Unit 5: Common Fractions & Decimals

# Topic B: Comparing Fractions & Decimals

In Unit 2 you compared simple fractions to simple fractions such as $\dfrac{1}{2}$               $\dfrac{1}{3}$

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

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

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

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

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

Example B

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

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

Exercise 2

Compare

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

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               $\dfrac{6}{7}$
2. $\dfrac{1}{1051}$               0.0032
3. 0.52               $\dfrac{2}{3}$
4. 0.6894               $\dfrac{103}{278}$
5. $\dfrac{1}{72}$               $\dfrac{2}{3}$

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. $\dfrac{3}{5}$
2. $\dfrac{6}{100}$
3. $\dfrac{3}{8}$
4. $\dfrac{5}{7}$
3. Compare the following fractions and decimals, use < , or >. (6 marks)
1. 0.862                 $\dfrac{6}{7}$
2. $\dfrac{3}{14}$                 0.35
3. $\dfrac{1}{10}$                   0.007
4. 0.3               $\dfrac{20}{26}$
5. 0.5                 $\dfrac{10}{21}$
6. $\dfrac{89}{90}$                  0.473
7. $\dfrac{1}{3}$                 $\dfrac{1}{9}$
4. Problems. 4 marks
2. 0.75 L