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Published on: 07/09/2019
Term 3 Fractions
Download Tamil Nadu 6th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.
Questions + Answers key
Take MCQ Maths Test1.
Simplify: \({3\over4}-{1\over2}\)
2.
Simplify: \({3\over7}+{2\over3}\)
3.
Add \(2\over3\)and\(3\over5\)
4.
The number which has its own reciprocal is ________
5.
\(8\div{1\over2}=\)_____
6.
\(5{1\over3}-3{1\over2}=\)_______
7.
\(3{1\over4}\times3{1\over 3}=9{1\over16}\)
8.
The reciprocal of an improper fraction is always a proper fraction
9.
The mixed fraction of \(13\over4\)is \(3{1\over4}\)
10.
The sum of any two proper fractions is always an improper fraction
11.
Convert mixed fractions into improper fractions and vice versa:
\(i)\ 3{7\over 18}\)
\(ii)\ {99\over7}\)
\(iii)\ {47\over6}\)
\(iv)\ 12{1\over9}\)
12.
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?
\(\frac{2}{3}\) of Rs. 150
\(\frac{3}{5}\) of Rs. 150
\(\frac{1}{5}\) of Rs. 150
\(\frac{4}{5}\) of Rs. 150
13.
The difference between \(3\over7\) and \(2\over9\) is
\(\frac{13}{63} \)
\(\frac{1}{9}\)
\(\frac{1}{7} \)
\(\frac{9}{16}\)
14.
Which of the following statement is incorrect?
\({1\over2}>{1\over3}\)
\({7\over8}>{6\over7}\)
\({8\over9}>{9\over10}\)
\({10\over11}>{9\over10}\)
15.
Mangai bought \(6{3\over4}\) kg of apples. If Kalai bought \(1{1\over2}\) times as Mangai bought, then how many kilograms of apples did Kalai buy?
16.
Which is smaller? The difference between \(2{1\over2}\ and\ 3{2\over3}\) or the sum of \(1{1\over2}\ and\ 2{1\over4}\)
17.
From his office, a person wants to reach his house on foot which is at a distance of \(5{3\over4}\)km. If he had walked \(2{1\over 2}km\) how much distance still he has to walk to reach his house?
1.
Common multiple of 2 and 4 is 4
Equivalent fraction of \(1\over2\) is
\({1\over2}={1\times2\over 2\times2}={2\over4}\)
Now
\({3\over 4}-{1\over2}={3\over4}-{2\over4}={3-2\over4}={1\over 4}\)
Therefore, Vani has \(1\over4\) amount of water in the bottle. This can be verified by the following diagram
2.
By Cross Multiplication technique 
\( ={(3\times3)+(2\times7)\over7\times3}={9+14\over21}={23\over 21}\)
3.
These are unlike fractions, aren’t they ? So first we need to convert them into like fractions ? Is it possible ? Yes, always. How do we do so ? The common multiple of 3 and 5 is 15. Hence, we find the equivalent fractions of \(2\over 3\)and \(3\over5\) with denominator 15.
\({2\over3}={2\times5\over 3\times5}={10\over 15}\)
\({3\over5}={3\times3\over 5\times3}={9\over 15}\)
\({2\over 3}+{3\over5}={10\over 15}+{9\over 15}={19\over 15}\)
4.
( )
1
5.
( )
16
6.
( )
\(1{5\over6}\)
7.
(b)
8.
(a)
9.
(a)
10.
(b)
11.
(i) \(3\cfrac { 7 }{ 8 } \)
Improper fraction = \(\cfrac { \left( 3\times 18 \right) +7 }{ 18 } \)
= \(\cfrac { 54+7 }{ 18 } =\cfrac { 61 }{ 18 } \)
(ii) \(\cfrac { 99 }{ 7 } \)
\(Mixed\ fraction=Qutient+\frac { Remainder }{ Divisor } \)
= \(14+\cfrac { 1 }{ 7 } \)
= \(14\cfrac { 1 }{ 7 } \)
(iii) \(\cfrac { 47 }{ 6 } \)
Mixed fraction = \(7\cfrac { 5 }{ 6 } \)
(iv) \(12\cfrac { 1 }{ 9 } \)
Mixed fraction = \(\cfrac { \left( 12\times 9 \right) +1 }{ 9 } \)
= \(\cfrac { 108+1 }{ 9 } =\cfrac { 109 }{ 9 }\)
12.
