Chapter 5 – Fractions
Practice set 17
1. Write the proper number in the box.
(1) \(\large \frac {1}{2}\) = \(\large \frac {□}{20}\)
Ans:
\(\large \frac {1}{2}\) = \(\large \frac {□}{20}\)
∴ \(\large \frac {1}{2}\) = \(\large \frac {1 \,×\, 10}{2\,×\, 10}\) = \(\large \frac {10}{20}\)
(2) \(\large \frac {3}{4}\) = \(\large \frac {15}{□}\)
Ans:
\(\large \frac {3}{4}\) = \(\large \frac {15}{□}\)
∴ \(\large \frac {3}{4}\) = \(\large \frac {3\,×\,5}{4\,×\,5}\) = \(\large \frac {15}{20}\)
(3) \(\large \frac {9}{11}\) = \(\large \frac {18}{□}\)
Ans:
\(\large \frac {9}{11}\) = \(\large \frac {18}{□}\)
∴ \(\large \frac {9}{11}\) = \(\large \frac {9\,×\,2}{11\,×\,2}\) = \(\large \frac {18}{22}\)
(4) \(\large \frac {10}{40}\) = \(\large \frac {□}{8}\)
Ans:
\(\large \frac {10}{40}\) = \(\large \frac {□}{8}\)
∴ \(\large \frac {10}{40}\) = \(\large \frac {10\,÷\,5}{40\,÷\,5}\) = \(\large \frac {2}{8}\)
(5) \(\large \frac {14}{26}\) = \(\large \frac {□}{13}\)
Ans:
\(\large \frac {14}{26}\) = \(\large \frac {□}{13}\)
∴ \(\large \frac {14}{26}\) = \(\large \frac {14\,÷\,2}{26\,÷\,2}\) = \(\large \frac {7}{13}\)
(6) \(\large \frac {□}{3}\) = \(\large \frac {4}{6}\)
Ans:
\(\large \frac {□}{3}\) = \(\large \frac {4}{6}\)
∴ \(\large \frac {□}{3}\) = \(\large \frac {4\,÷\,2}{6\,÷\,2}\) = \(\large \frac {4}{6}\)
(7) \(\large \frac {1}{□}\) = \(\large \frac {4}{20}\)
Ans:
\(\large \frac {1}{□}\) = \(\large \frac {4}{20}\)
∴ \(\large \frac {1}{□}\) = \(\large \frac {4\,÷\,4}{20\,÷\,4}\) = \(\large \frac {4}{20}\)
(8) \(\large \frac {□}{5}\) = \(\large \frac {10}{25}\)
Ans:
\(\large \frac {□}{5}\) = \(\large \frac {10}{25}\)
∴ \(\large \frac {□}{5}\) = \(\large \frac {10\,÷\,5}{5\,÷\,5}\) = \(\large \frac {10}{25}\)
2. Find an equivalent fraction with denominator 18, for each of the following fractions.
\(\large \frac {1}{2}\)
Ans:
\(\large \frac {1}{2}\) = \(\large \frac {1\,×\,9}{2\,×\,9}\) = \(\large \frac {9}{18}\)
\(\large \frac {2}{3}\)
Ans:
\(\large \frac {2}{3}\) = \(\large \frac {2\,×\,6}{3\,×\,6}\) = \(\large \frac {12}{18}\)
\(\large \frac {4}{6}\)
Ans:
\(\large \frac {4}{6}\) = \(\large \frac {4\,×\,3}{6\,×\,3}\) = \(\large \frac {12}{18}\)
\(\large \frac {2}{9}\)
Ans:
\(\large \frac {2}{9}\) = \(\large \frac {2\,×\,2}{9\,×\,2}\) = \(\large \frac {4}{18}\)
\(\large \frac {7}{9}\)
Ans:
\(\large \frac {7}{9}\) = \(\large \frac {7\,×\,2}{9\,×\,2}\) = \(\large \frac {14}{18}\)
\(\large \frac {5}{3}\)
Ans:
\(\large \frac {5}{3}\) = \(\large \frac {5\,×\,6}{3\,×\,6}\) = \(\large \frac {30}{18}\)
