Maths

• Ordering values or numbers into a list when they're all jumbled up merely requires you to work through from the largest part of the numbers that's tens of thousands in this case then work down through to the thousands hundreds tens units until you've ordered them from smallest to largest or vice versa
• You deal with decimals in the same way it's just that we go into T hundreds thousands Etc
• Ordering fractions is a bit trickier as it can often require you to do so for those with different denominators
• To make fractions have the same denominator

  Multiply the top and the bottom of one or both of the fractions
• If three doesn't go into eight nicely, multiply both by the other's denominator
• Equal symbol


  Shows that an unknown value or an expression with one in is the same as another
• Inequality symbols


  Show that one number or an unknown value or number is not equal to another
• Arrows


  Show if one is larger or smaller than another
• Line underneath


  Means equal to or greater than
• Interval


  When a value can be between two numbers, but one of the symbols must be all equal to as well to make sure that intervals don't overlap
• Estimating or approximating


  Useful when you need a quick answer that doesn't have to be exactly right
• Rounding to one significant figure or Sig fig or SF


  Allows you to do a mental calculation quickly
• 32 * 68


  Approximately 2,100
• Truncating


  Making a number shorter
• 1,534 truncated to two sigfigs is 1,500
• 0.028 654 truncated to three sigfigs is 0.287
• Resolution of a ruler

  The smallest division on the ruler, e.g. 1 cm
• Error interval


  The value could be anywhere between the upper and lower bounds of the measurement
• Uncertainty in a measurement or value

  The error interval is always half the accuracy of the measurement or half the resolution
• Adding numbers


  Place them on top of each other, start on the right and carry the number of tens to the next column
• Subtracting numbers


  It matters which one is on top, start on the right and if the top number is smaller than the bottom, carry a one from the next column
• Multiplying numbers


  Use the grid method, give the hundreds tens units their own column and row, do the individual multiplications and write the answer in each box, then add up the total
• Short division


  Put the number you're dividing in the box and the number you're dividing by outside on the left, start on the left by dividing each digit carrying whatever remains over to the next digit
• Subtracting a negative number is the same as adding the positive version of that number
• Multiplying a positive number by a negative number, the answer must be negative. If they're both negative, the answer must be positive as the negatives cancel
• BIDMAS/BODMAS


  The order of operations: Brackets, Indices/Powers, Divide and Multiply, Add and Subtract
• Power/Index


  A number raised to a power, calculated before anything else
• Putting brackets around multiplies or divides is better than BIDMAS
• Converting between decimals, fractions and percentages


  Decimals can be converted to percentages by multiplying by 100, fractions can be converted by dividing the numerator by the denominator
• A recurring decimal has a dot above the repeating digit(s)
• Reciprocal


  1 divided by that number, or the same as the number raised to the power of -1
• Income


  All the money you earn, usually talked about per month
• Salary


  The total amount of money you're paid in your job every year before income tax is deducted
• PAYE (Pay As You Earn)


  Income tax taken from your paycheck before the money goes into your account
• Take-home pay


  What you're left with after income tax is deducted
• Expenses


  Money spent by a self-employed person on things needed for their business
• Profit


  Income minus expenses
• Personal allowance


  Amount you can earn without paying income tax (£12,570 in the UK)
• Income tax


  20% paid on earnings over the personal allowance in the UK
• VAT (Value Added Tax)

  Tax paid on most purchases, usually 20% in the UK