(d)
\(\frac{4}{5}\) of Rs. 150
13.
(a)
\(\frac{13}{63} \)
14.
(d)
\({10\over11}>{9\over10}\)
15.
Mangai bought = \(6\cfrac { 3 }{ 4 } kg\) of apple
Kalai bought = \(1\cfrac { 1 }{ 2 } \) times as Mangai bought
= \(\left[ 1\cfrac { 1 }{ 2 } \times 6\cfrac { 3 }{ 4 } \right] kg\) of apples
= \(\cfrac { 3 }{ 2 } \times \cfrac { 27 }{ 4 } \)
= \(\cfrac { 81 }{ 8 } \)
\(\therefore \) Kalai bought = \(10\cfrac { 1 }{ 8 } \) kg of apples.
16.
Difference between \(2\cfrac { 1 }{ 2 }\ and\ 3\cfrac { 1 }{ 2 } \)
Difference = \(3\cfrac { 2 }{ 3 } -2\cfrac { 1 }{ 2 } \)
= \(\cfrac { 11 }{ 3 } -\cfrac { 5 }{ 2 } \)
= \(\cfrac { \left( 11\times 2 \right) -\left( 5\times 3 \right) }{ 6 } =\cfrac { 22-15 }{ 6 } \)
= \(\cfrac { 7 }{ 6 } \) ...(1)
Also given
Sum of \(1\cfrac { 1 }{ 2 }\ and\ 2\cfrac { 1 }{ 4 } \)
Sum =\(1\cfrac { 1 }{ 2 } +2\cfrac { 1 }{ 4 } \)
= \(\cfrac { 3 }{ 2 } +\cfrac { 9 }{ 4 } \)
= \(\cfrac { \left( 3\times 2 \right) +9 }{ 4 } =\cfrac { 6+9 }{ 4 } =\cfrac { 15 }{ 4 } \)
From (1) and (2),
Difference = \(\cfrac { 7 }{ 6 } \), Sum = \(\cfrac { 15 }{ 4 } \)
\(\cfrac { 7 }{ 6 } ,\cfrac { 15 }{ 4 } \)
\(\Rightarrow\) Lcm of 6 and 4 is 12
\(\cfrac { 7 }{ 6 } \times \cfrac { 2 }{ 2 } =\cfrac { 14 }{ 12 } ,\cfrac { 15 }{ 4 } \times \cfrac { 3 }{ 3 } =\cfrac { 45 }{ 12 } \)
\(\cfrac { 14 }{ 12 } <\cfrac { 45 }{ 12 } \Rightarrow \cfrac { 7 }{ 6 } <\cfrac { 15 }{ 4 } \)
\(\therefore \) The difference between \(2\cfrac { 1 }{ 2 }\ and\ 3\cfrac { 2 }{ 3 } \)
17.
Total distance = \(5\cfrac { 3 }{ 4 } km=\cfrac { 23 }{ 4 } km\)
He had walked = \(2\cfrac { 1 }{ 2 } km=\cfrac { 5 }{ 2 } km\)
Difference = \(\left( \cfrac { 23 }{ 4 } -\cfrac { 5 }{ 2 } \right) km\)
= \(\cfrac { 23-\left( 5\times 2 \right) }{ 4 } =\cfrac { 23-10 }{ 4 } =\cfrac { 13 }{ 4 } km\)
\(\therefore 3\cfrac { 1 }{ 4 } km\) distance still he has to walk to reach his house
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Tamilnadu Stateboard 6th Standard Subjects
Tamilnadu Stateboard Standards
