The DAV Class 5 Maths Book Solutions Pdf and DAV Class 5 Maths Chapter 4 Brain Teasers Solutions of Fractional Numbers offer comprehensive answers to textbook questions.
DAV Class 5 Maths Ch 4 Brain Teasers Solutions
Question 1.
Tick (✓) the correct answer.
(a) \(\frac{1}{3}-\frac{1}{9}\) is
(i) \(\frac{1}{9}\)
(ii) \(\frac{2}{9}\)
(iii) \(\frac{1}{3}\)
(iv) \(\frac{1}{2}\)
Solution:
\(\frac{1}{3}-\frac{1}{9}\)
LCM = 9
\(\frac{1}{3}-\frac{1}{9}\) = \(\frac{3}{9}-\frac{1}{9}\)
= \(\frac{3-1}{9}\)
= \(\frac{2}{9}\)
So option (ii) is correct.
(b) A fraction is greater than one, if-
(i) Numerator = Denominator
(ii) Numerator < Denominator (iii) Numerator > Denominator
(iv) Numerator = 1
Solution:
Numerator > Denominator
Option (iii) is correct.
(c) \(\frac{2}{3}\) of an hour = _____ minutes.
(i) 40 minutes
(ii) 50 minutes
(iii) 60 minutes
(iv) 20 minutes
Solution:
\(\frac{2}{3}\) of hour
1 hour = 60 minutes.
\(\frac{2}{3}\) of hour = \(\frac{2}{3}\) × 60 = 40 minutes.
So option (i) is correct.
(d) What number should be added to \(\frac{8}{9}\) to get \(\frac{9}{8}\)?
(i) \(\frac{9}{8}\)
(ii) 1
(iii) \(\frac{17}{72}\)
(iv) \(\frac{19}{72}\)
Solution:
\(\frac{9}{8}-\frac{8}{9}\)
(First convert the fractions into like fractions).
LCM = 72
\(\frac{9}{8}-\frac{8}{9}\) = \(\frac{81}{72}-\frac{64}{72}\) = \(\frac{17}{72}\)
So option (iii) is correct.
(e) What fraction is the shaded portion?
(i) 2
(ii) 1\(\frac{1}{2}\)
(iii) 1\(\frac{3}{4}\)
(iv) 2\(\frac{3}{4}\)
Solution:
So option (iv) is correct.
Question 2.
Find the sum:
(a) 7 + 1\(\frac{1}{2}\) + \(\frac{9}{5}\)
Solution:
7 + 1\(\frac{1}{2}\) + \(\frac{9}{5}\) = \(\frac{7}{1}+\frac{3}{2}+\frac{9}{5}\)
(First convert into like fraction by finding LCM)
LCM of 1, 2 and 5 = 10
\(\frac{7}{1}+\frac{3}{2}+\frac{9}{5}\) = \(\frac{70}{10}+\frac{15}{10}+\frac{18}{10}\)
= \(\frac{70+15+18}{10}\)
= \(\frac{103}{10}\)
= 10\(\frac{3}{10}\)
(b) 2\(\frac{1}{2}\) + 1\(\frac{1}{4}\) + 2\(\frac{4}{5}\)
Solution:
2\(\frac{1}{2}\) + 1\(\frac{1}{4}\) + 2\(\frac{4}{5}\) = \(\frac{5}{2}+\frac{5}{4}+\frac{14}{5}\)
First convert into like fraction by finding LCM
LCM of 2, 4 and 5 = 20
\(\frac{5}{2}+\frac{5}{4}+\frac{14}{5}\) = \(\frac{50}{20}+\frac{25}{20}+\frac{56}{20}\)
= \(\frac{50+25+56}{20}\)
= \(\frac{131}{20}\)
= 6\(\frac{11}{20}\)
Question 3.
Subtract.
(a) 4\(\frac{1}{2}\) from 6
Solution:
6 – 4\(\frac{1}{2}\) = \(\frac{6}{1}-\frac{9}{2}\) (convert into like fractions)
LCM of 1 and 2 = 2
\(\frac{6}{1}-\frac{9}{2}\) = \(\frac{12}{2}-\frac{9}{2}\)
= \(\frac{3}{2}\)
= 1\(\frac{1}{2}\)
(b) 2\(\frac{1}{2}\) from 7\(\frac{3}{5}\)
Solution:
Question 4.
Find the value of \(2 \frac{3}{5}+3 \frac{1}{2}-2 \frac{1}{8}\)
Solution:
Question 5.
Sheetal needs 1\(\frac{1}{2}\) metres red ribbon, \(\frac{3}{4}\) metres yellow ribbon and one metre black ribbon to make a doll. Find the total length of ribbon needed.
Solution:
Length of red ribbon = 1\(\frac{1}{2}\) m = \(\frac{3}{2}\) m.
