Samacheer Kalvi Class 5 Maths Solutions Term 3 Chapter 6 Fractions Exercise 6.3

Tamilnadu Samacheer Kalvi 5th Maths Solutions Term 3 Chapter 6 Fractions 6.3

Question 1. Convert the following into like fractions
(i) \( \frac{1}{4}, \frac{3}{8} \)
(ii) \( \frac{2}{5}, \frac{1}{7} \)
(iii) \( \frac{2}{5}, \frac{3}{10} \)
(iv) \( \frac{2}{7}, \frac{1}{6} \)
(v) \( \frac{1}{3}, \frac{3}{4} \)
(vi) \( \frac{5}{6}, \frac{4}{5} \)
(vii) \( \frac{1}{8}, \frac{3}{7} \)
(viii) \( \frac{1}{6}, \frac{4}{9} \)
Answer:
(i) To make the denominators the same, we notice that 8 is double 4. So, we change \( \frac{1}{4} \) into \( \frac{2}{8} \).
\( \frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8} \)
Now, \( \frac{2}{8} \) and \( \frac{3}{8} \) are like fractions because they both have 8 as the denominator. Having a common denominator makes it easier to compare or add these fractions.
(ii) First, we find a common multiple for 5 and 7, which is 35. We convert \( \frac{2}{5} \) to \( \frac{14}{35} \) by multiplying both top and bottom by 7.
\( \frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35} \)
Next, we convert \( \frac{1}{7} \) to \( \frac{5}{35} \) by multiplying both top and bottom by 5.
\( \frac{1}{7} = \frac{1 \times 5}{7 \times 5} = \frac{5}{35} \)
So, \( \frac{14}{35} \) and \( \frac{5}{35} \) are the like fractions. The least common multiple (LCM) is often the easiest common denominator to work with.
(iii) Since 10 is twice 5, we use 10 as the common denominator. We change \( \frac{2}{5} \) to \( \frac{4}{10} \) by multiplying the numerator and denominator by 2.
\( \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \)
This makes \( \frac{4}{10} \) and \( \frac{3}{10} \) the like fractions needed. Choosing the larger denominator if it's a multiple of the smaller one saves a step.
(iv) To find a common denominator for 7 and 6, we find their common multiple, which is 42. We convert \( \frac{2}{7} \) to \( \frac{12}{42} \) by multiplying both parts by 6.
\( \frac{2}{7} = \frac{2 \times 6}{7 \times 6} = \frac{12}{42} \)
Then, we convert \( \frac{1}{6} \) to \( \frac{7}{42} \) by multiplying both parts by 7.
\( \frac{1}{6} = \frac{1 \times 7}{6 \times 7} = \frac{7}{42} \)
So, \( \frac{12}{42} \) and \( \frac{7}{42} \) are the like fractions. Multiplying the two denominators together (7 * 6 = 42) is a simple way to find a common denominator when they don't share common factors.
(v) We use 12 as the common denominator since it is a multiple of both 3 and 4. We change \( \frac{1}{3} \) to \( \frac{4}{12} \) by multiplying both top and bottom by 4.
\( \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \)
Then, we change \( \frac{3}{4} \) to \( \frac{9}{12} \) by multiplying both top and bottom by 3.
\( \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \)
This gives us \( \frac{4}{12} \) and \( \frac{9}{12} \) as like fractions. The smallest common multiple helps keep the numbers in the fractions easy to manage.
(vi) We find that 30 is a common multiple for both 6 and 5, so we use it as the common denominator. To convert \( \frac{5}{6} \), we multiply both numerator and denominator by 5, getting \( \frac{25}{30} \).
\( \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} \)
To convert \( \frac{4}{5} \), we multiply both by 6, getting \( \frac{24}{30} \).
\( \frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30} \)
Thus, \( \frac{25}{30} \) and \( \frac{24}{30} \) are the like fractions. When the denominators don't share factors, multiplying them together (6 * 5 = 30) often gives the least common denominator.
(vii) For 8 and 7, 56 is a common multiple, so we make 56 the common denominator. We convert \( \frac{1}{8} \) to \( \frac{7}{56} \) by multiplying both top and bottom by 7.
\( \frac{1}{8} = \frac{1 \times 7}{8 \times 7} = \frac{7}{56} \)
We convert \( \frac{3}{7} \) to \( \frac{24}{56} \) by multiplying both top and bottom by 8.
\( \frac{3}{7} = \frac{3 \times 8}{7 \times 8} = \frac{24}{56} \)
So, \( \frac{7}{56} \) and \( \frac{24}{56} \) are the like fractions. Finding the least common multiple helps simplify calculations later on.
(viii) First, we list the multiples of 6 and 9 to find their smallest common multiple, which is 18.
Multiples of 6: 6, 12, 18, 24, 30, 36, ......
Multiples of 9: 9, 18, 27, 36, 45, ......
Smallest common multiple: 18
We convert \( \frac{1}{6} \) to \( \frac{3}{18} \) by multiplying both numerator and denominator by 3.
\( \frac{1}{6} = \frac{1 \times 3}{6 \times 3} = \frac{3}{18} \)
We convert \( \frac{4}{9} \) to \( \frac{8}{18} \) by multiplying both by 2.
\( \frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18} \)
Therefore, \( \frac{3}{18} \) and \( \frac{8}{18} \) are the like fractions. Finding the LCM ensures that the new denominators are the smallest possible, making future calculations simpler.
In simple words: To change fractions into "like fractions," we must make their bottom numbers (denominators) the same. We do this by finding a number that both denominators can divide into evenly, which is called the common denominator. Then, we multiply the top and bottom of each fraction by a number so that its denominator becomes the common denominator.

🎯 Exam Tip: Always look for the least common multiple (LCM) of the denominators to make calculations simpler and avoid larger numbers.