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Unit 5: Common Fractions & Decimals

Topic B: Comparing Fractions & Decimals

In Unit 2 you compared simple fractions to simple fractions such as 1212               1313

Now, you are going to be asked to compare fractions with larger and less common denominators such as 7878 and 17281728

Find the equivalent fractions of both the fractions and then compare.
12(×3×3)=3612(×3×3)=36 and 13(×2×2)=2613(×2×2)=26 so 36263626

78(×7×7)=495678(×7×7)=4956 and 1728(×2×2)=34561728(×2×2)=3456 so 4956345649563456

Exercise 1

Change the fractions to have the same denominators. Decide which is larger. Use > , < , = to mark your answer. There is space below each problem to work out your equivalent fractions.

  1. 1414                3535
  2. 5858                3434
  3. 1515                2323
  4. 2323                3434
  5. 49564956                 3434
  6. 75907590                 10111011
  7. 33703370                 1212
  8. 1313                1919

Answers to Exercise One

  1. <
  2. <
  3. <
  4. <
  5. >
  6. <
  7. <
  8. >

Comparing Fractions to Decimals and Decimals to Fractions

Now that you know how to convert between fractions and decimals, you are also going to be able to compare them.

Example A

Which is larger: 3838 or 0.125?

  1. Decide to convert either the fraction into a decimal, or the decimal into a fraction. Let’s pick converting the fraction into a decimal.
  2. Do the conversion3838 =0.37583.00024  60564040     = 0.375
  3. Compare 0.375>_0.125
  4. Write a math sentence to show your answer: 38>_0.125

Example B

Which is larger78 or 0.6?

  1. Pick which you will convert, the decimal into the fraction, or the fraction into the decimal.  Let’s pick converting the decimal this time.
  2. Convert 0.6= 610(÷2÷2)=35
  3. Compare 783578(×5×5)=354035(×8×8)=2440
  4. Write a math sentence to show your answer 38>_0.6

TIP: You may find that converting the fractions to the decimals could speed things up.

Exercise 2

Compare

  1. 0.25                15
  2. 18                0.8
  3. 16                 0.125
  4. 0.2               310
  5. 0.3725               23
  6. 25               0.5
  7. 0.3725               15

Answers to Exercise Two

  1. >
  2. <
  3. >
  4. <
  5. <
  6. <
  7. >

Exercise 3

Compare the following numbers to each other. Use > or < .

  1. 0.345               67
  2. 11051               0.0032
  3. 0.52               23
  4. 0.6894               103278
  5. 172               23

Answers to Exercise Three

  1. >
  2. <
  3. >
  4. <
  5. <

Topic B Self-Test

Mark /18  Aim 15 / 18

  1. Write as common fractions in lowest terms. (4 marks)
    1. 3.6
    2. 8.125
    3. 0.75
    4. 0.45
  2. Write as decimals. Round your answers to 3 decimal places. (4 marks)
    1. 35
    2. 6100
    3. 38
    4. 57
  3. Compare the following fractions and decimals, use < , or >. (6 marks)
    1. 0.862                 67
    2. 314                 0.35
    3. 110                   0.007
    4. 0.3               2026
    5. 0.5                 1021
    6. 8990                  0.473
    7. 13                 19
  4. Problems. 4 marks
    1. May babysat for 414 hours. She is paid $4.75 an hour. How much did she earn?
    2. Diane bought 1.5 litres of milk. Her thirsty kids drank half of it as soon as she got home. How much milk is left?

Answers to Topic B Self-Test

    1. 31021
    2. 818
    3. 34
    4. 920
    1. 0.3
    2. 0.06
    3. 0.375
    4. 0.174
    1. >
    2. <
    3. >
    4. <
    5. >
    6. >
    1. $20.19
    2. 0.75 L

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Adult Literacy Fundamental Mathematics: Book 5 - 2nd Edition Copyright © by Liz Girard; Wendy Tagami; and Leanne Caillier-Smith is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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