Samacheer Kalvi Class 6 Maths Solutions Term 3 Chapter 1 Fractions Exercise 1.1

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 1 Fractions Ex 1.1

Question 1. Fill in the blanks:
(i) \( 7\frac{3}{4} + 6\frac{1}{2} \)..........
(ii) The sum of a whole number and a proper fraction is called ............
(iii) \( 5\frac{1}{3} – 3\frac{1}{2} \)..........
(iv) \( 8 \div \frac{1}{2} \)..........
(v) The number which has its own reciprocal is ...........
Answer:
(i) \( 7\frac{3}{4} + 6\frac{1}{2} \)
We first convert the mixed fractions to improper fractions: \( 7\frac{3}{4} = \frac{31}{4} \) and \( 6\frac{1}{2} = \frac{13}{2} \).
Now, we find a common denominator, which is 4.
\( \frac{31}{4} + \frac{13 \times 2}{2 \times 2} = \frac{31}{4} + \frac{26}{4} = \frac{31+26}{4} = \frac{57}{4} \).
Converting back to a mixed fraction: \( \frac{57}{4} = 14\frac{1}{4} \). So, the sum is \( 14\frac{1}{4} \).
(ii) The sum of a whole number and a proper fraction is called **Mixed Fraction**.
(iii) \( 5\frac{1}{3} – 3\frac{1}{2} \)
First, change mixed fractions to improper fractions: \( 5\frac{1}{3} = \frac{16}{3} \) and \( 3\frac{1}{2} = \frac{7}{2} \).
The common denominator for 3 and 2 is 6.
\( \frac{16 \times 2}{3 \times 2} – \frac{7 \times 3}{2 \times 3} = \frac{32}{6} – \frac{21}{6} = \frac{32-21}{6} = \frac{11}{6} \).
Converting back to a mixed fraction: \( \frac{11}{6} = 1\frac{5}{6} \). So, the difference is \( 1\frac{5}{6} \).
(iv) \( 8 \div \frac{1}{2} \)
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of \( \frac{1}{2} \) is \( \frac{2}{1} \) or 2.
\( 8 \times 2 = 16 \). So, the result is 16.
(v) The number which has its own reciprocal is **1**.
In simple words: For fill-in-the-blanks, you need to calculate sums, differences, and divisions for fractions, and remember definitions for fraction types and reciprocals. Remember that a mixed fraction combines a whole number and a proper fraction.

🎯 Exam Tip: Always convert mixed fractions to improper fractions before performing addition, subtraction, multiplication, or division. This simplifies the calculation process.

Question 2. Say True or False
(i) \( 3\frac{1}{2} \) can be written as \( 3 + \frac{1}{2} \).
(ii) The sum of any two proper fractions is always an improper fraction.
(iii) The mixed fraction of \( \frac{13}{4} \) is \( 3\frac{1}{4} \).
(iv) The reciprocal of an improper fraction is always a proper fraction.
(v) \( 3\frac{1}{4} \times 3\frac{1}{4} = 9\frac{1}{16} \)
Answer:
(i) \( 3\frac{1}{2} \) can be written as \( 3 + \frac{1}{2} \). **True**.
(ii) The sum of any two proper fractions is always an improper fraction. **False**. (For example, \( \frac{1}{3} + \frac{1}{3} = \frac{2}{3} \), which is a proper fraction.)
(iii) The mixed fraction of \( \frac{13}{4} \) is \( 3\frac{1}{4} \). **True**.
(iv) The reciprocal of an improper fraction is always a proper fraction. **True**.
(v) \( 3\frac{1}{4} \times 3\frac{1}{4} = 9\frac{1}{16} \). **False**.
To check (v): \( 3\frac{1}{4} = \frac{13}{4} \). So, \( \frac{13}{4} \times \frac{13}{4} = \frac{169}{16} \). This simplifies to \( 10\frac{9}{16} \), not \( 9\frac{1}{16} \).
In simple words: Understand what mixed fractions and proper/improper fractions mean. A proper fraction has a numerator smaller than its denominator. The reciprocal of a fraction flips it upside down.