3. Find an equivalent fraction with denominator 5, for each of the following fractions.
\(\large \frac {6}{15}\)
Ans:
\(\large \frac {6}{15}\) = \(\large \frac {6\,÷\,3}{15\,÷\,3}\) = \(\large \frac {2}{5}\)
\(\large \frac {10}{25}\)
Ans:
\(\large \frac {10}{25}\) = \(\large \frac {10\,÷\,5}{25\,÷\,5}\) = \(\large \frac {2}{5}\)
\(\large \frac {12}{30}\)
Ans:
\(\large \frac {12}{30}\) = \(\large \frac {12\,÷\,7}{30\,÷\,6}\) = \(\large \frac {2}{5}\)
\(\large \frac {6}{10}\)
Ans:
\(\large \frac {6}{10}\) = \(\large \frac {6\,÷\,2}{10\,÷\,2}\) = \(\large \frac {4}{5}\)
\(\large \frac {21}{35}\)
Ans:
\(\large \frac {21}{35}\) = \(\large \frac {21\,÷\,7}{35\,÷\,7}\) = \(\large \frac {3}{5}\)
4. From the fractions given below, pair off the equivalent fractions.
\(\large \frac {2}{3}\)
Ans:
\(\large \frac {2}{3}\) = \(\large \frac {2\,×\,2}{3\,×\,2}\) = \(\large \frac {4}{6}\)
\(\large \frac {5}{7}\)
Ans:
\(\large \frac {5}{7}\) = \(\large \frac {5\,×\,2}{7\,×\,2}\) = \(\large \frac {10}{14}\)
\(\large \frac {5}{11}\)
Ans:
\(\large \frac {5}{11}\) = \(\large \frac {5\,×\,3}{11\,×\,3}\) = \(\large \frac {15}{33}\)
\(\large \frac {7}{9}\)
Ans:
\(\large \frac {7}{9}\) = \(\large \frac {7\,×\,2}{9\,×\,2}\) = \(\large \frac {14}{18}\)
5. Find two equivalent fractions for each of the following fractions.
\(\large \frac {7}{9}\)
Ans:
\(\large \frac {7}{9}\) = \(\large \frac {7\,×\,2}{9\,×\,2}\) = \(\large \frac {14}{18}\)
\(\large \frac {7}{9}\) = \(\large \frac {7\,×\,3}{9\,×\,3}\) = \(\large \frac {21}{27}\)
\(\large \frac {4}{5}\)
Ans:
\(\large \frac {4}{5}\) = \(\large \frac {4\,×\,2}{5\,×\,2}\) = \(\large \frac {8}{10}\)
\(\large \frac {4}{5}\) = \(\large \frac {4\,×\,3}{5\,×\,3}\) = \(\large \frac {12}{15}\)
\(\large \frac {3}{11}\)
Ans:
\(\large \frac {3}{11}\) = \(\large \frac {3\,×\,2}{11\,×\,2}\) = \(\large \frac {6}{22}\)
\(\large \frac {3}{11}\) = \(\large \frac {3\,×\,3}{11\,×\,3}\) = \(\large \frac {9}{33}\)
Practice set 18
Convert the given fractions into like fractions.
(1) \(\large \frac {3}{4}\), \(\large \frac {5}{8}\)
Ans: The number 8 is a multiple of both 4 and 8. So, make 8 as the common denominator.
\(\large \frac {3}{4}\), \(\large \frac {5}{8}\)
\(\large \frac {3\,×\,2}{4\,×\,2}\), \(\large \frac {5}{8}\)
∴ \(\large \frac {6}{8}\), \(\large \frac {5}{8}\)
Therefore, \(\large \frac {6}{8}\), \(\large \frac {5}{8}\) are the required like fractions.
(2) \(\large \frac {3}{5}\), \(\large \frac {3}{7}\)
Ans: The number 35 is a multiple of both 5 and 7. So, make 35 as the common denominator.
\(\large \frac {3}{5}\), \(\large \frac {3}{7}\)
\(\large \frac {3\,×\,7}{5\,×\,7}\), \(\large \frac {3\,×\,5}{7\,×\,5}\)
∴ \(\large \frac {21}{35}\), \(\large \frac {15}{35}\)
Therefore, \(\large \frac {21}{35}\), \(\large \frac {15}{35}\) are the required like fractions.