Length of yellow ribbon = \(\frac{3}{4}\) m.
Length of black ribbon = 1 m.
Total length of ribbon = \(\frac{3}{2}+\frac{3}{4}+\frac{1}{1}\)
= \(\frac{6+3+4}{4}\)
= \(\frac{13}{4}\)
= 3\(\frac{1}{4}\)
Total length of ribbon needed is 3\(\frac{1}{4}\) m.
Question 6.
Renu’s mother bought five litres of milk, 2\(\frac{1}{2}\) litres milk was used for making sweets, \(\frac{3}{4}\) litres for making tea. How many litres of milk is left?
Solution:
Total quality of milk = 5 l
Quantity of milk used in making sweets = 2\(\frac{1}{2}\) = \(\frac{5}{2}\) l
Milk used for making tea = \(\frac{3}{4}\) l
Total quantity of milk used = \(\frac{5}{2}+\frac{3}{4}\)
LCM of 2 and 4 = 4
\(\frac{5}{2}+\frac{3}{4}\) = \(\frac{10+3}{4}\) = \(\frac{13}{4}\) l
Milk left = \(\frac{5}{1}-\frac{13}{4}\)
LCM of 1 and 4 = 4
\(\frac{5}{1}-\frac{13}{4}\) = \(\frac{20}{4}-\frac{13}{4}\)
= \(\frac{7}{4}\)
= 1\(\frac{3}{4}\) l
1\(\frac{3}{4}\) litre of milk is left.
Question 7.
Reduce into lowest terms.
(a) \(\frac{8}{12}\)
Solution:
\(\frac{8}{12}=\frac{4}{6}=\frac{2}{3}\)
(b) \(\frac{35}{63}\)
Solution:
\(\frac{35}{63}=\frac{5}{9}\)
(c) \(\frac{44}{99}\)
Solution:
\(\frac{44}{99}=\frac{4}{9}\)
(d) \(\frac{6}{10}\)
Solution:
\(\frac{6}{10}=\frac{3}{5}\)
Question 8.
Arrange in ascending order.
(a) \(\frac{3}{4}, \frac{7}{10}, \frac{1}{2}, \frac{5}{8}\)
Solution:
(b) \(1 \frac{5}{6}, \frac{11}{9}, \frac{5}{16}, 3\)
Solution:
Question 9.
Find the product.
(a) \(\frac{4}{12} \times \frac{21}{18} \times \frac{35}{25}\)
Solution:
(b) \(1 \frac{1}{4} \times 2 \frac{3}{5} \times 2 \frac{4}{5}\)
Solution:
Question 10.
Solve these division sums.
(a) \(9 \frac{5}{8} \div 2 \frac{1}{4}\)
Solution:
(b) 52 ÷ 2\(\frac{3}{5}\)
Solution:
Question 11.
State which of the following statements are true.
(а) The reciprocal of \(\frac{9}{7}\) is 1\(\frac{2}{7}\).
Solution:
False
Explanation: The reciprocal of \(\frac{9}{7}\) is \(\frac{7}{9}\)
(b) The multiplicative inverse of 1 is 1.
Solution:
True
(c) \(\frac{1}{2} \div \frac{1}{4}\) means how many quarters in \(\frac{1}{2}\).
Solution:
True
(d) The product of fractional number and one is one.
Solution:
False
Explanation: fractional number × 1 = fractional number
(e) \(\frac{4}{9} \div \frac{4}{9}=\frac{81}{16}\)
Solution:
False
Explanation: \(\frac{4}{9} \div \frac{4}{9}=1\)
(f) \(0 \div \frac{2}{3}=\frac{2}{3}\)
Solution:
False
Explanation: 0 ÷ \(\frac{2}{3}\) = 0
Question 12.
A family consumes 2\(\frac{1}{2}\) litres of milk every day. What is the total consumption of milk by the family in the month of April?
Solution:
Consumption of milk in one day = 2\(\frac{1}{2}\) l
Consumption of milk in the month of April (30 days) = \(\frac{5}{2}\) × 30 = 75
Total consumption of milk by the family in the month of April is 75 litres.
Question 13.
Mala has 36 toffees. She gives \(\frac{4}{9}\) of them to her friend. How many toffees are left with her?
Solution:
Total no. of toffees = 36
No. of toffees given = \(\frac{4}{9}\) of 36
Toffees left = \(\frac{4}{9}\) × 36 = 16
16 toffees are left with her.
Question 14.
If the shaded portion has a value of \(\frac{1}{3}\), what is the value of the whole shape?
Solution:
Let 1 small triangle show \(\frac{1}{3}\) part.
In above fig. there are 5 rectangles which makes 5 × 2 = 10 triangles.
3 more triangles are also present.
