The DAV Class 5 Maths Book Solutions Pdf and **DAV Class 5 Maths Chapter 4 Worksheet 1** Solutions of Fractional Numbers offer comprehensive answers to textbook questions.

## DAV Class 5 Maths Ch 4 Worksheet 1 Solutions

Question 1.

Encircle the fraction in its lowest term. The first one is done for you.

(a) \(\frac{2}{5}, \frac{4}{10}, \frac{8}{20}, \frac{6}{15}\)

Solution:

(b) \(\frac{4}{24}, \frac{6}{36}, \frac{1}{6}, \frac{3}{18}\)

Solution:

(c) \(\frac{5}{15}, \frac{2}{6}, \frac{4}{12}, \frac{1}{3}\)

Solution:

(d) \(\frac{4}{5}, \frac{12}{15}, \frac{32}{40}, \frac{16}{20}\)

Solution:

(e) \(\frac{6}{10}, \frac{24}{40}, \frac{3}{5}, \frac{18}{30}\)

Solution:

Question 2.

Tick (✓) those fractions which are in the lowest term.

(a) \(\frac{6}{10}\)

Solution:

✗

(b) \(\frac{5}{32}\)

Solution:

(c) \(\frac{1}{8}\)

Solution:

(d) \(\frac{5}{8}\)

Solution:

(e) \(\frac{13}{15}\)

Solution:

(f) \(\frac{81}{90}\)

Solution:

✗

(g) \(\frac{21}{15}\)

Solution:

✗

(h) \(\frac{26}{42}\)

Solution:

✗

Question 3.

Reduce into the lowest term.

(a) \(\frac{9}{12}\)

Solution:

\(\frac{9}{12}\)

HCF of 9 and 12 is 3.

\(\frac{9}{12} \div \frac{3}{3}=\frac{3}{4}\) is the lowest term.

(b) \(\frac{6}{20}\)

Solution:

\(\frac{6}{20}\)

HCF of 6 and 20 is 2

\(\frac{6}{20} \div \frac{2}{2}=\frac{3}{10}\) is the lowest term.

(c) \(\frac{10}{22}\)

Solution:

HCF of 10 and 22 is 2

\(\frac{10}{22} \div \frac{2}{2}=\frac{5}{11}\) is the lowest term.

(d) \(\frac{18}{24}\)

Solution:

HCF of 18 and 24 is 6

\(\frac{18}{24} \div \frac{6}{6}=\frac{3}{4}\) is the lowest term.

(e) \(\frac{28}{56}\)

Solution:

HCF of 28 and 56 is 28.

\(\frac{28}{56} \div \frac{28}{28}=\frac{1}{2}\) is the lowest term.

(f) \(\frac{12}{60}\)

Solution:

HCF of 12 and 60 is 12.

\(\frac{12}{60} \div \frac{12}{12}=\frac{1}{5}\) is the lowest term.

(g) \(\frac{15}{45}\)

Solution:

HCF of 15 and 45 is 15.

\(\frac{15}{45} \div \frac{15}{15}=\frac{1}{3}\) is the lowest term.

(h) \(\frac{48}{54}\)

Solution:

The HCF of 48 and 54 is 6.

\(\frac{48}{54} \div \frac{6}{6}=\frac{8}{9}\) is the lowest term.

(i) \(\frac{36}{48}\)

Solution:

The HCF of 36 and 48 is 12.

\(\frac{36}{48} \div \frac{12}{12}=\frac{3}{4}\) is the lowest term.

(j) \(\frac{22}{55}\)

Solution:

The HCF of 22 and 55 is 11.

\(\frac{22}{55} \div \frac{11}{11}=\frac{2}{5}\) is the lowest term.

Review Exercise

Question 1.

Write the next three equivalent fractions.

(i) \(\frac{2}{6}, \frac{4}{12}, \frac{6}{18}\), ____, _____, _____

Solution:

\(\frac{8}{24}, \frac{10}{30}, \frac{12}{36}\)

(ii) \(\frac{1}{7}, \frac{2}{14}, \frac{3}{21}\), ____, _____, _____

Solution:

\(\frac{4}{28}, \frac{5}{35}, \frac{6}{42}\)

(iii) \(\frac{5}{9}, \frac{10}{18}, \frac{15}{27}\), ____, _____, _____

Solution:

\(\frac{20}{36}, \frac{25}{45}, \frac{30}{54}\)

Question 2.

Convert the following into improper fractions. The first is done for you.

(a) \(3 \frac{1}{5}\) = __________

Solution:

\(3 \frac{1}{5}\) = \(\frac{16}{5}\left(\frac{(3 \times 5)+1}{5}\right)\)

(b) \(5 \frac{1}{7}\) = __________

Solution:

\(5 \frac{1}{7}\) = \(\frac{36}{7}\left(\frac{7 \times 5+1}{7}\right)\)

(c) \(33 \frac{1}{3}\) = _________

Solution:

\(33 \frac{1}{3}\) = \(\frac{100}{3}\left(\frac{33 \times 3+1}{3}\right)\)

(d) \(2 \frac{2}{9}\) = __________

Solution:

\(2 \frac{2}{9}\) = \(\frac{20}{9}\left(\frac{2 \times 9+2}{9}\right)\)

Question 3.