(3) \(\large \frac {4}{5}\), \(\large \frac {3}{10}\)
Ans: The number 10 is a multiple of both 5 and 10. So, make 10 as the common denominator.
\(\large \frac {4}{5}\), \(\large \frac {3}{10}\)
\(\large \frac {4\,×\,2}{5\,×\,2}\), \(\large \frac {3}{10}\)
∴ \(\large \frac {8}{10}\), \(\large \frac {3}{10}\)
Therefore, \(\large \frac {8}{10}\), \(\large \frac {3}{10}\) are the required like fractions.
(4) \(\large \frac {2}{9}\), \(\large \frac {1}{6}\)
Ans: The number 18 is a multiple of both 9 and 6. So, make 18 as the common denominator.
\(\large \frac {2}{9}\), \(\large \frac {1}{6}\)
\(\large \frac {2\,×\,2}{9\,×\,2}\), \(\large \frac {1\,×\,3}{6\,×\,3}\)
∴ \(\large \frac {4}{18}\), \(\large \frac {3}{18}\)
Therefore, \(\large \frac {4}{18}\), \(\large \frac {3}{18}\) are the required like fractions.
(5) \(\large \frac {1}{4}\), \(\large \frac {2}{3}\)
Ans: The number 12 is a multiple of both 4 and 3. So, make 12 as the common denominator.
\(\large \frac {1}{4}\), \(\large \frac {2}{3}\)
\(\large \frac {1\,×\,3}{4\,×\,3}\), \(\large \frac {2\,×\,4}{3\,×\,4}\)
∴ \(\large \frac {3}{12}\), \(\large \frac {8}{12}\)
Therefore, \(\large \frac {3}{12}\), \(\large \frac {8}{12}\) are the required like fractions.
(6) \(\large \frac {5}{6}\), \(\large \frac {4}{5}\)
Ans: The number 30 is a multiple of both 6 and 5. So, make 30 as the common denominator.
\(\large \frac {5}{6}\), \(\large \frac {4}{5}\)
\(\large \frac {5\,×\,5}{6\,×\,5}\), \(\large \frac {4\,×\,6}{5\,×\,6}\)
∴ \(\large \frac {25}{30}\), \(\large \frac {24}{30}\)
Therefore, \(\large \frac {25}{30}\), \(\large \frac {24}{30}\) are the required like fractions.
(7) \(\large \frac {3}{8}\), \(\large \frac {1}{6}\)
Ans: The number 24 is a multiple of both 8 and 6. So, make 24 as the common denominator.
\(\large \frac {3}{8}\), \(\large \frac {1}{6}\)
\(\large \frac {3\,×\,3}{8\,×\,3}\), \(\large \frac {1\,×\,4}{6\,×\,4}\)
∴ \(\large \frac {9}{24}\), \(\large \frac {4}{24}\)
Therefore, \(\large \frac {9}{24}\), \(\large \frac {4}{24}\) are the required like fractions.
(8) \(\large \frac {1}{6}\), \(\large \frac {4}{9}\)
Ans: The number 18 is a multiple of both 6 and 9. So, make 18 as the common denominator.
\(\large \frac {1}{6}\), \(\large \frac {4}{9}\)
\(\large \frac {1\,×\,3}{6\,×\,3}\), \(\large \frac {4\,×\,2}{9\,×\,2}\)
∴ \(\large \frac {3}{18}\), \(\large \frac {8}{18}\)
Therefore, \(\large \frac {3}{18}\), \(\large \frac {8}{18}\) are the required like fractions.
Practice set 19
Write the proper symbol from < , > , or = in the box.
