RS Aggarwal 2021-2022 for Class 6 Maths Chapter 5- Fractions
RS Aggarwal Class 6 Math Solution Chapter 5- Fractions Test Paper-5 is available here. RS Aggarwal Class 6 Math Solutions are solved by expert teachers in step by step, which help the students to understand easily. RS Aggarwal textbooks are responsible for a strong foundation in Maths. These textbook solutions help students in exams as well as their daily homework routine. The solutions included are easy to understand, and each step in the solution is described to match the students’ understanding.
Rs Aggarwal Class 6 Math Solution Chapter 5- Fractions
Test Paper-5
A.1. Define a fraction. Give five example of fractions.
Solution:
A fraction is defined as a number representing a part of a whole, where the whole may be a single object or a group of objects.
Examples: 27 , 75 , 113 , 146 , 49
2. What fraction of an hour is 35 minutes?
Solution:
1 hour = 60 minutes
∴ Fraction for 35 minutes = 3576012 = 712
So, 712 part of an hour is equal to 35 minutes.
3. Find the equivalent fraction of 58 with denominator 56.
Solution:
To make denominator 56, we multiply both numerator and denominator by 7
∴ 58 = 5×78×7 = 3556
So, the required equivalent fraction is 3556
4. Represent 235 on the number line.
Solution:
Let OA = AB = BC = 1 unit
∴ OB = 2 units and OC = 3 units
Divide BC into 5 equal parts and take 3 parts out to reach point P.
Clearly, point P represents the number 235.
5. Find the sum of 245 + 1310 + 3115
Solution:
245 + 1310 + 3115
= 145 + 1310 + 4615
L.C.M of 5, 10, 15 = 30
= 84+39+9230
= 21543306
= 436 = 716
6. The cost of a pen is Rs. 1623 and that of a pencil is Rs. 416 Which cost more and by how much?
Solution:
Cost of a pen = Rs. 1623 = Rs. 503 = Rs. 50× = Rs. frac\{100}{6}
Cost of pencil = Rs. 4frac\{1}{6} = Rs. frac\{25}{6}
Rs. frac\{100}{6} > Rs. frac\{25}{6}
So, the cost of pen is more than pencil.
Now we find difference between their cost.
Rs. (frac\{50}{3} − frac\{25}{6})
= Rs. (frac\{100 − 25}{6})
= Rs. frac\{cancel 75^25}{cancel 6^2}
= Rs. frac\{25}{2}
= Rs. 12frac\{1}{2}
Hence, the cost of a pen is Rs. 12frac\{1}{2} more than the cost of a pencil.
7. Of frac\{3}{4} and frac\{5}{7}, which is greater and by how much?
Solution:
First we compare frac\{3}{4} and frac\{5}{7}
By cross multiply
3 × 7 = 21 and 5 × 4 = 20
So, 21 > 20
∴ frac\{3}{4} > frac\{5}{7}
Now, we find their difference.
frac\{3}{4} − frac\{5}{7}
= frac\{21 − 20}{28}
= frac\{1}{28}
Hence, frac\{3}{4} is greater than frac\{5}{7} by frac\{1}{28}.
8. Convert the fractions frac\{1}{2} , frac\{2}{3} , frac\{4}{9} and frac\{5}{6} into like fractions.
Solution:
The given fractions are frac\{1}{2} , frac\{2}{3} , frac\{4}{9} and frac\{5}{6}
L.C.M. of 2, 3, 9 and 6 = 18
Now, we have:
frac\{1}{2} = frac\{1 × 9}{2 × 9} = frac\{9}{18}
frac\{2}{3} = frac\{2 × 6}{3 × 6} = frac\{12}{18}
frac\{4}{9} = frac\{4 × 2}{9 × 2} = frac\{8}{18}
frac\{5}{6} = frac\{5 × 3}{6 × 3} = frac\{15}{18}
Hence, frac\{9}{18} , frac\{12}{18} , frac\{8}{18} and frac\{15}{18} are like fractions.
9. Find the equivalent fraction of frac\{3}{5} having denominator 30.
Solution:
To make denominator 30, we multiply both numerator and denominator by 6
∴ frac\{3}{5} = frac\{3 × 6}{5 × 6} = frac\{18}{30}
So, the required equivalent fraction is frac\{18}{30}
10. Reduce frac\{84}{98} to the simplest form.
Solution:
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
The factors of 98 are 1, 2, 7, 14, 49, 98.
The common factors of 84 and 98 are 1, 2, 7, 14.
The H.C.F. of 84 and 98 is 14.
Dividing both the numerator and the denominator by the H.C.F.
frac\{84}{98} = frac\{84 ÷ 14}{98 ÷ 14} = frac{6}{7}
B Mark (✓) against the correct answer in each of the following:
11. frac\{24}{11} is an example of
(a) a proper fraction.
(b) an improper fraction.
(c) a mixed fraction.
(d) none of these.
Solution: The correct option is (b) an improper fraction
In an improper fraction, the numerator is greater than the denominator.
12. frac\{3}{8} is an example of
(a) a proper fraction.
(b) an improper fraction.
(c) a mixed fraction.
(d) none of these.
Solution: The correct option is (a) proper fraction
In a proper fraction, the numerator is less than the denominator.
