JSS1: MATHEMATICS  1ST TERM

Whole Numbers I  Week 13 Topics1 Quiz

Whole Numbers II  Week 21 Topic1 Quiz

Counting in Base Two  Week 34 Topics1 Quiz

Arithmetic Operations  Week 43 Topics1 Quiz

Lowest Common Multiple (LCM)  Week 52 Topics1 Quiz

Highest Common Factor  Week 61 Topic1 Quiz

Fraction  Week 77 Topics1 Quiz

Basic Operations with Fractions I  Week 83 Topics1 Quiz

Basic Operations with Fractions II  Week 91 Topic1 Quiz

Directed Numbers  Week 103 Topics1 Quiz

Estimation and Approximation I  Week 113 Topics1 Quiz

Estimation and Approximation II  Week 126 Topics1 Quiz
Arranging Fractions in Order of Size
Topic Content:
 Fractions with Same Denominators
 Fraction with Different Denominators
 Worked Examples
Fractions with Same Denominators:
The four shapes below are of the same size and they are divided in different ways.
You can see that;
\(\frac{4}{5}\) is greater than \(\frac{3}{5}\)
\(\frac{3}{5}\) is greater than \(\frac{2}{5}\)
When a set of fractions have equal denominators, and the denominators of the fractions are equal (i.e. the same), the one with the largest numerator is the largest fraction and the one with the smallest numerator is the least.
⇒ the order of size is:
\( \frac{1}{5}, \: \frac{2}{5}, \:\frac{3}{5}, \:\frac{4}{5}\) in ascending order.
\( \frac{4}{5}, \: \frac{3}{5}, \:\frac{2}{5}, \:\frac{1}{5}\) in descending order.
Fraction with Different Denominators:
Three shapes of the same size are shown below. It is obvious from these shapes that:
\(\frac{1}{2}\) is larger than \(\frac{1}{4}\)
\(\frac{1}{4}\) is larger than \(\frac{2}{9}\)
\(\frac{1}{2}, \: \frac{1}{4}, \: \frac{2}{9}\) in descending order
Worked Example 7.3.1:
Which is greater \(\frac{4}{5}\) or \(\frac{2}{3} \scriptsize\: ?\)
Solution:
Find the LCM of the denominators i.e. LCM of 3 and 5 is 15.
Write each fraction with the same denominator (i.e. is) by using equivalent fractions.
\( \frac {2}{3}= \frac {2}{3} \: \times \: \frac {5}{5}= \frac {10}{15} \) \( \frac {4}{5} = \frac {4}{5} \: \times \: \frac {3}{3}= \frac {12}{15} \)This means \(\normalsize \frac{2}{3} = \frac{10}{15} \scriptsize \: and \: \normalsize \frac{4}{5} = \frac{12}{15} \)
Comparing the size of the numerators of the equivalent fraction, \( \frac{4}{5}\) is greater than \( \frac{2}{3}\).
Worked Example 7.3.2:
Arrange the following factors in ascending order: \( \frac {2}{3}, \frac {3}{8}, \frac {1}{4}, \: \frac {5}{6} \)
Solution:
Find the LCM of the denominator 3, 8, 4 and 5 is 24
Therefore, the equivalent fractions are:
\( \frac {2}{3} = \frac {2}{3} \: \times \: \frac {8}{8}= \frac {16}{24} \) \( \frac {3}{8} = \frac {3}{8} \: \times \: \frac {3}{3}= \frac {9}{24} \) \( \frac {1}{4} = \frac {1}{4} \: \times \: \frac {6}{6}= \frac {6}{24} \) \( \frac {5}{6} = \frac {5}{6} \: \times \: \frac {4}{4}= \frac {20}{24} \)By comparing the sizes of the numerators of the equivalent fractions in ascending order, we have
\( \frac {6}{24}, \frac {9}{24}, \frac {16}{24}, \frac {20}{24} \)Here, the given fractions in descending order gives:
\( \frac {1}{4}, \frac {3}{8}, \frac {2}{3}, \frac {5}{6} \)