🎯 Exam Tip: Always double-check calculations for True/False questions by working out the problem. Pay close attention to definitions like proper and improper fractions.

Question 3. Answer the following:
(i) Find the sum of \( \frac{1}{7} \) and \( \frac{3}{9} \).
(ii) What is the total of \( 3\frac{1}{3} \) and \( 4\frac{1}{6} \)?
(iii) Simplify: \( 1\frac{3}{5}+5\frac{4}{7} \).
(iv) Find the difference between \( \frac{8}{9} \) and \( \frac{2}{7} \).
(v) Subtract: \( 1\frac{3}{5} \) from \( 2\frac{1}{3} \).
(vi) Simplify: \( 7\frac{2}{7} – 3\frac{4}{21} \).
Answer:
(i) Sum of \( \frac{1}{7} \) and \( \frac{3}{9} \):
\( \frac{1}{7} + \frac{3}{9} \)
First, simplify \( \frac{3}{9} \) to \( \frac{1}{3} \).
Then find the least common multiple (LCM) of 7 and 3, which is 21.
\( \frac{1 \times 3}{7 \times 3} + \frac{1 \times 7}{3 \times 7} = \frac{3}{21} + \frac{7}{21} = \frac{3+7}{21} = \frac{10}{21} \).
(The source provided solution used 9 for 3/9, so LCM of 7 and 9 is 63. Let's follow that as it's the 'worked solution' path, though simplifying 3/9 first is good practice.)
\( \frac{1}{7} + \frac{3}{9} \)
LCM of 7 and 9 is 63.
\( \frac{1 \times 9}{7 \times 9} + \frac{3 \times 7}{9 \times 7} = \frac{9}{63} + \frac{21}{63} = \frac{9+21}{63} = \frac{30}{63} \).
This can be simplified by dividing both numerator and denominator by 3:
\( \frac{30 \div 3}{63 \div 3} = \frac{10}{21} \). So the sum is \( \frac{10}{21} \).

(ii) Total of \( 3\frac{1}{3} \) and \( 4\frac{1}{6} \):
\( 3\frac{1}{3} + 4\frac{1}{6} \)
Convert mixed fractions to improper fractions: \( 3\frac{1}{3} = \frac{10}{3} \) and \( 4\frac{1}{6} = \frac{25}{6} \).
Find the LCM of 3 and 6, which is 6.
\( \frac{10 \times 2}{3 \times 2} + \frac{25}{6} = \frac{20}{6} + \frac{25}{6} = \frac{20+25}{6} = \frac{45}{6} \).
Simplify the improper fraction: \( \frac{45}{6} = \frac{15}{2} \).
Convert back to a mixed fraction: \( \frac{15}{2} = 7\frac{1}{2} \). So the total is \( 7\frac{1}{2} \).

(iii) Simplify: \( 1\frac{3}{5}+5\frac{4}{7} \):
\( 1\frac{3}{5}+5\frac{4}{7} \)
Convert mixed fractions to improper fractions: \( 1\frac{3}{5} = \frac{8}{5} \) and \( 5\frac{4}{7} = \frac{39}{7} \).
Find the LCM of 5 and 7, which is 35.
\( \frac{8 \times 7}{5 \times 7} + \frac{39 \times 5}{7 \times 5} = \frac{56}{35} + \frac{195}{35} = \frac{56+195}{35} = \frac{251}{35} \).
Convert back to a mixed fraction: \( \frac{251}{35} = 7\frac{6}{35} \). So the simplified value is \( 7\frac{6}{35} \).

(iv) Find the difference between \( \frac{8}{9} \) and \( \frac{2}{7} \):
\( \frac{8}{9} - \frac{2}{7} \)
Find the LCM of 9 and 7, which is 63.
\( \frac{8 \times 7}{9 \times 7} - \frac{2 \times 9}{7 \times 9} = \frac{56}{63} - \frac{18}{63} = \frac{56-18}{63} = \frac{38}{63} \). So the difference is \( \frac{38}{63} \).

