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

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

Find the equivalent fractions of both the fractions and then compare.
${\displaystyle \frac{1}{2}}\left({\displaystyle \frac{\times 3}{\times 3}}\right)={\displaystyle \frac{3}{6}}$ and ${\displaystyle \frac{1}{3}}\left({\displaystyle \frac{\times 2}{\times 2}}\right)={\displaystyle \frac{2}{6}}$ so ${\displaystyle \frac{3}{6}}\ge {\displaystyle \frac{2}{6}}$

${\displaystyle \frac{7}{8}}\left({\displaystyle \frac{\times 7}{\times 7}}\right)={\displaystyle \frac{49}{56}}$ and ${\displaystyle \frac{17}{28}}\left({\displaystyle \frac{\times 2}{\times 2}}\right)={\displaystyle \frac{34}{56}}$ so ${\displaystyle \frac{49}{56}}\ge {\displaystyle \frac{34}{56}}$

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.

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. ${\displaystyle \frac{3}{5}}$
   2. ${\displaystyle \frac{6}{100}}$
   3. ${\displaystyle \frac{3}{8}}$
   4. ${\displaystyle \frac{5}{7}}$
3. Compare the following fractions and decimals, use < , or >. (6 marks)
   1. 0.862                 ${\displaystyle \frac{6}{7}}$
   2. ${\displaystyle \frac{3}{14}}$                 0.35
   3. ${\displaystyle \frac{1}{10}}$                   0.007
   4. 0.3               ${\displaystyle \frac{20}{26}}$
   5. 0.5                 ${\displaystyle \frac{10}{21}}$
   6. ${\displaystyle \frac{89}{90}}$                  0.473
   7. ${\displaystyle \frac{1}{3}}$                 ${\displaystyle \frac{1}{9}}$
4. Problems. 4 marks
   1. May babysat for $4\frac{1}{4}$ 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. 1. $3{\displaystyle \frac{10}{21}}$
   2. $8{\displaystyle \frac{1}{8}}$
   3. ${\displaystyle \frac{3}{4}}$
   4. ${\displaystyle \frac{9}{20}}$
2. 1. 0.3
   2. 0.06
   3. 0.375
   4. 0.174
3. 1. >
   2. <
   3. >
   4. <
   5. >
   6. >
4. 1. $20.19
   2. 0.75 L