(1) \(\large \frac {3}{7}\) ⬜ \(\large \frac {3}{7}\)
Ans:
\(\large \frac {3}{7}\) = \(\large \frac {3}{7}\)
(2) \(\large \frac {3}{8}\) ⬜ \(\large \frac {2}{8}\)
Ans:
\(\large \frac {3}{8}\) > \(\large \frac {2}{8}\)
(3) \(\large \frac {2}{11}\) ⬜ \(\large \frac {10}{11}\)
Ans:
\(\large \frac {2}{11}\) < \(\large \frac {10}{11}\)
(4) \(\large \frac {5}{15}\) ⬜ \(\large \frac {10}{30}\)
Ans:
\(\large \frac {5}{15}\) ⬜ \(\large \frac {10}{30}\)
∴ \(\large \frac {5\,×\,2}{15\,×\,2}\) ⬜ \(\large \frac {10}{30}\)
∴ \(\large \frac {10}{30}\) = \(\large \frac {10}{30}\)
∴ \(\large \frac {5}{15}\) = \(\large \frac {10}{30}\)
(5) \(\large \frac {5}{8}\) ⬜ \(\large \frac {5}{9}\)
Ans:
\(\large \frac {5}{8}\) ⬜ \(\large \frac {5}{8}\)
∴ \(\large \frac {5\,×\,9}{8\,×\,9}\) ⬜ \(\large \frac {5\,×\,8}{9\,×\,8}\)
∴ \(\large \frac {45}{72}\) > \(\large \frac {40}{72}\)
∴ \(\large \frac {5}{8}\) > \(\large \frac {5}{9}\)
(6) \(\large \frac {4}{7}\) ⬜ \(\large \frac {4}{11}\)
Ans:
\(\large \frac {4}{7}\) ⬜ \(\large \frac {4}{11}\)
∴ \(\large \frac {4\,×\,11}{7\,×\,11}\) ⬜ \(\large \frac {4\,×\,7}{11\,×\,7}\)
∴ \(\large \frac {44}{77}\) > \(\large \frac {28}{77}\)
∴ \(\large \frac {4}{7}\) > \(\large \frac {4}{11}\)
(7) \(\large \frac {10}{11}\) ⬜ \(\large \frac {10}{13}\)
Ans:
\(\large \frac {10}{11}\) ⬜ \(\large \frac {10}{13}\)
∴ \(\large \frac {10\,×\,13}{11\,×\,13}\) ⬜ \(\large \frac {10\,×\,11}{13\,×\,11}\)
∴ \(\large \frac {130}{143}\) > \(\large \frac {110}{143}\)
∴ \(\large \frac {10}{11}\) > \(\large \frac {10}{13}\)
(8) \(\large \frac {1}{5}\) ⬜ \(\large \frac {1}{9}\)
Ans:
\(\large \frac {1}{5}\) ⬜ \(\large \frac {1}{9}\)
∴ \(\large \frac {1\,×\,9}{5\,×\,9}\) ⬜ \(\large \frac {1\,×\,5}{9\,×\,5}\)
∴ \(\large \frac {9}{45}\) > \(\large \frac {5}{45}\)
∴ \(\large \frac {1}{5}\) > \(\large \frac {1}{9}\)
(9) \(\large \frac {5}{6}\) ⬜ \(\large \frac {1}{8}\)
Ans:
\(\large \frac {5}{6}\) ⬜ \(\large \frac {1}{8}\)
∴ \(\large \frac {5\,×\,4}{6\,×\,4}\) ⬜ \(\large \frac {1\,×\,3}{8\,×\,3}\)
∴ \(\large \frac {20}{24}\) > \(\large \frac {3}{24}\)
∴ \(\large \frac {5}{6}\) > \(\large \frac {1}{8}\)
(10) \(\large \frac {5}{12}\) ⬜ \(\large \frac {1}{6}\)
Ans:
\(\large \frac {5}{12}\) ⬜ \(\large \frac {1}{6}\)
∴ \(\large \frac {5}{12}\) ⬜ \(\large \frac {1\,×\,2}{6\,×\,2}\)
∴ \(\large \frac {5}{12}\) > \(\large \frac {2}{12}\)
∴ \(\large \frac {5}{12}\) > \(\large \frac {1}{6}\)
(11) \(\large \frac {7}{8}\) ⬜ \(\large \frac {14}{16}\)
Ans:
