Unit 5: Common Fractions & Decimals

Topic B: Comparing Fractions & Decimals

In Unit 2 you compared simple fractions to simple fractions such as [latex]\dfrac{1}{2}[/latex]               [latex]\dfrac{1}{3}[/latex]

Now, you are going to be asked to compare fractions with larger and less common denominators such as [latex]\tfrac{7}{8}[/latex] and [latex]\tfrac{17}{28}[/latex]

Find the equivalent fractions of both the fractions and then compare.
[latex]\dfrac{1}{2}\left(\dfrac{×3}{×3}\right) = \dfrac{3}{6}[/latex] and [latex]\dfrac{1}{3}\left(\dfrac{×2}{×2}\right)=\dfrac{2}{6}[/latex] so [latex]\dfrac{3}{6}≥\dfrac{2}{6}[/latex]

[latex]\dfrac{7}{8}\left(\dfrac{×7}{×7}\right)=\dfrac{49}{56}[/latex] and [latex]\dfrac{17}{28}\left(\dfrac{×2}{×2}\right)=\dfrac{34}{56}[/latex] so [latex]\dfrac{49}{56}≥\dfrac{34}{56}[/latex]

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. [latex]\dfrac{1}{4}[/latex]                [latex]\dfrac{3}{5}[/latex]
  2. [latex]\dfrac{5}{8}[/latex]                [latex]\dfrac{3}{4}[/latex]
  3. [latex]\dfrac{1}{5}[/latex]                [latex]\dfrac{2}{3}[/latex]
  4. [latex]\dfrac{2}{3}[/latex]                [latex]\dfrac{3}{4}[/latex]
  5. [latex]\dfrac{49}{56}[/latex]                 [latex]\dfrac{3}{4}[/latex]
  6. [latex]\dfrac{75}{90}[/latex]                 [latex]\dfrac{10}{11}[/latex]
  7. [latex]\dfrac{33}{70}[/latex]                 [latex]\dfrac{1}{2}[/latex]
  8. [latex]\dfrac{1}{3}[/latex]                [latex]\dfrac{1}{9}[/latex]

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: [latex]\dfrac{3}{8}[/latex] 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 conversion[latex]\dfrac{3}{8}[/latex] =[latex]\begin{array}{r}0.375\\ 8\enclose{longdiv}{3.000}\\ 24\downarrow \ \ \\ \hline60\hspace{0.8em}\\56\downarrow\\\hline40\hspace{0.1em}\\40\hspace{0.1em}\\\hline\end{array}[/latex]     = 0.375
  3. Compare [latex]0.375\underline{\hspace{0.5em}>\hspace{0.5em}}0.125[/latex]
  4. Write a math sentence to show your answer: [latex]\dfrac{3}{8}\underline{\hspace{0.5em}>\hspace{0.5em}}0.125[/latex]

Example B

Which is larger[latex]\dfrac{7}{8}[/latex] 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= [latex]\dfrac{6}{10}\left(\dfrac{ ÷ 2}{ ÷ 2}\right) = \dfrac{3}{5}[/latex]
  3. Compare [latex]\dfrac{7}{8}\dfrac{3}{5}[/latex][latex]\longrightarrow\dfrac{7}{8}\left(\dfrac{ × 5}{ × 5}\right) = \dfrac{35}{40}[/latex][latex]\dfrac{3}{5}\left(\dfrac{ × 8}{ × 8}\right) = \dfrac{24}{40}[/latex]
  4. Write a math sentence to show your answer [latex]\dfrac{3}{8}\underline{\hspace{0.5em} >\hspace{0.5em}}0.6[/latex]

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

Exercise 2

Compare

  1. 0.25                [latex]\dfrac{1}{5}[/latex]
  2. [latex]\dfrac{1}{8}[/latex]                0.8
  3. [latex]\dfrac{1}{6}[/latex]                 0.125
  4. 0.2               [latex]\dfrac{3}{10}[/latex]
  5. 0.3725               [latex]\dfrac{2}{3}[/latex]
  6. [latex]\dfrac{2}{5}[/latex]               0.5
  7. 0.3725               [latex]\dfrac{1}{5}[/latex]

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               [latex]\dfrac{6}{7}[/latex]
  2. [latex]\dfrac{1}{1051}[/latex]               0.0032
  3. 0.52               [latex]\dfrac{2}{3}[/latex]
  4. 0.6894               [latex]\dfrac{103}{278}[/latex]
  5. [latex]\dfrac{1}{72}[/latex]               [latex]\dfrac{2}{3}[/latex]

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. [latex]\dfrac{3}{5}[/latex]
    2. [latex]\dfrac{6}{100}[/latex]
    3. [latex]\dfrac{3}{8}[/latex]
    4. [latex]\dfrac{5}{7}[/latex]
  3. Compare the following fractions and decimals, use < , or >. (6 marks)
    1. 0.862                 [latex]\dfrac{6}{7}[/latex]
    2. [latex]\dfrac{3}{14}[/latex]                 0.35
    3. [latex]\dfrac{1}{10}[/latex]                   0.007
    4. 0.3               [latex]\dfrac{20}{26}[/latex]
    5. 0.5                 [latex]\dfrac{10}{21}[/latex]
    6. [latex]\dfrac{89}{90}[/latex]                  0.473
    7. [latex]\dfrac{1}{3}[/latex]                 [latex]\dfrac{1}{9}[/latex]
  4. Problems. 4 marks
    1. May babysat for [latex]4 \tfrac{1}{4}[/latex] 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. [latex]3\dfrac{10}{21}[/latex]
    2. [latex]8\dfrac{1}{8}[/latex]
    3. [latex]\dfrac{3}{4}[/latex]
    4. [latex]\dfrac{9}{20}[/latex]
    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 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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