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## 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 ÷ $$\frac{1}{2}$$ ………..
(v) The number which has its own reciprocal is ……….
Solution:

(ii) Mixed Fraction

(iii) 5$$\frac{1}{3}$$ – 3$$\frac{1}{2}$$
= $$\frac{16}{3}$$ – $$\frac{7}{2}$$ = $$\frac{32-21}{6}$$ = $$\frac{11}{6}$$
= 1$$\frac{5}{6}$$

(iv) 8 ÷ $$\frac{1}{2}$$
= 8 × $$\frac{2}{1}$$
= 16

(v) 1

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$$\frac{1}{4}$$ × 3$$\frac{1}{4}$$ = 9$$\frac{1}{16}$$
Solution:
(i) True
(ii) False
(iii) True
(iv) True
(v) False

Question 3.
(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$$\frac{4}{21}$$
Solution:
(i) $$\frac{1}{7}$$ + $$\frac{3}{9}$$
= $$\frac{9+21}{63}$$ = $$\frac{30}{63}$$ = $$\frac{10}{21}$$

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$$\frac{1}{9}$$
Solution:
(i) 3$$\frac{7}{18}$$ = $$\frac{61}{18}$$
(ii) $$\frac{99}{7}$$ = 14$$\frac{1}{7}$$
(iii) $$\frac{47}{6}$$ = 7$$\frac{5}{6}$$
(iv) 12$$\frac{1}{9}$$ = $$\frac{109}{9}$$

Question 5.
Multiply the following:
(i) $$\frac{2}{3}$$ × 6
(ii) 8$$\frac{1}{3}$$ × 5
(iii) $$\frac{3}{8}$$ × $$\frac{4}{5}$$
(iv) 3$$\frac{5}{7}$$ × 1$$\frac{1}{13}$$
Solution:
(i) $$\frac{2}{3}$$ × 6 = 4

(ii) 8$$\frac{1}{3}$$ × 5
= $$\frac{25}{3}$$ × 5
= $$\frac{125}{3}$$
= 41$$\frac{2}{3}$$

(iii) $$\frac{3}{8}$$ × $$\frac{4}{5}$$
= $$\frac{12}{40}$$ = $$\frac{3}{10}$$

(iv) 3$$\frac{5}{7}$$ × 1$$\frac{1}{13}$$
= $$\frac{26}{7}$$ × $$\frac{14}{13}$$
= $$\frac{4}{1}$$
= 4

Question 6.
Divide the following
(i) $$\frac{3}{7}$$ ÷ 4
(ii) $$\frac{4}{3}$$ ÷ $$\frac{5}{9}$$
(iii) 4$$\frac{1}{5}$$ ÷ 3$$\frac{3}{4}$$
(iv) 9$$\frac{2}{3}$$ ÷ 1$$\frac{2}{3}$$
Solution:
(i) $$\frac{3}{7}$$ ÷ 4
= $$\frac{3}{7}$$ × $$\frac{1}{4}$$ = $$\frac{3}{28}$$

(ii) $$\frac{4}{3}$$ ÷ $$\frac{5}{9}$$
= $$\frac{4}{3}$$ × $$\frac{9}{5}$$
= $$\frac{12}{5}$$
= 2$$\frac{2}{5}$$

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?
Solution:
Total weight of vegetables bought

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?
Solution:

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?
Solution:
Distance walked in an hour = 4$$\frac{1}{2}$$ km
Distance covered in 3$$\frac{1}{2}$$
Hours

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?
Solution:
Total length = 15$$\frac{3}{4}$$
Length of the small pieces = 2$$\frac{1}{4}$$
Small curtains obtained

= 7

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) $$\frac{10}{11}$$ > $$\frac{9}{10}$$
Solution:
(d) $$\frac{10}{11}$$ > $$\frac{9}{10}$$

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) $$\frac{9}{16}$$
Solution:
(a) $$\frac{13}{63}$$

Question 13.
The reciprocal of $$\frac{53}{17}$$ is
(a) $$\frac{53}{17}$$
(b) 5$$\frac{3}{17}$$
(c) $$\frac{17}{53}$$
(d) 3$$\frac{5}{17}$$
Solution:
(c) $$\frac{17}{53}$$

Question 14.
If $$\frac{6}{7}=\frac{\mathbf{A}}{49}$$, then the value of A is
(a) 42
(b) 36
(c) 25
(d) 48
Solution:
(a) 42
Hint: $$\frac{6 \times 49}{7}=42$$

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
(d) $$\frac{1}{5}$$ of Rs 150
Solution:
(c) $$\frac{4}{5}$$ of Rs 150