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Numbers

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Published in: Mathematics
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Fractions Decimals Percentages Equivalence and conversions between them

Divya J / Dubai

15 years of teaching experience

Qualification: CAIE and Pearson Examiner for IGCSE an AS Levels, Masters in Mathematics

Teaches: SAT, ACT, Maths, IGCSE/AS/AL, Physics, Biology, Chemistry, Mathematics

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  1. Mathematics Lecture No Numbers Today's Targets Fractions Decimals O Percentages Equivalence and conversions between them .- 03
  2. Fractions Proper fractions Improper fractions Mixed Fraction/ Mixed Number Like Fractions Unlike fractions Changing a mixed number to an improper fraction and vice versa Convert the improper fraction to mixed fraction Simplifying fractions Operations on fractions Changing a fraction to a decimal and percentage and vice versa Recurring decimals to fractions
  3. Question Simplify: (a)
  4. Question Evaluate the following (b)
  5. Question Change to improper
  6. Question Change to mixed number
  7. Question Change the following fraction to percentage
  8. Question Convert each of the following percentage to fractions in their simplest form. 25%
  9. Question Change the following fractions to decimals
  10. Question Change the following decimal to fraction. 0.04
  11. Question Convert the following decimals to fractions, giving your answer in its simplest form: (a) (b) 0.0009
  12. Question Write the following recurring decimals as fractions in lowest form. 0.264
  13. [M16 22, Q6] Write the recurring decimal 0.4 as a fraction. [0.4 means 0.444 ..........l
  14. [M17 22, Q6] Write the recurring decimal 0.1 i as a fraction. Show all your working. • [21
  15. [Su 22, QB] Without using your calculator, work out - Write down all the steps of your working. [31
  16. [WIG 21, Q12] (a) Write $0.70 as a fraction of $5.60, giving your answer in its lowest terms.
  17. [WIG 21, Q12] (b) Write the recurring decimal 0. as a fraction in its lowest terms. [0. ié means 0.181818...........]
  18. [W15, 41, Ql(a)] (a) Luc is painting the doors in his house. He uses — of a tin of paint for each door. Work out the least number of tins of paint Luc needs to paint 7 doors • [31
  19. [W13, 41, Ql(a-i)] David sells fruit at the market. (a) In one week, David sells 120 kg of tomatoes and 80 kg of grapes. (i) Write 80 kg as a fraction of the total mass of tomatoes and grapes. Give your answer in its lowest terms.
  20. Revision Proper fractions: A proper fraction is a fraction whose numerator value is less than that of the denominator. Improper fractions: An improper fraction (sometimes called a top-heavy fraction) has its numerator more than its denominator. Mixed Fraction/ Mixed Number: A mixed number is made up of a whole number and a proper fraction. Like Fractions: When two fractions have the same denominator, then they are said to be like fractions. Unlike fractions: When two fractions have different denominators, then they are said to be unlike fractions.
  21. Revision Changing a mixed number to an improper fraction and vice versa Step-I: Multiply the whole number by denominator. Step-2: Add the numerator to the result of step 1. Step-3: Write the result of step 2 as the numerator on top of the same denominator, i.e., original divisor (denominator) will be the new denominator. To convert the improper fraction to mixed fraction, follow the steps given below: Step-I: Divide the numerator by denominator. Step-2: Now, write down the quotient as the whole number part. Step-3: Write the remainder as the numerator on top of the same denominator, i.e., original divisor (denominator) will be the new denominator.
  22. Revision To simplify a fraction, we divide the numerator (the top of the fraction) and the denominator (the bottom of the fraction) by the same amount, until we can't simplify anymore. This form of fraction is called its simplest form. Another way of saying 'simplest form' is 'lowest terms'.
  23. Revision A recurring decimal is any number with a repeated digit or section of repeated digits after a decimal point. We show this with a dot above both the start and the end of the repeated section. Converting recurring decimals as fractions: Write out the first few decimal places to show the recurring pattern and then: 1. 2. 3. 4. Write the recurring decimal x = Multiply both sides by 10 repeatedly until two lines have the same recurring decimal part (in order). Subtract those two lines DIVIDE both sides to get x = (and cancel if necessary to get fraction in lowest terms)

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