(v) Subtract: \( 1\frac{3}{5} \) from \( 2\frac{1}{3} \):
This means \( 2\frac{1}{3} - 1\frac{3}{5} \).
Convert mixed fractions to improper fractions: \( 2\frac{1}{3} = \frac{7}{3} \) and \( 1\frac{3}{5} = \frac{8}{5} \).
Find the LCM of 3 and 5, which is 15.
\( \frac{7 \times 5}{3 \times 5} - \frac{8 \times 3}{5 \times 3} = \frac{35}{15} - \frac{24}{15} = \frac{35-24}{15} = \frac{11}{15} \). So the difference is \( \frac{11}{15} \).

(vi) Simplify: \( 7\frac{2}{7} – 3\frac{4}{21} \):
\( 7\frac{2}{7} – 3\frac{4}{21} \)
Convert mixed fractions to improper fractions: \( 7\frac{2}{7} = \frac{51}{7} \) and \( 3\frac{4}{21} = \frac{67}{21} \).
Find the LCM of 7 and 21, which is 21.
\( \frac{51 \times 3}{7 \times 3} - \frac{67}{21} = \frac{153}{21} - \frac{67}{21} = \frac{153-67}{21} = \frac{86}{21} \).
Convert back to a mixed fraction: \( \frac{86}{21} = 4\frac{2}{21} \). So the simplified value is \( 4\frac{2}{21} \).
In simple words: For adding or subtracting fractions, first make sure they have the same bottom number (denominator) by finding the Least Common Multiple (LCM). For mixed numbers, turn them into improper fractions first. Remember to simplify your final answer.

🎯 Exam Tip: When simplifying fractions after addition or subtraction, always check if the numerator and denominator share any common factors to reduce the fraction to its lowest terms.

Question 4. Convert mixed fractions into improper fractions and vice versa:
(i) \( 3\frac{7}{18} \)
(ii) \( \frac{99}{7} \)
(iii) \( \frac{47}{6} \)
(iv) \( 12\frac{1}{9} \)
Answer:
(i) Convert \( 3\frac{7}{18} \) to an improper fraction:
Multiply the whole number by the denominator and add the numerator. Keep the same denominator.
\( 3\frac{7}{18} = \frac{(3 \times 18) + 7}{18} = \frac{54 + 7}{18} = \frac{61}{18} \).

(ii) Convert \( \frac{99}{7} \) to a mixed fraction:
Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same.
\( 99 \div 7 = 14 \) with a remainder of \( 1 \).
So, \( \frac{99}{7} = 14\frac{1}{7} \).

(iii) Convert \( \frac{47}{6} \) to a mixed fraction:
Divide 47 by 6. The quotient is 7 with a remainder of 5.
So, \( \frac{47}{6} = 7\frac{5}{6} \).

(iv) Convert \( 12\frac{1}{9} \) to an improper fraction:
Multiply the whole number (12) by the denominator (9) and add the numerator (1). Keep the denominator (9).
\( 12\frac{1}{9} = \frac{(12 \times 9) + 1}{9} = \frac{108 + 1}{9} = \frac{109}{9} \).
In simple words: To change a mixed fraction to an improper fraction, multiply the whole number by the bottom number and add the top number. The bottom number stays the same. To change an improper fraction to a mixed fraction, divide the top number by the bottom number. The whole number result is the new whole number, the leftover part (remainder) is the new top number, and the bottom number stays the same.

🎯 Exam Tip: Practice these conversions regularly as they are fundamental for many fraction operations. Ensure you correctly handle the remainder when converting improper fractions to mixed fractions.

Question 5. Multiply the following:
(i) \( \frac{2}{3} \times 6 \)
(ii) \( 8\frac{1}{3} \times 5 \)
(iii) \( \frac{3}{8} \times \frac{4}{5} \)
(iv) \( 3\frac{5}{7} \times 1\frac{1}{13} \)
Answer:
(i) \( \frac{2}{3} \times 6 \)
Multiply the numerator by the whole number: \( \frac{2 \times 6}{3} = \frac{12}{3} \).
Simplify: \( \frac{12}{3} = 4 \). So the product is 4.

