Mathematics 7th grade | UNIT 7: Fractions 7.3 Comparing fractions
There are several different ways that you can compare two fractions. One way is to use diagrams like these.
In the first rectangle $\frac{1}{3}$ is shaded.
In the second rectangle $\frac{1}{4}$ is shaded.
You can see that $\frac{1}{4}$ is smaller than $\frac{1}{3}$, so you write $\frac{1}{4} < \frac{1}{3}$
Or you can say that $\frac{1}{3}$ is bigger than $\frac{1}{4}$, so you write $\frac{1}{3} > \frac{1}{4}$.
Another way to compare two fractions is to use your calculator.
Take the fraction $\frac{1}{3}$. To change $\frac{1}{3}$ into a decimal, work out $1 \div 3$. "The answer is 0/33…
0/33... is called a recurring decimal. The three dots at the end show that the number goes on for ever.
So $\frac{1}{3} = 0/33...$
Now do the same to $\frac{1}{4}$. To change $\frac{1}{4}$ into a decimal, work out $1 - 4$. The answer is 0/25. So $\frac{1}{4} = 0/25$.
You can now compare the decimal numbers. 0/25 is smaller than 0/33... so you can write $\frac{1}{4} < \frac{1}{3}$.
Worked example 7.3
a: i- Write the fractions $\frac{3}{4}$ and $\frac{7}{8}$ in the correct positions on this (
) number line.
ii- Which is the larger fraction?
b: Use your calculator to work out which is the smaller fraction out of $\frac{3}{5}$ and $\frac{2}{3}$
a: i- (
) The black lines show the eighths and the red lines show the quarters.
ii- $\frac{7}{8}$ is the larger.
$\frac{7}{8}$ is closer to 1 than $\frac{3}{4}$, so is the bigger of the two.
b: $\frac{3}{5} = 3 \div 5 = 0/6$
Divide the numerator by the denominator.
$\frac{2}{3} = 2 \div 3 = 0/66...$
Write down the first two decimal places then ... to show the decimal carries on.
$\frac{3}{5}$ is the smaller.
Exercise 7.3
1) a: Copy the number line.
Write the fractions $\frac{1}{2}$ and $\frac{2}{3}$ in the correct positions on the number line.
b: Which is the larger fraction?
2) a: Copy the number line.
Write the fractions $\frac{4}{5}$ and $\frac{7}{10}$ in the correct positions on the number line.
b: Which is the larger fraction?
3) In each part of the question copy the shapes, then:
• shade in the fraction that is shown next to each shape
• write down which is the smaller of the two fractions.
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4) Use your calculator to work out which is the larger of the two fractions in each pair.
a: $\frac{1}{4}$ and $\frac{3}{10}$
b: $\frac{5}{8}$ and $\frac{13}{20}$
c: $\frac{1}{6}$ and $\frac{2}{15}$
d: $\frac{2}{7}$ and $\frac{3}{8}$
5) Write the symbol cor > between each pair of fractions.
a: $\frac{3}{4}....\frac{7}{8}$
b: $\frac{2}{5}....\frac{3}{7}$
c: $\frac{7}{{15}}....\frac{{11}}{{25}}$
d: $\frac{8}{{15}}....\frac{{12}}{{15}}$
6) $\frac{1}{8}$ is bigger than $\frac{1}{7}$ because 8 is bigger than ${7^3}$. Is this correct? Explain your answer.
7) This is part of Roman's homework. Is he right? Explain your answer.
Question
which is larger, $\frac{6}{{31}}$ or $\frac{9}{{47}}$?
Solution
$\frac{6}{{31}} = 6 \div 31 = 0.19\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{9}{{47}} = 9 \div 47 = 0/19$
Neither is larger as they are both the same size.
8) Hassan says: 'I am thinking of a fraction. My fraction is bigger than $\frac{2}{5}$ but smaller than $\frac{2}{3}$
When I divide the numerator by the denominator I get an answer of 0/533.'
What fraction is Hassan thinking of?