Samacheer Kalvi Class 5 Maths Solutions Term 3 Chapter 6 Fractions Exercise 6.5

Question 1. Add the following fractions
(i) \( \frac { 1 }{ 5 } + \frac { 3 }{ 5 } \)
Answer:
(i) \( \frac { 1 }{ 5 } + \frac { 3 }{ 5 } = \frac { 1+3 }{ 5 } = \frac { 4 }{ 5 } \)
In simple words: When fractions have the same bottom number (denominator), you just add the top numbers (numerators) and keep the bottom number the same. We combine the parts to get the total.

🎯 Exam Tip: Always check if the fractions have a common denominator before adding or subtracting. If they don't, you need to find one first.

Question 1. (ii) \( \frac { 1 }{ 7 } + \frac { 3 }{ 7 } \)
Answer:
(ii) \( \frac { 1 }{ 7 } + \frac { 3 }{ 7 } = \frac { 1+3 }{ 7 } = \frac { 4 }{ 7 } \)
In simple words: Like with the first problem, we add the top numbers 1 and 3 because the bottom number 7 is the same. This gives us 4 over 7.

🎯 Exam Tip: Remember that adding fractions is like combining pieces of the same size. \( \frac { 1 }{ 7 } \) means one piece out of seven, and \( \frac { 3 }{ 7 } \) means three pieces out of seven.

Question 1. (iii) \( \frac { 5 }{ 12 } + \frac { 2 }{ 12 } \)
Answer:
(iii) \( \frac { 5 }{ 12 } + \frac { 2 }{ 12 } = \frac { 5+2 }{ 12 } = \frac { 7 }{ 12 } \)
In simple words: The bottom number (12) is the same, so we add the top numbers (5 and 2) to get 7. The total is 7 parts out of 12.

🎯 Exam Tip: When adding fractions, the sum of the numerators represents the total number of parts, and the denominator represents the total number of equal parts that make up a whole.

Question 1. (iv) \( \frac { 3 }{ 9 } + \frac { 7 }{ 9 } \)
Answer:
(iv) \( \frac { 3 }{ 9 } + \frac { 7 }{ 9 } = \frac { 3+7 }{ 9 } = \frac { 10 }{ 9 } \)
In simple words: We add 3 and 7 to get 10, keeping the bottom number 9. This fraction is greater than 1 whole, as 10 is bigger than 9.

🎯 Exam Tip: An improper fraction like \( \frac { 10 }{ 9 } \) means you have more than one whole. You can convert it to a mixed number (1 \( \frac { 1 }{ 9 } \)) if the question asks for it.

Question 1. (v) \( \frac { 2 }{ 15 } + \frac { 3 }{ 15 } \)
Answer:
(v) \( \frac { 2 }{ 15 } + \frac { 3 }{ 15 } = \frac { 2+3 }{ 15 } = \frac { 5 }{ 15 } \)
In simple words: Add the top numbers 2 and 3 to get 5. Keep the bottom number 15 the same. The fraction is \( \frac { 5 }{ 15 } \).

🎯 Exam Tip: Always simplify your answer if possible. \( \frac { 5 }{ 15 } \) can be simplified to \( \frac { 1 }{ 3 } \) by dividing both the top and bottom by 5.

Question 1. (vi) \( \frac { 2 }{ 7 } + \frac { 1 }{ 7 } + \frac { 3 }{ 7 } \)
Answer:
(vi) \( \frac { 2 }{ 7 } + \frac { 1 }{ 7 } + \frac { 3 }{ 7 } = \frac { 2+1+3 }{ 7 } = \frac { 6 }{ 7 } \)
In simple words: When adding three fractions with the same bottom number, you just add all three top numbers together. Here, 2 plus 1 plus 3 equals 6, so the answer is 6 out of 7.

🎯 Exam Tip: The rule of adding only the numerators when denominators are the same applies to any number of fractions, not just two.