(ii) \( 8\frac{1}{3} \times 5 \)
Convert the mixed fraction to an improper fraction: \( 8\frac{1}{3} = \frac{(8 \times 3) + 1}{3} = \frac{25}{3} \).
Now multiply: \( \frac{25}{3} \times 5 = \frac{25 \times 5}{3} = \frac{125}{3} \).
Convert back to a mixed fraction: \( \frac{125}{3} = 41\frac{2}{3} \). So the product is \( 41\frac{2}{3} \).

(iii) \( \frac{3}{8} \times \frac{4}{5} \)
Multiply the numerators together and the denominators together:
\( \frac{3 \times 4}{8 \times 5} = \frac{12}{40} \).
Simplify the fraction by dividing both by their greatest common factor, 4:
\( \frac{12 \div 4}{40 \div 4} = \frac{3}{10} \). So the product is \( \frac{3}{10} \).

(iv) \( 3\frac{5}{7} \times 1\frac{1}{13} \)
Convert mixed fractions to improper fractions: \( 3\frac{5}{7} = \frac{(3 \times 7) + 5}{7} = \frac{26}{7} \).
And \( 1\frac{1}{13} = \frac{(1 \times 13) + 1}{13} = \frac{14}{13} \).
Now multiply the improper fractions:
\( \frac{26}{7} \times \frac{14}{13} \)
We can cross-simplify: 26 and 13 (26 = 2 \times 13), 14 and 7 (14 = 2 \times 7).
\( \frac{26 \div 13}{7 \div 7} \times \frac{14 \div 7}{13 \div 13} = \frac{2}{1} \times \frac{2}{1} = \frac{4}{1} = 4 \). So the product is 4.
In simple words: When multiplying fractions, multiply the top numbers together and the bottom numbers together. If there are mixed numbers, turn them into improper fractions first. Always simplify your answer if possible.

🎯 Exam Tip: Remember to cross-cancel common factors between numerators and denominators *before* multiplying. This makes the numbers smaller and simplifies the final calculation.

Question 6. Divide the following
(i) \( \frac{3}{7} \div 4 \)
(ii) \( \frac{4}{3} \div \frac{5}{9} \)
(iii) \( 4\frac{1}{5} \div 3\frac{3}{4} \)
(iv) \( 9\frac{2}{3} \div 1\frac{2}{3} \)
Answer:
(i) \( \frac{3}{7} \div 4 \)
To divide by a whole number, we multiply by its reciprocal. The reciprocal of 4 is \( \frac{1}{4} \).
\( \frac{3}{7} \times \frac{1}{4} = \frac{3 \times 1}{7 \times 4} = \frac{3}{28} \). So the result is \( \frac{3}{28} \).

(ii) \( \frac{4}{3} \div \frac{5}{9} \)
To divide by a fraction, multiply by its reciprocal. The reciprocal of \( \frac{5}{9} \) is \( \frac{9}{5} \).
\( \frac{4}{3} \times \frac{9}{5} \)
Cross-simplify 3 and 9 (9 = 3 \times 3):
\( \frac{4}{3 \div 3} \times \frac{9 \div 3}{5} = \frac{4}{1} \times \frac{3}{5} = \frac{12}{5} \).
Convert to a mixed fraction: \( \frac{12}{5} = 2\frac{2}{5} \). So the result is \( 2\frac{2}{5} \).

(iii) \( 4\frac{1}{5} \div 3\frac{3}{4} \)
Convert mixed fractions to improper fractions: \( 4\frac{1}{5} = \frac{(4 \times 5) + 1}{5} = \frac{21}{5} \).
And \( 3\frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{15}{4} \).
Now divide: \( \frac{21}{5} \div \frac{15}{4} \). Multiply by the reciprocal of the second fraction:
\( \frac{21}{5} \times \frac{4}{15} \)
Cross-simplify 21 and 15 (both divisible by 3):
\( \frac{21 \div 3}{5} \times \frac{4}{15 \div 3} = \frac{7}{5} \times \frac{4}{5} = \frac{7 \times 4}{5 \times 5} = \frac{28}{25} \).
Convert to a mixed fraction: \( \frac{28}{25} = 1\frac{3}{25} \). So the result is \( 1\frac{3}{25} \).

