Write the following fractions in ascending order:
(i) [tex]\frac{25}{36}[/tex], [tex]\frac{5}{9}[/tex], [tex]\frac{2}{3}[/tex], [tex]\frac{5}{6}[/tex]
(ii) [tex]\frac{2}{5}[/tex], [tex]\frac{7}{15}[/tex], [tex]\frac{9}{10}[/tex], [tex]\frac{17}{20}[/tex]
Answer (1)
To write the fractions in ascending order, we need to compare the fractions by expressing them with a common denominator so that we can accurately determine their order.
(i) Fractions: 36 25 , 9 5 , 3 2 , 6 5
Determine a common denominator:
The denominators provided are 36, 9, 3, and 6.
The least common multiple (LCM) of these numbers is 36.
Convert each fraction to have the common denominator of 36:
36 25 remains the same since it's already over 36.
9 5 = 9 × 4 5 × 4 = 36 20
3 2 = 3 × 12 2 × 12 = 36 24
6 5 = 6 × 6 5 × 6 = 36 30
Order the converted fractions in ascending order:
36 20 , 36 24 , 36 25 , 36 30
Therefore, the fractions in ascending order are: 9 5 , 3 2 , 36 25 , 6 5
(ii) Fractions: 5 2 , 15 7 , 10 9 , 20 17
Determine a common denominator:
The denominators provided are 5, 15, 10, and 20.
The least common multiple (LCM) of these numbers is 60.
Convert each fraction to have the common denominator of 60:
5 2 = 5 × 12 2 × 12 = 60 24
15 7 = 15 × 4 7 × 4 = 60 28
10 9 = 10 × 6 9 × 6 = 60 54
20 17 = 20 × 3 17 × 3 = 60 51
Order the converted fractions in ascending order:
60 24 , 60 28 , 60 51 , 60 54
Therefore, the fractions in ascending order are: 5 2 , 15 7 , 20 17 , 10 9
By comparing fractions with the same denominators, we're able to determine their order from smallest to largest effectively.