\(\large \frac {7}{8}\) ⬜ \(\large \frac {14}{16}\)
∴ \(\large \frac {7\,×\,2}{8\,×\,2}\) ⬜ \(\large \frac {14}{16}\)
∴ \(\large \frac {14}{16}\) = \(\large \frac {14}{16}\)
∴ \(\large \frac {7}{8}\) = \(\large \frac {14}{16}\)
(12) \(\large \frac {4}{9}\) ⬜ \(\large \frac {4}{9}\)
Ans:
\(\large \frac {4}{9}\) = \(\large \frac {4}{9}\)
(13) \(\large \frac {5}{18}\) ⬜ \(\large \frac {1}{9}\)
Ans:
\(\large \frac {5}{18}\) ⬜ \(\large \frac {1}{9}\)
∴ \(\large \frac {5}{18}\) ⬜ \(\large \frac {1\,×\,2}{9\,×\,2}\)
∴ \(\large \frac {5}{18}\) > \(\large \frac {2}{18}\)
∴ \(\large \frac {5}{18}\) > \(\large \frac {1}{9}\)
(14) \(\large \frac {2}{3}\) ⬜ \(\large \frac {4}{7}\)
Ans:
\(\large \frac {2}{3}\) ⬜ \(\large \frac {4}{7}\)
∴ \(\large \frac {2\,×\,7}{3\,×\,7}\) ⬜ \(\large \frac {4\,×\,3}{7\,×\,3}\)
∴ \(\large \frac {14}{21}\) > \(\large \frac {12}{21}\)
∴ \(\large \frac {2}{3}\) > \(\large \frac {4}{7}\)
(15) \(\large \frac {3}{7}\) ⬜ \(\large \frac {5}{9}\)
Ans:
\(\large \frac {3}{7}\) ⬜ \(\large \frac {5}{9}\)
∴ \(\large \frac {3\,×\,9}{7\,×\,9}\) ⬜ \(\large \frac {5\,×\,7}{9\,×\,7}\)
∴ \(\large \frac {27}{63}\) < \(\large \frac {35}{63}\)
∴ \(\large \frac {3}{7}\) < \(\large \frac {5}{9}\)
(16) \(\large \frac {4}{15}\) ⬜ \(\large \frac {1}{5}\)
Ans:
\(\large \frac {4}{15}\) ⬜ \(\large \frac {1}{5}\)
∴ \(\large \frac {4}{15}\) ⬜ \(\large \frac {1\,×\,3}{5\,×\,3}\)
∴ \(\large \frac {4}{15}\) > \(\large \frac {3}{15}\)
∴ \(\large \frac {4}{15}\) > \(\large \frac {1}{5}\)
Practice set 20
1. Add
(1) \(\large \frac {1}{5}\) + \(\large \frac {3}{5}\)
Ans:
\(\large \frac {1}{5}\) + \(\large \frac {3}{5}\)
= \(\large \frac {1\,+\,3}{5}\)
= \(\large \frac {4}{5}\)
∴ \(\large \frac {1}{5}\) + \(\large \frac {3}{5}\) = \(\large \frac {4}{5}\)
(2) \(\large \frac {2}{7}\) + \(\large \frac {4}{7}\)
Ans:
\(\large \frac {2}{7}\) + \(\large \frac {4}{7}\)
= \(\large \frac {2\,+\,4}{7}\)
= \(\large \frac {6}{7}\)
∴ \(\large \frac {2}{7}\) + \(\large \frac {4}{7}\) = \(\large \frac {6}{7}\)
(3) \(\large \frac {7}{12}\) + \(\large \frac {2}{12}\)
Ans:
\(\large \frac {7}{12}\) + \(\large \frac {2}{12}\)
= \(\large \frac {7\,+\,2}{12}\)
= \(\large \frac {9}{12}\)
= \(\large \frac {3\,×\,3}{3\,×\,4}\)
= \(\large \frac {3}{4}\)
∴ \(\large \frac {7}{12}\) + \(\large \frac {2}{12}\) = \(\large \frac {3}{4}\)
(4) \(\large \frac {2}{9}\) + \(\large \frac {7}{9}\)
Ans:
\(\large \frac {2}{9}\) + \(\large \frac {7}{9}\)
= \(\large \frac {2\,+\,7}{9}\)
= \(\large \frac {9}{9}\)
= 1