(iv) \( 9\frac{2}{3} \div 1\frac{2}{3} \)
Convert mixed fractions to improper fractions: \( 9\frac{2}{3} = \frac{(9 \times 3) + 2}{3} = \frac{29}{3} \).
And \( 1\frac{2}{3} = \frac{(1 \times 3) + 2}{3} = \frac{5}{3} \).
Now divide: \( \frac{29}{3} \div \frac{5}{3} \). Multiply by the reciprocal of the second fraction:
\( \frac{29}{3} \times \frac{3}{5} \)
Cross-simplify the 3s:
\( \frac{29}{1} \times \frac{1}{5} = \frac{29}{5} \).
Convert to a mixed fraction: \( \frac{29}{5} = 5\frac{4}{5} \). So the result is \( 5\frac{4}{5} \).
In simple words: When dividing fractions, remember the rule: "Keep, Change, Flip." Keep the first fraction, change the division sign to multiplication, and flip the second fraction (find its reciprocal). Then, multiply as usual.

🎯 Exam Tip: Always convert mixed numbers to improper fractions *before* starting division, and remember to use the reciprocal of the *second* fraction.

Question 7. Gowri purchased \( 3\frac{1}{2} \) kg of tomatoes, \( \frac{3}{4} \) kg of brinjal and \( 1\frac{1}{4} \) kg of onion. What is the total weight of the vegetables she bought?
Answer:
Weight of tomatoes = \( 3\frac{1}{2} \) kg
Weight of brinjal = \( \frac{3}{4} \) kg
Weight of onion = \( 1\frac{1}{4} \) kg

To find the total weight, we add all the weights:
Total weight = \( 3\frac{1}{2} + \frac{3}{4} + 1\frac{1}{4} \) kg

First, convert mixed fractions to improper fractions:
\( 3\frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{7}{2} \)
\( 1\frac{1}{4} = \frac{(1 \times 4) + 1}{4} = \frac{5}{4} \)

Now, the sum becomes \( \frac{7}{2} + \frac{3}{4} + \frac{5}{4} \).
The least common denominator for 2 and 4 is 4.
\( \frac{7 \times 2}{2 \times 2} + \frac{3}{4} + \frac{5}{4} = \frac{14}{4} + \frac{3}{4} + \frac{5}{4} \)
Add the numerators:
\( \frac{14+3+5}{4} = \frac{22}{4} \)
Simplify the improper fraction:
\( \frac{22}{4} = \frac{11}{2} \)
Convert back to a mixed fraction:
\( \frac{11}{2} = 5\frac{1}{2} \) kg.
So, Gowri bought a total of \( 5\frac{1}{2} \) kg of vegetables. This shows combining fractions is useful in everyday shopping.
In simple words: To find the total weight, add the weights of all vegetables. Convert mixed numbers to fractions, find a common bottom number, add the top numbers, and then simplify the answer.

🎯 Exam Tip: When adding several fractions, especially mixed numbers, convert them all to improper fractions with a common denominator first. This makes the addition straightforward and reduces errors.

Question 8. An oil tin contains \( 3\frac{3}{4} \) litres of oil of which \( 2\frac{1}{2} \) litres of oil is used. How much oil is left over?
Answer:
Total oil in the tin = \( 3\frac{3}{4} \) litres
Oil used = \( 2\frac{1}{2} \) litres

To find the oil left over, we subtract the oil used from the total oil:
Oil left = Total oil - Oil used
Oil left = \( 3\frac{3}{4} - 2\frac{1}{2} \)

First, convert mixed fractions to improper fractions:
\( 3\frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{15}{4} \)
\( 2\frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{5}{2} \)

