Samacheer Kalvi Class 5 Maths Solutions Term 3 Chapter 6 Fractions Exercise 6.7

Question 1. Multiply the following
(i) \( \frac{1}{7} \times 4 \)
(ii) \( \frac{3}{8} \times 5 \)
(iii) \( \frac{7}{11} \times 6 \)
(iv) \( \frac{21}{50} \times 2 \)
(v) \( \frac{15}{32} \times 3 \)
Answer:
(i) To multiply a fraction by a whole number, we multiply the numerator by the whole number and keep the denominator the same.
\( \frac{1 \times 4}{7} = \frac{4}{7} \)
(ii) Following the same rule, we multiply the numerator of the fraction by the whole number.
\( \frac{3 \times 5}{8} = \frac{15}{8} \)
(iii) We multiply the numerator by 6, keeping the denominator as 11.
\( \frac{7 \times 6}{11} = \frac{42}{11} \)
(iv) Again, multiply the numerator by 2 and keep the denominator 50.
\( \frac{21 \times 2}{50} = \frac{42}{50} \)
(v) For the last part, multiply the numerator 15 by 3.
\( \frac{15 \times 3}{32} = \frac{45}{32} \)
In simple words: When you multiply a fraction by a whole number, you only multiply the top number (numerator) by the whole number. The bottom number (denominator) stays exactly the same.

🎯 Exam Tip: Remember that a whole number can be thought of as a fraction with a denominator of 1 (e.g., \( 4 = \frac{4}{1} \)), which helps in understanding why only the numerator is multiplied.

Question 2. John has 300 ml of water in a glass and he drinks \( \frac{2}{3} \) of the water. How many ml of water does he drink?
Answer: John has 300 ml of water. He drinks \( \frac{2}{3} \) of this amount. To find out how much water he drinks, we multiply the total amount of water by the fraction. We need to find \( \frac{2}{3} \) of 300 ml.
Water in glass = 300 ml
Amount of water John drinks = \( \frac{2}{3} \times 300 \)
\( = \frac{2 \times 300}{3} \)
\( = \frac{600}{3} \)
\( = 200 \) ml
So, John drinks 200 ml of water.
In simple words: John had 300 ml of water. He drank two-thirds of it. To find two-thirds of 300, we multiply \( \frac{2}{3} \) by 300, which gives us 200 ml.

🎯 Exam Tip: When you need to find a fraction "of" a number, it means you should multiply the fraction by that number. Simplify the calculation by dividing first if possible, like \( 300 \div 3 = 100 \), then \( 100 \times 2 = 200 \).