Given fractions are \(\frac{7}{2}\) and \(\frac{3}{5}\)
Here, the denominators are 2 and 5.
And least common multiple of 2 and 5 is 10.
Hence for both fractions let’s have same denominator of 10.
Now for \(\frac{7}{2}\) multiply both the numerator and the denominator by 5.
\(\frac{7}{2}=\frac{7 \times 5}{2 \times 5}=\frac{35}{10}\)
And for \(\frac{3}{5}\) multiply both the numerator and the denominator by 2, we get,
\(\frac{3 \times 2}{5 \times 2}=\frac{6}{10}\)
Hence, the equivalent fractions with the same denominator are:
\(\frac{35}{10}\) and \(\frac{6}{10}\)
(b) \(\frac{8}{3}\) and \(\frac{5}{6}\)
Solution:
Given fractions are \(\frac{8}{3}\) and \(\frac{5}{6}\)
Here, the denominators are 3 and 6.
And least common multiple of 3 and 6 is 6.
Now for \(\frac{8}{3}\) multiply both the numerator and the denominator by 2.
\(\frac{8}{3}=\frac{8 \times 2}{3 \times 2}=\frac{16}{6}\)
\(\frac{5}{6}\) already have a denominator 6.
Hence, the equivalent fractions with the same denominator are:
\(\frac{16}{6}\) and \(\frac{5}{6}\)
(c) \(\frac{3}{4}\) and \(\frac{3}{5}\)
Solution:
Given fractions are \(\frac{3}{4}\) and \(\frac{3}{5}\)
Here, the denominators are 4 and 5.
And least common multiple of 4 and 5 is 20.
Now for \(\frac{3}{4}\) multiply both the numerator and the denominator by 5.
\(\frac{3}{4}=\frac{3 \times 5}{4 \times 5}=\frac{15}{20}\)
And for \(\frac{3}{5}\) multiply both the numerator and the denominator by 4, we get
\(\frac{3}{5}=\frac{3 \times 4}{5 \times 4}=\frac{12}{20}\)
So, the equivalent fractions with the same denominator are:
\(\frac{15}{20}\) and \(\frac{12}{20}\)
(d) \(\frac{6}{7}\) and \(\frac{8}{5}\)
Solution:
Given fractions are \(\frac{6}{7}\) and \(\frac{8}{5}\)
Here, the denominators are 7 and 5.
And least common multiple of 7 and 5 is 35.
Now for \(\frac{6}{7}\) multiply both the numerator and the denominator by 5.
\(\frac{6}{7}=\frac{6 \times 5}{7 \times 5}=\frac{30}{35}\)
And for \(\frac{8}{5}\) multiply both the numerator and the denominator by 7, we get
\(\frac{8}{5}=\frac{8 \times 7}{5 \times 7}=\frac{56}{35}\)
So, the equivalent fractions with the same denominator are:
\(\frac{30}{35}\) and \(\frac{56}{35}\)
(e) \(\frac{9}{4}\) and \(\frac{5}{2}\)
Solution:
Given fractions are \(\frac{9}{4}\) and \(\frac{5}{2}\)
Here, the denominators are 4 and 2.
And least common multiple of 4 and 2 is 4.
Now for \(\frac{5}{2}\) multiply both the numerator and the denominator by 2.
\(\frac{5}{2}=\frac{5 \times 2}{2 \times 2}=\frac{10}{4}\)
and \(\frac{9}{4}\) already have a denominator 4
So, the equivalent fractions with the same denominator are:
\(\frac{9}{4}\) and \(\frac{10}{4}\)
(f) \(\frac{1}{10}\) and \(\frac{2}{9}\)
Solution:
Given fractions are and \(\frac{1}{10}\) and \(\frac{2}{9}\)
Here, the denominators are 10 and 9.
And least common multiple of 10 and 9 is 90.
Now for \(\frac{1}{10}\) multiply both the numerator and the denominator by 9.
\(\frac{1}{10}=\frac{1 \times 9}{10 \times 9}=\frac{9}{90}\)
And for 2 multiply both the numerator and the denominator by 10, we get
\(\frac{2}{9}=\frac{2 \times 10}{9 \times 10}=\frac{20}{90}\)
So, the equivalent fractions with the same denominator are:’
\(\frac{9}{90}\) and \(\frac{20}{90}\)
(g) \(\frac{8}{3}\) and \(\frac{11}{4}\)
Solution:
Given fractions are \(\frac{8}{3}\) and \(\frac{11}{4}\)
Here, the denominators are 3 and 4.
And least common multiple of 3 and 4 is 12.
Now for \(\frac{8}{3}\) multiply both the numerator and the denominator by 4.
\(\frac{8}{3}=\frac{8 \times 4}{3 \times 4}=\frac{32}{12}\)
And for \(\frac{11}{4}\) multiply both the numerator and the denominator by 3, we get
\(\frac{11}{4}=\frac{11 \times 3}{4 \times 3}=\frac{33}{12}\)
So, the equivalent fractions with the same denominator are:
\(\frac{32}{12}\) and \(\frac{33}{12}\)
(h) \(\frac{13}{6}\) and \(\frac{1}{9}\)
Solution:
Given fractions are \(\frac{13}{6}\) and \(\frac{1}{9}\)
Here, the denominators are 6 and 9.
And least common multiple of 6 and 9 is 18.
Now for \(\frac{13}{6}\) multiply both the numerator and the denominator by 3.
\(\frac{13}{6}=\frac{13 \times 3}{6 \times 3}=\frac{39}{18}\)
And for \(\frac{1}{9}\) multiply both the numerator and the denominator by 2, we get
\(\frac{1}{9}=\frac{1 \times 2}{9 \times 2}=\frac{2}{18}\)
So, the equivalent fractions with the same denominator are:
\(\frac{39}{18}\) and \(\frac{2}{18}\)
7.7 Simplest form of a Fraction Figure it Out (Page No. 173)