Question 1. (vii) \( \frac { 3 }{ 10 } + \frac { 5 }{ 10 } + \frac { 2 }{ 10 } \)
Answer:
(vii) \( \frac { 3 }{ 10 } + \frac { 5 }{ 10 } + \frac { 2 }{ 10 } = \frac { 3+5+2 }{ 10 } = \frac { 10 }{ 10 } = 1 \)
In simple words: We add the top numbers 3, 5, and 2, which gives 10. Since the bottom number is also 10, \( \frac { 10 }{ 10 } \) means one whole thing.

🎯 Exam Tip: When the numerator and the denominator of a fraction are the same, the fraction is equal to 1 whole, representing all parts of a single item.

Question 1. (viii) \( \frac { 2 }{ 9 } + \frac { 1 }{ 9 } \)
Answer:
(viii) \( \frac { 2 }{ 9 } + \frac { 1 }{ 9 } = \frac { 2+1 }{ 9 } = \frac { 3 }{ 9 } \)
In simple words: Add 2 and 1 to get 3, then put it over the common bottom number 9. The sum is 3 out of 9.

🎯 Exam Tip: Always remember to simplify the resulting fraction if possible. For example, \( \frac { 3 }{ 9 } \) can be simplified to \( \frac { 1 }{ 3 } \) by dividing both numbers by 3.

Question 1. (ix) \( \frac { 3 }{ 8 } + \frac { 2 }{ 8 } \)
Answer:
(ix) \( \frac { 3 }{ 8 } + \frac { 2 }{ 8 } = \frac { 3+2 }{ 8 } = \frac { 5 }{ 8 } \)
In simple words: By adding the top numbers 3 and 2, we get 5. The bottom number 8 stays the same, so the total is 5 out of 8.

🎯 Exam Tip: Practice adding fractions with the same denominator often. It's a fundamental skill for understanding fractions and larger math concepts.

Question 2. Mother gave \( \frac { 2 }{ 8 } \) of guava to Meena and \( \frac { 3 }{ 8 } \) of guava to Geetha. How many parts of the guava did she give them altogether?
Answer:
Meena received \( = \frac { 2 }{ 8 } \) of the guava.
Geetha received \( = \frac { 3 }{ 8 } \) of the guava.
To find the total, we add the parts:
Total sum \( = \frac { 2 }{ 8 } + \frac { 3 }{ 8 } = \frac { 2+3 }{ 8 } = \frac { 5 }{ 8 } \)
So, the mother gave them \( \frac { 5 }{ 8 } \) of the guava altogether. Guavas are a healthy fruit, rich in Vitamin C.
In simple words: Meena got 2 parts and Geetha got 3 parts of the guava, all divided into 8 pieces. So, together they got 2 + 3 = 5 parts out of 8 total parts.

🎯 Exam Tip: When solving word problems, identify the known parts and what you need to find. "Altogether" or "total" usually means you need to add.

Question 3. The girls of Std V cleaned \( \frac { 3 }{ 5 } \) of a field, while the boys cleaned \( \frac { 1 }{ 5 } \) part of the field. What part of the field was cleaned altogether?
Answer:
The girls cleaned \( = \frac { 3 }{ 5 } \) of the field.
The boys cleaned \( = \frac { 1 }{ 5 } \) of the field.
To find the total part cleaned, we add the fractions:
Total sum \( = \frac { 3 }{ 5 } + \frac { 1 }{ 5 } = \frac { 3+1 }{ 5 } = \frac { 4 }{ 5 } \)
Therefore, \( \frac { 4 }{ 5 } \) part of the field was cleaned altogether. Cleaning a field helps improve its productivity.
In simple words: The girls cleaned 3 parts and the boys cleaned 1 part of the field, both out of 5 total parts. So, in total, 3 + 1 = 4 parts were cleaned out of 5.

🎯 Exam Tip: Always make sure your final answer directly addresses the question asked, stating the total part of the field cleaned in this case.