ADDING AND SUBTRACTING FRACTIONS

We Need Equivalent Fractions To Add and Subtract Fractions ALL the denominators must be the SAME before you do anything else ! This is called Finding A Common Denominator which is done by using Equivalent Fractions and Common Multiples. Can you remember what these are ?

Reminder of Equivalent Fractions REMINDER: Equivalent Fractions are obtained by multiplying a fraction top and bottom by the SAME number. e.g. 1/3 (x3) gives 3/9. 1/3 = 3/9, They are Equivalent Fractions, the numbers top & bottom are different but the whole number is the same.

Reminder Of Common Multiples A MULTIPLE of any number is simply the number that is obtained by any multiplication. e.g. 56 is a multiple of 7, 108 is a multiple of 9, 120 is a multiple of 8 ......... and so on (Remember: A FACTOR is the other way e.g. 7 is a factor of 56, 9 is a factor of 108, 8 is a factor of 120 ...... and so on)

Finding A Common Denominator Question: Find 1/5 + 2/3 Find a Common Multiple of the denominators 5 and 3, one way is to multiply them together 5x3 = 15. Convert 1/5 and 2/3 to Equivalent Fractions with a Common Denominator of 15, 1/5 = 3/15, 2/3 = 10/15 (doing same top & bottom) Add numerators (top numbers) 3/15 + 10/15 = 13/15 - the answer ! Lets do another ....

Adding Fractions Question: Find 2/5 + 4/7 1. Common Multiple of denominators 5 and 7 is 7x5 = 35 2. Convert to Equivalent Fractions “thirty-fifths” 2/5 becomes 14/35 and 4/7 becomes 20/35 (because we must do the same top & bottom) 3. Because denominators are the same we can add numerators 14/35 + 20/35 = 34/35

Subtracting Fractions Subtracting fractions has the same method BUT in the final step you SUBTRACT instead of add. Question Find 3/5 – 1/4 Common Multiple = 20 Convert 3/5 to 12/20 and 1/4 to 5/20 Denominators are the same so we can answer the question 12/20 – 5/20 = 7/20

Quick Test 1. 1/2 + 3/7, Common Denominator = ? 2. 3/4 + 1/5, Common Denominator = ? 3. 7/8 – 2/5, Common Denominator = ? 4. 5/9 – 1/3, Common Denominator = ?

Quick Test Answers 1. 1/2 + 3/7, Common Denominator = 14 7/14 + 6/14 = 13/14 3/4 + 1/5, Common Denominator = 20 15/20 + 4/20 = 19/20 3. 7/8 – 2/5, Common Denominator = 40 35/40 – 16/40 = 19/40 4. 5/9 – 1/3, Common Denominator = 9 5/9 – 3/9 = 2/9 (9 and 3 already multiples !)

Summary Before we can add or subtract fractions we need to make some adjustments We use Common Multiples for NEW Denominators and convert to Equivalent Fractions. When we have Common Denominators we can add or subtract the numerators