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.
- [latex]\dfrac{1}{4}[/latex] [latex]\dfrac{3}{5}[/latex]
- [latex]\dfrac{5}{8}[/latex] [latex]\dfrac{3}{4}[/latex]
- [latex]\dfrac{1}{5}[/latex] [latex]\dfrac{2}{3}[/latex]
- [latex]\dfrac{2}{3}[/latex] [latex]\dfrac{3}{4}[/latex]
- [latex]\dfrac{49}{56}[/latex] [latex]\dfrac{3}{4}[/latex]
- [latex]\dfrac{75}{90}[/latex] [latex]\dfrac{10}{11}[/latex]
- [latex]\dfrac{33}{70}[/latex] [latex]\dfrac{1}{2}[/latex]
- [latex]\dfrac{1}{3}[/latex] [latex]\dfrac{1}{9}[/latex]
Answers to Exercise One
- <
- <
- <
- <
- >
- <
- <
- >
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?
- Decide to convert either the fraction into a decimal, or the decimal into a fraction. Let’s pick converting the fraction into a decimal.
- 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
- Compare [latex]0.375\underline{\hspace{0.5em}>\hspace{0.5em}}0.125[/latex]
- 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?
- Pick which you will convert, the decimal into the fraction, or the fraction into the decimal. Let’s pick converting the decimal this time.
- Convert 0.6= [latex]\dfrac{6}{10}\left(\dfrac{ ÷ 2}{ ÷ 2}\right) = \dfrac{3}{5}[/latex]
- 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]
- 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
- 0.25 [latex]\dfrac{1}{5}[/latex]
- [latex]\dfrac{1}{8}[/latex] 0.8
- [latex]\dfrac{1}{6}[/latex] 0.125
- 0.2 [latex]\dfrac{3}{10}[/latex]
- 0.3725 [latex]\dfrac{2}{3}[/latex]
- [latex]\dfrac{2}{5}[/latex] 0.5
- 0.3725 [latex]\dfrac{1}{5}[/latex]
Answers to Exercise Two
- >
- <
- >
- <
- <
- <
- >
Exercise 3
Compare the following numbers to each other. Use > or < .
- 0.345 [latex]\dfrac{6}{7}[/latex]
- [latex]\dfrac{1}{1051}[/latex] 0.0032
- 0.52 [latex]\dfrac{2}{3}[/latex]
- 0.6894 [latex]\dfrac{103}{278}[/latex]
- [latex]\dfrac{1}{72}[/latex] [latex]\dfrac{2}{3}[/latex]
Answers to Exercise Three
- >
- <
- >
- <
- <
Topic B Self-Test
Mark /18 Aim 15 / 18
- Write as common fractions in lowest terms. (4 marks)
- 3.6
- 8.125
- 0.75
- 0.45
- Write as decimals. Round your answers to 3 decimal places. (4 marks)
- [latex]\dfrac{3}{5}[/latex]
- [latex]\dfrac{6}{100}[/latex]
- [latex]\dfrac{3}{8}[/latex]
- [latex]\dfrac{5}{7}[/latex]
- Compare the following fractions and decimals, use < , or >. (6 marks)
- 0.862 [latex]\dfrac{6}{7}[/latex]
- [latex]\dfrac{3}{14}[/latex] 0.35
- [latex]\dfrac{1}{10}[/latex] 0.007
- 0.3 [latex]\dfrac{20}{26}[/latex]
- 0.5 [latex]\dfrac{10}{21}[/latex]
- [latex]\dfrac{89}{90}[/latex] 0.473
- [latex]\dfrac{1}{3}[/latex] [latex]\dfrac{1}{9}[/latex]
- Problems. 4 marks
- May babysat for [latex]4 \tfrac{1}{4}[/latex] hours. She is paid $4.75 an hour. How much did she earn?
- 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
-
- [latex]3\dfrac{10}{21}[/latex]
- [latex]8\dfrac{1}{8}[/latex]
- [latex]\dfrac{3}{4}[/latex]
- [latex]\dfrac{9}{20}[/latex]
-
- 0.3
- 0.06
- 0.375
- 0.174
-
- >
- <
- >
- <
- >
- >
-
- $20.19
- 0.75 L