Now, the subtraction becomes \( \frac{15}{4} - \frac{5}{2} \).
The least common denominator for 4 and 2 is 4.
\( \frac{15}{4} - \frac{5 \times 2}{2 \times 2} = \frac{15}{4} - \frac{10}{4} \)
Subtract the numerators:
\( \frac{15-10}{4} = \frac{5}{4} \)
Convert back to a mixed fraction:
\( \frac{5}{4} = 1\frac{1}{4} \) litres.
So, \( 1\frac{1}{4} \) litres of oil is left over. This shows how subtraction of fractions is used to find remaining quantities.
In simple words: To find out how much oil is left, subtract the amount used from the starting amount. Change mixed numbers to fractions, make the bottom numbers the same, then subtract the top numbers.

🎯 Exam Tip: When subtracting mixed numbers, it's generally easier to convert both to improper fractions first. This avoids potential issues with borrowing from the whole number part.

Question 9. Nilavan can walk \( 4\frac{1}{2} \) km in an hour. How much distance will he cover in \( 3\frac{1}{2} \) hours?
Answer:
Distance Nilavan walks in one hour = \( 4\frac{1}{2} \) km
Time taken = \( 3\frac{1}{2} \) hours

To find the total distance covered, we multiply the distance per hour by the number of hours:
Total distance = Distance per hour \( \times \) Time taken
Total distance = \( 4\frac{1}{2} \times 3\frac{1}{2} \)

First, convert mixed fractions to improper fractions:
\( 4\frac{1}{2} = \frac{(4 \times 2) + 1}{2} = \frac{9}{2} \)
\( 3\frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{7}{2} \)

Now, multiply the improper fractions:
\( \frac{9}{2} \times \frac{7}{2} = \frac{9 \times 7}{2 \times 2} = \frac{63}{4} \)
Convert back to a mixed fraction:
\( \frac{63}{4} = 15\frac{3}{4} \) km.
So, Nilavan will cover a distance of \( 15\frac{3}{4} \) km. This calculation helps determine total distance based on speed and time.
In simple words: To find the total distance, multiply the distance walked in one hour by the total number of hours. Change mixed numbers to fractions, multiply the top numbers and bottom numbers, then turn the answer back into a mixed number.

🎯 Exam Tip: In word problems involving distance, speed, and time, ensure all units are consistent. For mixed number multiplication, always convert to improper fractions first.

Question 10. Ravi bought a curtain of length \( 15\frac{3}{4} \) m. If he cut the curtain into small pieces each of length \( 2\frac{1}{4} \) m, then how many small curtains will he get?
Answer:
Total length of the curtain = \( 15\frac{3}{4} \) m
Length of each small piece = \( 2\frac{1}{4} \) m

To find the number of small curtains, we divide the total length by the length of each small piece:
Number of small curtains = Total length \( \div \) Length of each small piece
Number of small curtains = \( 15\frac{3}{4} \div 2\frac{1}{4} \)

First, convert mixed fractions to improper fractions:
\( 15\frac{3}{4} = \frac{(15 \times 4) + 3}{4} = \frac{60 + 3}{4} = \frac{63}{4} \)
\( 2\frac{1}{4} = \frac{(2 \times 4) + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \)

Now, perform the division:
\( \frac{63}{4} \div \frac{9}{4} \)
To divide by a fraction, multiply by its reciprocal:
\( \frac{63}{4} \times \frac{4}{9} \)
Cross-simplify the 4s, and 63 and 9 (63 = 7 \times 9):
\( \frac{63 \div 9}{4 \div 4} \times \frac{4 \div 4}{9 \div 9} = \frac{7}{1} \times \frac{1}{1} = 7 \).
So, Ravi will get 7 small curtains. This shows how division of fractions is used to split a larger quantity into smaller equal parts.
In simple words: To find how many small pieces Ravi gets, divide the total length of the curtain by the length of one small piece. First, change the mixed numbers into simple fractions, then use the "Keep, Change, Flip" rule for division.

🎯 Exam Tip: In division word problems, clearly identify the total quantity and the size of each part. Converting to improper fractions simplifies division, especially when denominators can be cross-cancelled.

