maths

• Adding fractions


  1. Find the lowest common multiple of the denominators

  2. Find equivalent fractions with the common denominator

  3. Add the numerators
• Adding mixed numbers


  1. Convert mixed numbers to top-heavy fractions

  2. Find the lowest common denominator

  3. Add the numerators
• Multiplying fractions


  1. Multiply the numerators

  2. Multiply the denominators
• Dividing fractions


  Multiply by the reciprocal of the number you're dividing by
• Reciprocal


  The number that, when multiplied by the original number, gives 1
• Multiplying decimals


  1. Ignore the decimal point and multiply the numbers

  2. Count the total number of decimal places and put the decimal point in the answer accordingly
• Dividing by decimals


  1. Multiply both the number you're dividing and the number you're dividing by by a power of 10 to make the divisor a whole number

  2. Divide the numerator by the denominator
• Divide the number you're dividing and the number you're dividing by by 10


  You get the same answer
• Convert 1.2 divided by 0.04 to whole numbers

  1. Multiply both numbers by 100

  2. 1.2 becomes 120

  3. 0.04 becomes 4
• Convert 17/20 to a decimal

  1. Divide the numerator by the denominator

  2. The answer is 0.85
• Convert 0.85 to a percentage

  1. Multiply by 100

  2. The answer is 85%
• Convert 0.315 to a fraction

  The fraction is 63/200
• Convert 194% to a fraction

  The fraction is 97/50
• Convert 2/11 to a decimal


  1. Divide 2 by 11

  2. The answer is 0.181818 (recurring decimal)
• Convert 0.181818 to a percentage

  1. Multiply by 100

  2. The answer is 18.1818%
• Recurring decimals can be written as fractions using algebra
• Convert 0.0262626 to a fraction

  1. Let x = 0.0262626

  2. Multiply x by 10 and 1000 to get two equations

  3. Solve the equations to get x = 26/990
• Round 394 to 2 significant figures


  The answer is 390
• Round 1273 to 2 significant figures


  The answer is 1300
• Round 7961 to 2 significant figures

  The answer is 8000
• Round 0.618 to 2 significant figures

  The answer is 0.62
• Round 20.501 to 2 significant figures

  The answer is 21
• The next topic is using a calculator
• Calculate 5^3 - √2 / tan(32)

  1. Use the calculator buttons to enter the expression

  2. The answer is 197.7786013
• Negative power of 2

  1 over 100
• Working out a negative power


  1. Put 1 over it

  2. Use the positive power on the denominator
• Fractional indices


  X to the power of 1/n = nth root of X
• Fractional indices


  • X to the power of 1/2 = square root of X
  • X to the power of 1/3 = cube root of X
  • X to the power of 1/4 = fourth root of X
• Working out fractional indices


  1. Whatever is on the denominator, take that root

  2. Whatever is on the numerator, do that power
• 16 to the power of 1/4 = 2
• 4 to the power of 5/2 = 32
• 125 to the power of 2/3 = 25
• 49 to the power of -1/2 = 1/7
• 64 to the power of -2/3 = 1/16
• Fractional indices of a fraction

  • Square root the numerator and denominator
  • Cube root the numerator and denominator
  • Take the root of the numerator and denominator based on the denominator of the power, then do the power on the result
• Negative fractional indices


  Take the reciprocal of the fraction, then apply the positive fractional power
• Lowest Common Multiple (LCM)


  The first number that appears in the multiples of both numbers
• Highest Common Factor (HCF)


  The largest number that divides both numbers without a remainder
• Product of primes


  Every whole number greater than 1 is either prime or can be written as a product of primes
• Writing a number as a product of primes

  1. Use a prime factor tree to break down the number into its prime factors

  2. Write the prime factors in index form