∴ \(\large \frac {2}{9}\) + \(\large \frac {7}{9}\) = 1
(5) \(\large \frac {3}{15}\) + \(\large \frac {4}{15}\)
Ans:
\(\large \frac {3}{15}\) + \(\large \frac {4}{15}\)
= \(\large \frac {3\,+\,4}{15}\)
= \(\large \frac {7}{15}\)
∴ \(\large \frac {3}{15}\) + \(\large \frac {4}{15}\) = \(\large \frac {7}{15}\)
(6) \(\large \frac {2}{7}\) + \(\large \frac {3}{7}\) + \(\large \frac {1}{7}\)
Ans:
\(\large \frac {2}{7}\) + \(\large \frac {3}{7}\) + \(\large \frac {1}{7}\)
= \(\large \frac {2\,+\,3\,+\,1}{7}\)
= \(\large \frac {6}{7}\)
∴ \(\large \frac {2}{7}\) + \(\large \frac {3}{7}\) + \(\large \frac {1}{7}\) = \(\large \frac {6}{7}\)
(7) \(\large \frac {2}{10}\) + \(\large \frac {4}{10}\) + \(\large \frac {3}{10}\)
Ans:
\(\large \frac {2}{10}\) + \(\large \frac {4}{10}\) + \(\large \frac {3}{10}\)
= \(\large \frac {2\,+\,4\,+\,3}{10}\)
= \(\large \frac {9}{10}\)
∴ \(\large \frac {2}{10}\) + \(\large \frac {4}{10}\) + \(\large \frac {3}{10}\) = \(\large \frac {9}{10}\)
(8) \(\large \frac {4}{9}\) + \(\large \frac {1}{9}\)
Ans:
\(\large \frac {4}{9}\) + \(\large \frac {1}{9}\)
= \(\large \frac {4\,+\,1}{9}\)
= \(\large \frac {5}{9}\)
∴ \(\large \frac {4}{9}\) + \(\large \frac {1}{9}\) = \(\large \frac {5}{9}\)
(9) \(\large \frac {5}{8}\) + \(\large \frac {3}{8}\)
Ans:
\(\large \frac {5}{8}\) + \(\large \frac {3}{8}\)
= \(\large \frac {5\,+\,3}{8}\)
= \(\large \frac {8}{8}\)
= 1
∴ \(\large \frac {5}{8}\) + \(\large \frac {3}{8}\) = 1
2. Mother gave \(\large \frac {3}{8}\ of one guava to Meena and \(\large \frac {2}{8}\ of the guava to Geeta. What part of the guava did she give them altogether?
Ans:
Mother gave \(\large \frac {3}{8}\ guava to Meena and \(\large \frac {2}{8}\ guava to Geeta.
Altogether she gave,
\(\large \frac {3}{8}\ + \(\large \frac {2}{8}\
= \(\large \frac {3\,+\,2}{8}\
= \(\large \frac {5}{8}\
Ans: Mother gave \(\large \frac {5}{8}\ part of the guava altogether.
3. The girls of Std V cleaned \(\large \frac {3}{4}\ of a field while the boys of Std IV cleaned \(\large \frac {1}{4}\. What part of the field was cleaned altogether?
Ans:
Girls cleaned \(\large \frac {3}{4}\ of field Boys cleaned \(\large \frac {2}{8}\ of field
Altogether they cleaned,
\(\large \frac {3}{4}\ + \(\large \frac {2}{8}\
= \(\large \frac {3\,×\,2}{4\,×\,2}\ + \(\large \frac {2}{8}\
= \(\large \frac {6}{8}\ + \(\large \frac {2}{8}\
= \(\large \frac {6\,+\,2}{8}\
= \(\large \frac {8}{8}\
= 1 (Whole field)
Ans: Altogether they cleaned the whole field.
