Grade 3

• Fraction addition and subtraction

  Adding and subtracting can be applied to mixed number fractions. Each has its own method that helps make sure the numerator and denominator are treated correctly.
• You can only add and subtract fractions when the bottom numbers, or denominators, are the same.
• Method to add or subtract fractions


  1. Multiply the two terms on the bottom to get the same denominator

  2. Multiply the top number on the first fraction with the bottom number of the second fraction to get the new top number of the first fraction

  3. Multiply the top number on the second fraction with the bottom number of the first fraction to get the new top number of the second fraction

  4. Now add/subtract the top numbers and keep the bottom number so that you now have one fraction

  5. Simplify the fraction if required
• Rewriting the calculation using equivalent fractions with a common denominator makes it easier to add or subtract fractions with different denominators.
• Product


  The result of multiplying one number by another, e.g. the product of 4 and 5 is 20 since 4 × 5 = 20
• Numerator


  Number written at the top of a fraction. The numerator is the number of parts used.
• Denominator


  Number written on the bottom of a fraction. The denominator is the number of equal parts.
• The word 'of' can be replaced by 'multiplied by' as it means the same thing
• Mixed number


  A number that is written using a whole number and a fraction, e.g. 3 4⁄5
• Improper fraction


  A fraction where the numerator is greater than the denominator, e.g. 9⁄4
• Highest common factor (HCF)


  The largest factor that will divide into the selected numbers. E.g. 10 is the highest common factor of 30 and 20.
• How to multiply fractions

  1. Multiply the numerators

  2. Multiply the denominators

  3. Simplify the answer
• Example 1: One half of one third equals one half multiplied by one third.

  • 1⁄2 of 1⁄3 is the same as 1⁄2 multiplied by 1⁄3. Work out 1⁄2 of 1⁄3
• How to multiply mixed numbers

  1. Rewrite the mixed numbers as improper fractions

  2. Multiply the numerators

  3. Multiply the denominators

  4. Simplify the answer if possible
• Example 1: Three and one quarter multiplied by one and one half.

  • Multiply 3 1⁄4 by 1 1⁄2
• Percent of a number

  Multiply the number by the fraction form or decimal form of the percent
• Finding percent of a number

  1. Multiply number by fraction form of percent

  2. Multiply number by decimal form of percent
• Percent means per 100
• Percent can be expressed as a fraction or decimal
• Multiplying by the fraction or decimal form of the percent gives the same result
• Sharing an amount into a given ratio

  1. Add the numbers in the ratio

  2. Divide the total amount by the sum of the ratio

  3. Multiply the result by each number in the ratio
• Ratio


  A way of expressing the relationship between two or more quantities
• Ratio


  • 4:3
  • 2:3:7
• Sharing 42 into the ratio 4:3

  1. Add 4 + 3 = 7

  2. Divide 42 by 7 = 6

  3. Multiply 6 by 4 = 24, 6 by 3 = 18
• The answer when sharing 42 into the ratio 4:3 is 24:18
• Sharing 90 pounds into the ratio 3:7

  1. Add 3 + 7 = 10

  2. Divide 90 by 10 = 9

  3. Multiply 9 by 3 = 27, 9 by 7 = 63
• The answer when sharing 90 pounds into the ratio 3:7 is 27 pounds:63 pounds
• Sharing 150 kilograms into the ratio 2:4:3

  1. Add 2 + 4 + 3 = 9

  2. Divide 150 by 9 = 16.67

  3. Multiply 16.67 by 2 = 33.33, 16.67 by 4 = 66.67, 16.67 by 3 = 50
• The answer when sharing 150 kilograms into the ratio 2:4:3 is 33.33 kilograms:66.67 kilograms:50 kilograms
• Solving ratio questions


  1. Find the value of one part

  2. Use the value of one part to calculate the share values
• Ratio


  A way of expressing the relationship between two or more quantities
• Ratio questions are common in GCSE exams, usually involving sharing an amount between two or three people
• Ratio question


  • Sharing 360 pounds in the ratio 7:3:2
• Steps to solve ratio questions

  • Find the value of one part

  2. Use the value of one part to calculate the share values
• The total number of parts in the ratio is the sum of the individual ratios
• The total of the share values equals the original amount of 360 pounds