Foundation maths: Section one - Numbers

Types of numbers and BIDMAS

• Types of numbers
• Integers
• An integer is another name for a whole number, whether it be positive, negative or zero.
• For example, -365, 0, 17 and 1,234,567,890 are all integers whereas 0.5, 2/3, -1000.1 and pi are not.
• Square and cube numbers
• When you multiply a number by itself, you get a square number. Square numbers include: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196 and 225.
• When you multiply a whole number by itself, then by itself again, you get a cube number. Cube numbers include: 1, 8, 27, 64, 125 and 1000.
• It's important to learn these off by heart.
• BIDMAS
• BIDMAS tells you the order in which these operations should be done.
• Brackets
• Indices
• Division
• Multiplication
• Addition
• Subtraction
• Note: The order in which division and multiplication are done depends on which comes first in the equation. The same applies for addition and subtraction.

Understanding 'real life' problems

• When trying to understand a word heavy maths problem make sure to:
• 1) Read the question carefully and work it what maths you need to solve the question.
• 2) Underline the relevant information - not all of he numbers are needed.
• 3) Write out the question in maths and answer it, showing all of the working clearly.
• 4) Don't forget to use the appropriate units e.g £, %

Multiplying and dividing by 10, 100, 1000 etc.

• Multiplying and dividing by 10
• To multiply, move the decimal point one place to the right and, if needed, add a zero at the end.
• To divide, move the decimal point one place to the left and, if needed, remove zeros after the decimal point.
• Multiplying and dividing by 100, 1000 etc.
• Use the same method as is used above, but instead of moving one space to the left or right, move the same number of spaces as there are zeros.
• Multiplying and dividing by numbers like 20, 300 etc.
• Multiply by 2, 3 or 7 etc. First, then move the decimal point so many places to the right according to how many zeros there are.
• Divide by 2, 3 or 7 etc. First, then move the decimal point so many places to the left according to how many zeros there are.

Multiplying and dividing whole numbers

• Multiplying whole numbers
• The traditional method:
• 1) Split I into separate multiplications.
• 2) Add up the results in columns (right to left).
• Example - Work out 46x27
• 46
• x27
• ------
• 322 - This is 7x46
• 4 - (Remainder)
• ------
• 920 - This is 20x46
• ------
• 1242 - This is 322+920
• Divding whole numbers.
• Short division method:
• 1) Set out the division as shown (748/22)
• ___
• 22| 748
• 2) Look at the first digit under the line. 7 doesn't divide by 22, so put a zero above and look at the next digit.
• 3) 22x3=66, so 22 into 74 goes 3 times with a remainder of 74-66=8
• 4) 22 into 88 goes 4 times exactly.
• So 748/22=34