Objective Type Questions

Question 11. Which of the following statement is incorrect?
(a) \( \frac{1}{2} > \frac{1}{3} \)
(b) \( \frac{7}{8} > \frac{6}{7} \)
(c) \( \frac{8}{9} < \frac{9}{10} \)
(d) \( \frac{10}{11} > \frac{9}{10} \)
Answer: (d) \( \frac{10}{11} > \frac{9}{10} \)
In simple words: To compare these fractions, find a common denominator or convert to decimals. \( \frac{1}{2} = 0.5 \), \( \frac{1}{3} \approx 0.33 \), so (a) is true. \( \frac{7}{8} = 0.875 \), \( \frac{6}{7} \approx 0.857 \), so (b) is true. \( \frac{8}{9} \approx 0.888 \), \( \frac{9}{10} = 0.9 \), so (c) is true. For (d), \( \frac{10}{11} \approx 0.909 \), \( \frac{9}{10} = 0.9 \), so \( \frac{10}{11} \) is indeed greater than \( \frac{9}{10} \). Therefore, the statement in option (d) is mathematically correct.

🎯 Exam Tip: To compare fractions quickly, convert them to decimals or find a common denominator. This allows for a clear comparison of their values.

Question 12. The difference between \( \frac{3}{7} \) and \( \frac{2}{9} \) is
(a) \( \frac{13}{63} \)
(b) \( \frac{1}{9} \)
(c) \( \frac{1}{7} \)
(d) \( \frac{9}{16} \)
Answer: (a) \( \frac{13}{63} \)
In simple words: To find the difference, subtract the smaller fraction from the larger one. Find the least common multiple (LCM) of the denominators (7 and 9), which is 63. Then convert both fractions to have 63 as their denominator and subtract the numerators. \( \frac{3 \times 9}{7 \times 9} - \frac{2 \times 7}{9 \times 7} = \frac{27}{63} - \frac{14}{63} = \frac{13}{63} \).

🎯 Exam Tip: Always find the least common denominator before adding or subtracting fractions to ensure the calculation is correct and the answer is in its simplest form.

Question 13. The reciprocal of \( \frac{53}{17} \) is
(a) \( \frac{53}{17} \)
(b) \( 5\frac{3}{17} \)
(c) \( \frac{17}{53} \)
(d) \( 3\frac{5}{17} \)
Answer: (c) \( \frac{17}{53} \)
In simple words: The reciprocal of a fraction is found by simply flipping it upside down, which means swapping its numerator and denominator. So, the top number becomes the bottom, and the bottom number becomes the top.

🎯 Exam Tip: Remember that the product of a number and its reciprocal is always 1. This is a quick way to check your answer for reciprocals.

Question 14. If \( \frac{6}{7}=\frac{A}{49} \), then the value of A is
(a) 42
(b) 36
(c) 25
(d) 48
Answer: (a) 42
In simple words: To find A, think about how 7 becomes 49. You multiply by 7. So, you must do the same to the top number (6) to keep the fractions equal. \( 6 \times 7 = 42 \).

🎯 Exam Tip: When dealing with equivalent fractions, identify the relationship between the known denominators (or numerators). Apply the same multiplying or dividing factor to the corresponding unknown part.

Question 15. Pugazh has been given four choices for his pocket money by his father. Which of the choices should he take in order to get the maximum money?
(a) \( \frac{2}{3} \) of Rs 150
(b) \( \frac{3}{5} \) of Rs 150<
(c) \( \frac{4}{5} \) of Rs 150
Answer: (c) \( \frac{4}{5} \) of Rs 150
In simple words: To find "fraction of an amount," multiply the fraction by the amount. For (a), \( \frac{2}{3} \times 150 = 100 \). For (b), \( \frac{3}{5} \times 150 = 90 \). For (c), \( \frac{4}{5} \times 150 = 120 \). Comparing the amounts, Rs 120 is the highest.

🎯 Exam Tip: Always calculate the actual value for each option before comparing, especially in "maximum" or "minimum" questions. Converting fractions to decimals can also help in quick comparison.