fractions, decimals, percentages, and recurring decimals

fractions, decimals, percentages, and recurring decimals

1. multiplication

   • to multiply fractions, multiply the top and bottom separately
     • EXAMPLE:
       • what is 2/3 x 1/3?
         • 2 x 1 = 2
           • 3 x 3 = 9
           • the answer is 2 / 9

2. division

   • you flip one of them, and the multiply
     • EXAMPLE:
       • what is 4/3 / 2/5?
         • same as 3/4 x 2/5
           • 3 x 2 = 6
             • 4 x 5 = 20
             • the answer is 6 / 20

3. addition and subtraction

   • first, make the denominators the same, and the add or subtract the numerators
     • EXAMPLE - SUBTRACTION:
       • 1/3 - 2/7
         • 7/21 - 6/21
           • 1/21
     • EXAMPLE - ADDITION:
       • 4/5 + 1/2
         • 8/10 + 5/10
           • 13/10

4. recognising recurring + terminating decimals

   • all fractions where the denominator has prime factors of only 2 or 5, it will have terminating decimals (they come to an end). all others will give recurring decimals.

5. how to convert to and from recurring decimals

   • turning a recurring decimal into a fraction when the first recurring number is after the decimal point
     • let r = your recurring decimal eg r = 0. ´2 3 ´4
       • 1000 r = 234. ´2 3 ´4
         • 1000 r - r = 234
           • 999r = 234
             • r = 234/999
   • turning recurring decimal to fraction when the first recurring number isn't right after the decimal point
     • so let r = your decimal, eg r = 0.1 ´6
       • multiply r by a power of 10, to move the recurring number to the decimal point, so 10r = 1. ´6
         • now multiply agian, to move the recurring point pass the decimal point, 100r = 16. ´6
           • 100r - 10r = 15
             • 90r = 15
               • r = 15 / 90 = 1/6
   • fractions into recurring decimals
     • eg, write 8/33 as a recurring decimal
       • find an equivalent with all 9s as the denominator, so 24/99
         • this tells you the recurring part, so 24/99 = 0. ´2´4
           • if you have a calculator, you can just do bus stop method and do the division to find out