Total value of whole shape = 13 × \(\frac{1}{3}\)
= \(\frac{13}{3}\)
= 4\(\frac{1}{3}\)
Additional Questions
Question 1.
Write the next four equivalent fractions.
(a) \(\frac{4}{7}, \frac{8}{14}, \frac{12}{21}\), ____, _____, _____, _____
Solution:
(b) \(\frac{2}{3}, \frac{4}{6}, \frac{6}{9}\), ____, _____, _____, _____
Solution:
(c) \(\frac{4}{5}, \frac{8}{10}, \frac{12}{15}\), ____, _____, _____, _____
Solution:
Question 2.
Find the missing numerals.
(a) 
Solution:
(b) 
Solution:
(c) 
Solution:
(d) 
Solution:
(e) 
Solution:
Question 3.
Compare the fractions by cross multiplication method.
(a) \(\frac{2}{7}\) and \(\frac{2}{8}\)
Solution:
\(\frac{2}{7}\) and \(\frac{2}{8}\)
2 × 8 = 16
7 × 2 = 14
\(\frac{2}{7}>\frac{2}{8}\) (because 16 > 14)
(b) \(\frac{3}{10}\) and \(\frac{2}{5}\)
Solution:
\(\frac{3}{10}\) and \(\frac{2}{5}\)
3 × 5 = 15
10 × 2 = 20
\(\frac{3}{10}<\frac{2}{5}\) (because 15 < 20)
(c) \(\frac{4}{9}\) and \(\frac{5}{18}\)
Solution:
\(\frac{4}{9}\) and \(\frac{5}{18}\)
4 × 18 = 72
9 × 5 = 45
\(\frac{4}{9}>\frac{5}{18}\) (because 72 > 45)
(d) \(\frac{9}{19}\) and \(\frac{9}{10}\)
Solution:
\(\frac{9}{19}\) and \(\frac{9}{10}\)
9 × 10 = 90
19 × 9 = 171
\(\frac{9}{19}<\frac{9}{10}\) (because 90 < 171)
Question 4.
Arrange the following in ascending order.
(a) \(\frac{2}{5}, \frac{2}{3}, \frac{7}{5}, \frac{11}{20}\)
Solution:
(b) \(1 \frac{1}{2}, \frac{9}{20}, \frac{13}{10}, \frac{8}{15}\)
Solution:
Question 5.
Multiply.
(a) 70 × \(\frac{14}{5}\)
Solution:
(b) 105 × 1\(\frac{1}{5}\)
Solution:
(c) 100 × 3\(\frac{1}{10}\)
Solution:
(d) 45 × 3\(\frac{1}{9}\)
Solution:
(e) 52 × \(\frac{3}{13}\)
Solution:
Question 6.
Find the reciprocal of the following:
(a) 2\(\frac{1}{7}\)
Solution:
2\(\frac{1}{7}\) = \(\frac{15}{7}\)
Reciprocal of \(\frac{15}{7}\) = \(\frac{7}{15}\)
(b) 8
Solution:
Reciprocal of 8 = \(\frac{1}{8}\)
(c) \(\frac{5}{12}\)
Solution:
Reciprocal of \(\frac{5}{12}\) = \(\frac{12}{5}\)
(d) 5\(\frac{1}{3}\)
Solution:
5\(\frac{1}{3}\) = \(\frac{16}{3}\)
Reciprocal of \(\frac{16}{3}\) = \(\frac{3}{16}\)
(e) 1\(\frac{3}{7}\)
Solution:
1\(\frac{3}{7}\) = \(\frac{10}{7}\)
Reciprocal of \(\frac{10}{7}\) = \(\frac{7}{10}\)
Question 7.
Arrange in ascending order:
(a) \(\frac{5}{6}, \frac{13}{3}, \frac{7}{18}, \frac{5}{8}\)
Solution:
\(\frac{7}{18}, \frac{5}{8}, \frac{5}{6}, \frac{13}{3}\)
(b) \(\frac{5}{6}, \frac{7}{5}, 2, \frac{5}{16}\)
Solution:
\(\frac{5}{16}, \frac{5}{6}, \frac{7}{5}, 2\)
Question 8.
Find the shaded portion:
(a) 
Solution:
1\(\frac{1}{4}\)
(b) 
Solution:
2\(\frac{1}{4}\)
Question 9.
State true or false:
(a) The product of fractional number and 0 is fractional number.
Solution:
False
(b) The reciprocal of \(\frac{2}{3}\) is \(\frac{3}{1}\).
Solution:
False
(c) \(\frac{1}{3} \div \frac{1}{4}\) means how many quarter in \(\frac{1}{3}\).
Solution:
True
(d) \(\frac{3}{7} \div \frac{2}{7}=\frac{3}{2}\)
Solution:
True