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