multiples in common. Example: If we multiply two numbers together the answer (product) is a multiple of both. 5 x 7 = 35 so 35 is a multiple of 5 and a multiple of 7. The lowest common multiple (LCM) of two numbers is the smallest number that both will divide into. To find it list the multiples of both and pick out the smallest number that appears in both lists.

4. Factors A factor of a number is any number that will divide (leaving no remainder ) into that number To find the factors of a number list all the pairs of numbers that multiply together to equal the number 18 / 6 = 3 so 6 is a factor of 18 Similarly 3 is a factor of 18 Factors of 18 are 1,2,3,6,9 and 18 18 = 1 x 18 18 = 2 x 9 18 = 3 x 6

5. Factors A factor of a number is any number that will divide (leaving no remainder) into that number 18 / 6 = 3 so 6 is a factor of 18 Similarly 3 is a factor of 18 To find the factors of a number list all the pairs of numbers that multiply together to equal the number 18 = 1 x 18 18 = 2 x 9 18 = 3 x 6 Factors of 18 are 1,2,3,6,9 and 18

6. Factors Numbers can have various factors in common. 1 is always a factor of any number. To find the highest common factor (HCF) list all the factors of both numbers and pick out largest one HCF is the largest number that will divide evenly into two numbers. FACTORS AND MULTIPLES ARE THE REVERSE OF EACH OTHER. 18 is a multiple of 6 6 is a factor of 18

7. Prime numbers A prime number is any number with exactly two factors only. The factors are 1 and the number itself. A prime number can only be divided by itself or 1 leaving no remainder. List the first ten primes

8. Prime factor and HCF To find the HCF Write out the prime factor multiplication of both numbers. Pick out the common factors The HCF is the product of the common factors 28 = 2 x 2 x 7 42 = 2 x 3 x 7 2 and 7 are common factors 14 = 2 x 7 is the HCF

9. Prime factors and LCM To find the LCM Write out the prime factor multiplication Pick out the common factors Pick out the remaining factors Multiply all the numbers 28 = 2 x 2 x 7 42 = 2 x 3 x 7 2 and 7 are common factors We also have 2 and 3 72 = 2 x 7 x 2 x 3 is the LCM

10. Squares 1 x 1 = 1 2 x 2 = 4 These are called the square numbers 2 written on the top and right of a number indicates that the number is to be squared or multiplied by itself.

11. Cubes 1 x 1 x 1 = 1 2 x 2 x 2 = 8 These are called the cube numbers 3 written on the top and right of a number indicates that the number is to be cubed or multiplied by itself three twice. The first ten squares are 1,4,9,16,25,36,49,64, 81 and 100 Knowing the square numbers helps in learning the times tables. The first five cubes are 1,8,27,64 and 125

12. BIDMAS This is the agreed order to perform maths operations. Bracket Indices Division Multiplication Addition Subtraction 2 + 6 x 4 = 26 not 32 (2+6) x 4 = 32

13. Rounding Whole Numbers Sometimes we do not need to know the number exactly. We usually want to use a certain degree of accuracy. We can round a number to the nearest ten, hundred, thousand etc. 139562 is in between 139560 and 169570 Which one is it closer to? The 2 in the units column tells us it is closer to 169560. We round down. 139562 is 139560 to the nearest 10.

14. Rounding Whole Numbers 139562 to the nearest 100 is either 139500 or 139600. The 6 in the ten column tells us it is nearer 139600 We round up. To round think of the two multiples the number is between Look at the following number If it is 5 or more round up. If it is 4 or less round down.

15. Significant figures When rounding we need to know how accurate we need to be. If talking about the number of people at a football match we would say 40,000 rather than 41,235 Being asked to round to 2 significant figures tells us to round leaving only 2 non- zero numbers. 41,235 to 2 sig. fig is 41,000. 139600 to 3 sig. fig is 140000

16. Approximation Sometimes we only want a rough answer to a question. When dealing with accurate number we can sometimes take shortcuts and use numbers that are easier to handle. 20.79 x 38.95 = 809.7705 exactly. We can work out a rough answer using 21 for 20.79 and 40 for 38.95. Roughly 20.79 x 38.95 = 840

17. Negative Numbers Not all numbers are bigger than 0 We sometimes need to consider what happens when numbers are less than the 0 that we are used to e.g. temperature and banking

18. Negative Numbers Which number is bigger? -10 or 5 -5 or 10 Put in order smallest to biggest 21, 7, -15, 28, -3. How can we combine positive and negative? 6 + 4 = 10 4 + 6 = 10 6 – 4 = 2 - 4 + 6 =2 4 – 6 = -2 -6 + 4 = -2 -4-6 =-10 -6-4 = -10

19. Negative Numbers Same signs +(+) and –(-) are positive Different signs +(-) and –(+) are negative -6 +(-4) = -6 -4 = -10 Similarly with multiplying and dividing Same sign positive Different sign negative (-4) x (-6) = 24 (-4) x 4 = -16