13. frac\{3}{8} and frac\{5}{12} on comparison give
(a) frac\{3}{8} > frac\{5}{12}
(b) frac\{3}{8} < frac\{5}{12}
(c) frac\{3}{8} = frac\{5}{12}
(d) none of these
Solution: The correct option is (b) frac\{3}{8} < frac\{5}{12}
Considering frac\{3}{8} and frac\{5}{12}
On cross multiplying, we get:
3 × 12 = 36 and 8 × 5 = 40
Clearly, 36 < 40
∴ frac\{3}{8} < frac\{5}{12}
14. The largest of the fraction frac\{2}{3}, frac\{5}{9}, frac\{1}{2} and frac\{7}{12} is
(a) frac\{2}{3}
(b) frac\{5}{9}
(c) frac\{7}{12}
(d) frac\{1}{2}
Solution: The correct option is (a) frac\{2}{3}
Explanation:
L.C.M. of 3, 9, 2 and 12 = 36
Now, we have:
frac\{2}{3} = frac\{2 × 12}{3 × 12} = frac\{24}{36}
frac\{5}{9} = frac\{5 × 4}{9 × 4} = frac\{20}{36}
frac\{1}{2} = frac\{1 × 18}{2 × 18} = frac\{18}{36}
frac\{7}{12} = frac\{7 × 3}{12 × 3} = frac\{21}{36}
Hence, frac\{24}{36} = frac\{2}{3} is the largest fraction.
15. 3frac\{3}{4} − 1frac\{1}{2} = ?
(a) 2frac\{1}{2}
(b) 2frac\{1}{4}
(c) 1frac\{1}{2}
(d) 1frac\{1}{4}
Solution: The correct option is (b) 2frac\{1}{4}
3frac\{3}{4} − 1frac\{1}{2}
= frac\{15}{4} − frac\{3}{2}
= frac\{15 − 6}{4}
= frac\{9}{4}
= 2frac\{1}{4}
16. Which of the following are like fractions?
(a) frac\{2}{3}, frac\{3}{4}, frac\{4}{5}, frac\{5}{6}
(b) frac\{2}{5}, frac\{2}{7}, frac\{2}{9}, frac\{2}{11}
(c) frac\{1}{8}, frac\{3}{8}, frac\{5}{8}, frac\{7}{8}
(d) none of these
Solution: The correct option is (c) frac\{1}{8}, frac\{3}{8}, frac\{5}{8}, frac\{7}{8}
Like fractions have same the denominator.
17. ? − frac\{8}{21} = frac\{8}{21}
(a) 0
(b) 1
(c) frac\{21}{8}
(d) frac\{16}{21}
Solution: The correct option is (d) frac\{16}{21}
? − frac\{8}{21} = frac\{8}{21}
? = frac\{8}{21} + frac\{8}{21}
? = frac\{8 + 8}{21}
? = frac\{16}{21}
C.18. Fill in the blanks:
(i) 9frac\{2}{3} + = 19
(ii) 6frac\{1}{6} − ? = frac\{29}{30}
(iii) 7 − 5frac\{2}{3} =
(iv) frac\{72}{90} reduced to simplest form is .
(v) frac\{42}{54} = frac\{7}{☐}
Solution:
(i) Let the required number be x
∴ 9frac\{2}{3} + x = 19
⇒ x = 19 − 9frac\{2}{3}
⇒ x = 19 − frac\{29}{3}
⇒ x = frac\{57 − 29}{3}
⇒ x = frac\{28}{3}
⇒ x = 9frac\{1}{3}
(ii) Let the required number be x
∴ 6frac\{1}{6} − x = frac\{29}{30}
⇒ x = 6frac\{1}{6} − frac\{29}{30}
⇒ x = frac\{37}{6} − frac\{29}{30}
⇒ x = frac\{185 − 29}{30}
⇒ x = frac\{156}{30}
⇒ x = 5frac\{cancel 6^1}{cancel 30^5}
⇒ x = 5frac\{1}{5}
(iii) Let the required number be x
∴ 7 − 5frac\{2}{3} = x
⇒ x = frac\{7}{1} − 5frac\{2}{3}
⇒ x = frac\{7}{1} − frac\{17}{3}
⇒ x = frac\{21 − 17}{3}
⇒ x = frac\{4}{3}
(iv) H.C.F 72 and 90 = 18
Now,
frac\{72}{90} = frac\{72 ÷ 18}{90 ÷ 18} = frac\{4}{5}
(v) frac\{42}{54} = frac\{7}{☐}
By cross multiply
42 × ☐ = 54 × 7
☐ = frac\{54 × 7}{42}
☐ = frac\{cancel 378^9}{cancel 42}
☐ = 9
D.19. Write 'T' for true and 'F' for false for each of the statements given below:
(a) 3frac\{1}{3} > frac\{33}{10}
(b) 8 − 1frac\{5}{6} = 7frac\{1}{6}
(c) frac\{1}{2}, frac\{1}{3} and frac\{1}{4} are like fractions
(d) frac\{3}{5} lies between 3 and 5.
(e) Among frac\{1}{2}, frac\{1}{3}, frac\{3}{4}. frac\{4}{3} the largest fraction is frac\{4}{3}.
Solution:
(a) T
(b) F (frac\{8}{1} − frac\{11}{6} = frac\{48 −11}{6} = frac\{37}{6} = 6frac\{1}{6})
(c) F (Because like fractions have the same denominator.)
(d) F (It lies between 0 and 1 as all proper fractions are less than 1.)
(e) T (Because it is an improper fraction, while the others are proper fractions.)
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