The DAV Class 5 Maths Book Solutions Pdf and DAV Class 5 Maths Chapter 4 Worksheet 2 Solutions of Fractional Numbers offer comprehensive answers to textbook questions.
DAV Class 5 Maths Ch 4 Worksheet 2 Solutions
Question 1.
Compare the fractions by cross multiplication method.
(a) \(\frac{1}{2}\) and \(\frac{1}{4}\)
Solution:
(b) \(\frac{3}{5}\) and \(\frac{3}{4}\)
Solution:
(c) \(\frac{9}{10}\) and \(\frac{2}{5}\)
Solution:
(d) \(\frac{4}{9}\) and \(\frac{5}{18}\)
Solution:
(e) \(\frac{3}{5}\) and \(\frac{3}{7}\)
Solution:
(f) \(\frac{11}{18}\) and \(\frac{1}{6}\)
Solution:
Question 2.
Compare the fractions by taking the LCM.
(a) \(\frac{7}{2}\) and \(\frac{5}{3}\)
Solution:
\(\frac{7}{2}\) and \(\frac{5}{3}\)
LCM of 2 and 3 is 6
\(\frac{7}{2} \times \frac{3}{3}=\frac{21}{6}\)
\(\frac{5}{3} \times \frac{2}{2}=\frac{10}{6}\)
Now we compare like fractions
\(\frac{21}{6}\) > \(\frac{10}{6}\)
∴ \(\frac{7}{6}\) > \(\frac{5}{3}\)
(b) \(\frac{5}{6}\) and \(\frac{3}{4}\)
Solution:
\(\frac{5}{6}\) and \(\frac{3}{4}\)
2 × 3 × 3 = 12
LCM of 6 and 4 is 12
\(\frac{5}{6} \times \frac{2}{2}=\frac{10}{12}\)
\(\frac{3}{4} \times \frac{3}{3}=\frac{9}{12}\)
Now we compare like fractions
\(\frac{10}{12}\) > \(\frac{9}{12}\)
∴ \(\frac{5}{6}\) > \(\frac{3}{4}\)
(c) \(\frac{1}{4}\) and \(\frac{2}{5}\)
Solution:
\(\frac{1}{4}\) and \(\frac{2}{5}\)
LCM of 5 and 5 is 20
\(\frac{1}{4} \times \frac{5}{5}=\frac{5}{20}\)
\(\frac{2}{5} \times \frac{4}{4}=\frac{8}{20}\)
Now we compare like fractions
\(\frac{5}{20}\) < \(\frac{8}{20}\)
∴ \(\frac{1}{4}\) < \(\frac{2}{5}\)
(d) \(\frac{3}{10}\) and \(\frac{3}{4}\)
Solution:
\(\frac{3}{10}\) and \(\frac{3}{4}\)
2 × 5 × 2 = 20
LCM of 10 and 4 is 20
\(\frac{3}{10} \times \frac{2}{2}=\frac{6}{20}\)
\(\frac{3}{4} \times \frac{5}{5}=\frac{15}{20}\)
Now we compare like fractions
\(\frac{6}{20}\) < \(\frac{15}{20}\)
∴ \(\frac{3}{10}\) < \(\frac{3}{4}\)
(e) \(\frac{3}{5}\) and \(\frac{5}{6}\)
Solution:
\(\frac{3}{5}\) and \(\frac{5}{6}\)
LCM of 5 and 6 is 30
\(\frac{3}{5} \times \frac{6}{6}=\frac{18}{30}\)
\(\frac{5}{6} \times \frac{5}{5}=\frac{25}{30}\)
Now we compare like fractions
\(\frac{18}{30}\) < \(\frac{25}{30}\)
∴ \(\frac{3}{5}\) < \(\frac{5}{6}\)
(f) \(\frac{2}{9}\) and \(\frac{3}{7}\)
Solution:
\(\frac{2}{9}\) and \(\frac{3}{7}\)
LCM of 9 and 7 is 63
\(\frac{2}{9} \times \frac{7}{7}=\frac{14}{63}\)
\(\frac{3}{7} \times \frac{9}{9}=\frac{27}{63}\)
Now we compare like fractions
\(\frac{14}{63}\) < \(\frac{27}{63}\)
∴ \(\frac{2}{9}\) < \(\frac{3}{7}\)
Question 3.
Compare the following pairs of fractional numbers.
(a) \(5 \frac{1}{2}\) and \(\frac{5}{2}\)
Solution:
(b) \(\frac{9}{7}\) and \(1 \frac{2}{7}\)
Solution:
(c) \(\frac{19}{7}\) and \(2 \frac{1}{6}\)
Solution:
(d) \(4 \frac{3}{4}\) and \(\frac{20}{5}\)
Solution:
(e) \(1 \frac{1}{2}\) and \(\frac{5}{4}\)
Solution:
(f) \(1 \frac{1}{5}\) and \(\frac{5}{4}\)
Solution:
DAV Class 5 Maths Chapter 4 Worksheet 2 Notes
In like fractions, the greater the numerator, the greater will be the value of the fractional number.
\(\frac{4}{7}>\frac{2}{7}\)
In Unlike fractions, with the same numerator, the greater the denominator, the smaller will be the value of the fractional numerator.
\(\frac{2}{10}<\frac{2}{8}\)
In case of \(\frac{3}{4}\) and \(\frac{7}{8}\)
Method 1: First we convert the unlike fractions \(\frac{3}{4}\) and \(\frac{7}{8}\) into like fractions.
For that find the Lowest Common Multiple (LCM) of denominators i.e., 4 and 8.
\(\frac{3}{4} \times \frac{2}{2}=\frac{6}{8}\)
\(\frac{7}{8} \times \frac{1}{1}=\frac{7}{8}\)
Now compare like fractions \(\frac{6}{8}\) and \(\frac{7}{8}\)
\(\frac{6}{8}<\frac{7}{8}\) (because 7 > 6)
Method 2: Quick Method of Comparing.
cross multiplication
3 × 8 = 24
4 × 7 = 28
\(\frac{3}{4}<\frac{7}{8}\) (because 24 < 28)