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)