Samacheer Kalvi Class 5 Maths Solutions Term 3 Chapter 6 Fractions Exercise 6.2

Question 1. Write the suitable number in the box.
(i) \( \frac { 1 }{ 2 } = \frac { \Box }{ 8 } \)
Answer: To make the denominator 8, we multiply 2 by 4. So, we must also multiply the numerator 1 by 4 to find the equivalent fraction.
\( \frac { 1 }{ 2 } = \frac { 1 \times 4 }{ 2 \times 4 } = \frac { 4 }{ 8 } \)
(ii) \( \frac { 1 }{ 3 } = \frac { 7 }{ \Box } \)
Answer: Here, the numerator 1 is multiplied by 7 to become 7. So, we multiply the denominator 3 by 7 too.
\( \frac { 1 }{ 3 } = \frac { 1 \times 7 }{ 3 \times 7 } = \frac { 7 }{ 21 } \)
(iii) \( \frac { 9 }{ 11 } = \frac { 18 }{ \Box } \)
Answer: The numerator 9 is multiplied by 2 to get 18. So, we multiply the denominator 11 by 2.
\( \frac { 9 }{ 11 } = \frac { 9 \times 2 }{ 11 \times 2 } = \frac { 18 }{ 22 } \)
(iv) \( \frac { 5 }{ 15 } = \frac { \Box }{ 3 } \)
Answer: The denominator 15 is divided by 5 to get 3. So, we divide the numerator 5 by 5 to find the missing number.
\( \frac { 5 }{ 15 } = \frac { 5 \div 5 }{ 15 \div 5 } = \frac { 1 }{ 3 } \)
(v) \( \frac { 14 }{ 26 } = \frac { \Box }{ 13 } \)
Answer: The denominator 26 is divided by 2 to get 13. So, we divide the numerator 14 by 2 to keep the fraction equivalent.
\( \frac { 14 }{ 26 } = \frac { 14 \div 2 }{ 26 \div 2 } = \frac { 7 }{ 13 } \)
(vi) \( \frac { \Box }{ 4 } = \frac { 8 }{ 16 } \)
Answer: We see that the denominator 16 is divided by 4 to get 4. So, we divide the numerator 8 by 4 to find the missing numerator.
\( \frac { 8 }{ 16 } = \frac { 8 \div 4 }{ 16 \div 4 } = \frac { 2 }{ 4 } \)
(vii) \( \frac { 1 }{ \Box } = \frac { 7 }{ 28 } \)
Answer: The numerator 7 is divided by 7 to get 1. So, we divide the denominator 28 by 7 to find the missing denominator.
\( \frac { 7 }{ 28 } = \frac { 7 \div 7 }{ 28 \div 7 } = \frac { 1 }{ 4 } \)
(viii) \( \frac { \Box }{ 5 } = \frac { 15 }{ 25 } \)
Answer: The denominator 25 is divided by 5 to get 5. So, we must also divide the numerator 15 by 5 to find the equivalent fraction.
\( \frac { 15 }{ 25 } = \frac { 15 \div 5 }{ 25 \div 5 } = \frac { 3 }{ 5 } \)
In simple words: To find an equivalent fraction, you must multiply or divide both the top and bottom numbers by the same non-zero number. This keeps the fraction's value the same, even if it looks different.

🎯 Exam Tip: Always remember to apply the same operation (multiplication or division) to both the numerator and the denominator to maintain the fraction's value.

Question 2. Find an equivalent fraction with denominator 18 for each of the following fractions \( \frac{1}{2}, \frac{2}{3}, \frac{4}{6}, \frac{2}{9}, \frac{7}{9}, \frac{5}{3} \)
Answer: To get a denominator of 18, we multiply the original denominator by the necessary number, and then multiply the numerator by the same number.
For \( \frac{1}{2} \): \( \frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18} \)
For \( \frac{2}{3} \): \( \frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18} \)
For \( \frac{4}{6} \): \( \frac{4}{6} = \frac{4 \times 3}{6 \times 3} = \frac{12}{18} \)
For \( \frac{2}{9} \): \( \frac{2}{9} = \frac{2 \times 2}{9 \times 2} = \frac{4}{18} \)
For \( \frac{7}{9} \): \( \frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18} \)
For \( \frac{5}{3} \): \( \frac{5}{3} = \frac{5 \times 6}{3 \times 6} = \frac{30}{18} \)
In simple words: We changed each fraction so that its bottom number is 18. We did this by multiplying both the top and bottom of each fraction by whatever number was needed to make the bottom 18.

🎯 Exam Tip: Always check if the original fraction can be simplified before finding an equivalent fraction, though it's not strictly necessary for this type of problem. Make sure to multiply both numerator and denominator by the same factor.

Question 3. Find an equivalent fraction with denominator 5 for each of the following fractions \( \frac{6}{15}, \frac{10}{25}, \frac{12}{30}, \frac{6}{10}, \frac{21}{35} \)
Answer: To get a denominator of 5, we divide the original denominator by the necessary number, and then divide the numerator by the same number.
For \( \frac{6}{15} \): \( \frac{6}{15} = \frac{6 \div 3}{15 \div 3} = \frac{2}{5} \)
For \( \frac{10}{25} \): \( \frac{10}{25} = \frac{10 \div 5}{25 \div 5} = \frac{2}{5} \)
For \( \frac{12}{30} \): \( \frac{12}{30} = \frac{12 \div 6}{30 \div 6} = \frac{2}{5} \)
For \( \frac{6}{10} \): \( \frac{6}{10} = \frac{6 \div 2}{10 \div 2} = \frac{3}{5} \)
For \( \frac{21}{35} \): \( \frac{21}{35} = \frac{21 \div 7}{35 \div 7} = \frac{3}{5} \)
In simple words: We simplified each fraction so that its bottom number became 5. We did this by dividing both the top and bottom of each fraction by a common number.

🎯 Exam Tip: When simplifying fractions, always look for the greatest common divisor (GCD) of the numerator and denominator to reduce the fraction in one step, or divide by common factors repeatedly until it cannot be simplified further.