Convert the following into a mixed number. The first one is done for you.

(i) \(\frac{50}{7}\) = ________

Solution:

(ii) \(\frac{11}{9}\) = ________

Solution:

(iii) \(\frac{23}{8}\) = ________

Solution:

(iv) \(\frac{78}{17}\) = ________

Solution:

Question 4.

Fill in the blanks.

(a) Fractions having the same denominators are called _______ fractions.

Solution:

like

(b) A fractional number whose numerator is more significant than its denominator is called an _________ fraction.

Solution:

improper

(c) \(\frac{1}{2}, \frac{1}{7}, \frac{1}{11}, \frac{1}{4}\) and \(\frac{1}{3}\) are called ________ fractions.

Solution:

unit

(d) \(3 \frac{1}{8}\) is a _______ number.

Solution:

mixed

(e)

Solution:

64

**DAV Class 5 Maths Chapter 4 Worksheet 1 Notes**

Equivalent Fractions:

Fractions which express the value of the same part of a whole are called Equivalent Fractions.

e.g., \(\frac{1}{2}, \frac{2}{4}, \frac{4}{8}, \frac{8}{16}\)

Improper Fractions:

Fractions whose numbers are greater than denominators are called Improper Fractions.

e.g., \(\frac{4}{2}, \frac{7}{3}, \frac{9}{2}\)

Proper Fractions:

Fractions whose numerators are smaller than denominators are called Proper Fractions.

e.g., \(\frac{2}{7}, \frac{5}{9}, \frac{3}{11}\)

Like Fractions:

Fractions having the same denominators are called Like Fractions.

e.g., \(\frac{3}{7}, \frac{2}{7}, \frac{8}{7}\)

Unlike Fractions:

Fractions having different denominators are called Unlike Fractions.

e.g., \(\frac{3}{5}, \frac{3}{13}, \frac{7}{9}\)

Unit Fractions:

Fractions whose numerators are equal to one are called Unit Fractions.

e.g., \(\frac{1}{7}, \frac{1}{9}, \frac{1}{15}\)

Mixed Number: An improper fraction written as a combination of a whole and a proper fraction is called a Mixed Number.

e.g., \(2 \frac{1}{9}, 3 \frac{1}{7}, 1 \frac{1}{3}\)

To reduce a fraction into the lowest terms, we go on dividing the numerator and denominator by their common factors till we are left with a fraction having 1 as the only common factor of both its numerator and denominator.

e.g., \(\frac{4}{9}=\frac{2}{3}\) (lowest term)

To get the product of a whole number and a fractional number, we multiply the whole number and numerator of the fractional number. The denominator remains the same.

e.g., \(8 \times \frac{2}{3}=\frac{8 \times 2}{3}=\frac{16}{3}\)

To get the product of two fractional numbers, we multiply the numerators and the denominators separately.

e.g., \(\frac{2}{5} \times \frac{3}{5}=\frac{2 \times 3}{5 \times 5}=\frac{6}{25}\)

By interchanging the numerator and the denominator of a fractional number, we get the reciprocal of that number.

e.g., \(\frac{4}{5}=\frac{5}{4}\) (reciprocal number)

When we divide a fractional number with a whole number or with another fractional number, we first change the division sign to the multiplication sign and multiply by the reciprocal of the divisor.

e.g., (i) \(4 \div \frac{2}{3}=4 \times \frac{3}{2}=\frac{12}{2}\) or 6

(ii) \(\frac{4}{2} \div \frac{3}{2}=\frac{4}{2} \times \frac{2}{3}=\frac{8}{6}=\frac{4}{3}\)

Fractions in the Lowest Terms

Let us take a fraction \(\frac{5}{3}\)

(a) \(\frac{5}{3} \times \frac{2}{2}=\frac{10}{6}\)

Numerator and Denominator are called terms of a fraction.

(b) \(\frac{5}{3} \times \frac{3}{3}=\frac{15}{9}\)

When we multiply the numerator and denominator of a fraction by a common number, we get higher terms of the fraction.

(c) \(\frac{6}{8} \div \frac{2}{2}=\frac{3}{4}\)

(d) \(\frac{10}{12} \div \frac{2}{2}=\frac{5}{6}\)

When we divide the numerator and denominator of a fraction by a common factor other than 1, we get lower terms of the fraction.

We cannot further divide \(\frac{3}{7}\) by a common number. It can be divided only by the common factor 1.

\(\frac{3}{7} \div \frac{1}{1}=\frac{3}{7}\)

So \(\frac{3}{7}\) is in the lowest terms.

In order to reduce a fraction into the lowest term, we go on dividing the numerator and denominator by their common factors till we are left with a fraction having 1 as the only common factor.

Example 1.

Reduce \(\frac{15}{25}\) in its lowest term.

Solution:

\(\frac{15}{25} \div \frac{5}{5}=\frac{3}{5}\) is in the lowest term.

Dividing by common factor 2. (because 3 and 5 have no common factor other than 1)

Simplification of Fractions by using HCF

Example 1.

Let us reduce \(\frac{18}{20}\) to the lowest term.

Solution:

HCF of 18 and 20 is 2.

\(\frac{18}{20} \div \frac{2}{2}\) (Divided by HCF)

\(\frac{9}{10}\) (is the lowest term)