A Guide to succeeding at Arithmetic

First, you must understand place value… Place value is the value of each digit in a number. It means understanding that 582 is made up of 500, 80 and 2 H T U 6 7 3 + 3 9 7 1 2 7 1 2

Remember to use the correct number operation Remember, when setting these questions out, to ensure the units, 10, 100s and 1000s are all underneath each other. And don’t forget to exchange if the top digit is smaller than the one below it. 6 7 0 6 4 1 - 5 0 2 6 5 6 2 Remember to use the correct number operation 6 5 6 2

Place value applies to decimals too. T U . t 9 1 1 0 1 0 . 0 1 - 5 . 4 - 5 . 4 4 . 6 4 . 6

It’s important to know square and cubed numbers too. A square number is a number multiplied by itself A cubed number is a number multiplied by itself three times 62 = 6 x 6 = 3 6 3 6 + 1 0 = 4 6 43 = 4 x 4 x 4 = 64 4 6

Multiplication calculations will always come up, so it is ESSENTIAL that you know ALL of your times tables and have QUICK recall. 5 x 4 = 2 0 x 1 0 = 2 0 0 2 0 0

If you know your times tables, it makes answering questions like these so much quicker! 2 3 5 5 1 5 7 0 0 1 8 0 5 5 REMEMBER your place holder When multiplying by a multiple of 10 1 8 0 5 5

If there’s a multiplication problem with a decimal place, take the decimal point out, then add it back in later… Remove the decimal point 3 . 9 3 9 3 .9 x 3 0 x 3 0 x 3 0 Then add back in, ensuring that you do the same to the answer. 1 1 7 0 1 1 7 .0 1 1 7

Long division – with a large number, it helps to find the first few multiples and jot these down. 1) How many 43s are there in 64? 1 5 21 43 86 129 172 215 2 marks. You can get 1 mark for your calculations! 2) How many 43s are in 215? 1 5

When adding or subtracting fractions, find a common denominator When adding or subtracting fractions, find a common denominator. If you change a denominator, change the numerator too! x3 5 15 This can then be simplified = 7 21 x3 ÷3 15 3 18 6 + = = 21 21 21 7 6 ÷3 7

When multiplying fractions, x the numerators, then the denominators. ÷6 12 2 30 5 ÷6 2 5

When dividing fractions, use KFC (keep, flip, change) 1 2 ÷ 1 1 1 x = 4 1 4 2 8 Keep 1 Change 8

To find a fraction of a number, divide by the denominator then multiply by the numerator 140 ÷ 5 = 28 28 x 2 = 56 Multiply by the numerator 56

To find a percentage when the % is a multiple of 10 (e To find a percentage when the % is a multiple of 10 (e.g 10%, 20%, etc) Divide the amount by 10 to find 10% 1800 ÷ 10 = 180 180 x 2 = 360 360 Then x the answer by the number of 10s

To find a percentage of an amount which ISN’T a multiple of 10, first find 1% by ÷ 100, then x by the percentage. This gives REMEMBER per cent means out of 100 650 ÷ 100 = 6.5 This gives us 1% 6.5 x 2 8 This gives us 28% 1 8 2 1 8 2