Practice set 21
1. Subtract
(1) \(\large \frac {5}{7}\) – \(\large \frac {1}{7}\)
Ans:
\(\large \frac {3}{15}\) – \(\large \frac {4}{15}\)
= \(\large \frac {3\,–\,4}{15}\)
= \(\large \frac {7}{15}\)
∴ \(\large \frac {5}{7}\) – \(\large \frac {1}{7}\) = \(\large \frac {7}{15}\)
(2) \(\large \frac {5}{8}\) – \(\large \frac {3}{8}\)
Ans:
\(\large \frac {5}{8}\) – \(\large \frac {3}{8}\)
= \(\large \frac {5\,–\,3}{8}\)
= \(\large \frac {2}{8}\)
= \(\large \frac {2\,×\,1}{2\,×\,4}\)
= \(\large \frac {1}{4}\)
∴ \(\large \frac {5}{8}\) – \(\large \frac {3}{8}\) = \(\large \frac {1}{4}\)
(3) \(\large \frac {7}{9}\) – \(\large \frac {2}{9}\)
Ans:
\(\large \frac {7}{9}\) – \(\large \frac {2}{9}\)
= \(\large \frac {7\,–\,2}{9}\)
= \(\large \frac {5}{9}\)
∴ \(\large \frac {7}{9}\) – \(\large \frac {2}{9}\) = \(\large \frac {5}{9}\)
(4) \(\large \frac {8}{11}\) – \(\large \frac {5}{11}\)
Ans:
\(\large \frac {8}{11}\) – \(\large \frac {5}{11}\)
= \(\large \frac {8\,–\,5}{11}\)
= \(\large \frac {3}{11}\)
∴ \(\large \frac {8}{11}\) – \(\large \frac {5}{11}\) = \(\large \frac {3}{11}\)
(5) \(\large \frac {9}{13}\) – \(\large \frac {4}{13}\)
Ans:
\(\large \frac {9}{13}\) – \(\large \frac {4}{13}\)
= \(\large \frac {9\,–\,4}{13}\)
= \(\large \frac {5}{13}\)
∴ \(\large \frac {9}{13}\) – \(\large \frac {4}{13}\) = \(\large \frac {5}{13}\)
(6) \(\large \frac {7}{10}\) – \(\large \frac {3}{10}\)
Ans:
\(\large \frac {7}{10}\) – \(\large \frac {3}{10}\)
= \(\large \frac {7\,–\,3}{10}\)
= \(\large \frac {4}{10}\)
= \(\large \frac {2\,×\,2}{2\,×\,5}\)
= \(\large \frac {2}{5}\)
∴ \(\large \frac {7}{10}\) – \(\large \frac {3}{10}\) = \(\large \frac {2}{5}\)
(7) \(\large \frac {9}{12}\) – \(\large \frac {2}{12}\)
Ans:
\(\large \frac {9}{12}\) – \(\large \frac {2}{12}\)
= \(\large \frac {9\,–\,2}{12}\)
= \(\large \frac {7}{12}\)
∴ \(\large \frac {9}{12}\) – \(\large \frac {2}{12}\) = \(\large \frac {7}{12}\)
(8) \(\large \frac {10}{15}\) – \(\large \frac {3}{15}\)
Ans:
\(\large \frac {10}{15}\) – \(\large \frac {3}{15}\)
= \(\large \frac {10\,–\,3}{15}\)
= \(\large \frac {7}{15}\)
∴ \(\large \frac {10}{15}\) – \(\large \frac {3}{15}\) = \(\large \frac {7}{15}\)
2. \(\large \frac {7}{10}\ of a wall is to be painted. Ramu has painted \(\large \frac {4}{10}\ of it. How much more needs to be painted?
Ans:
\(\large \frac {7}{10}\ of a wall is to be painted.
Ramu has painted \(\large \frac {4}{10}\ of it.
So, the part of the wall which needs to be painted is,
\(\large \frac {7}{10}\ – \(\large \frac {4}{10}\
= \(\large \frac {7\,–\,4}{10}\)
= \(\large \frac {3}{10}\)
∴ \(\large \frac {3}{10}\) more of the wall needs to be painted.
Practice set 22
1. Add
(1) \(\large \frac {1}{8}\) + \(\large \frac {3}{4}\)
Ans:
\(\large \frac {1}{8}\) + \(\large \frac {3}{4}\)
= \(\large \frac {1}{8}\) + \(\large \frac {3\,×\,2}{4\,×\,2}\)
= \(\large \frac {1}{8}\) + \(\large \frac {6}{8}\)
= \(\large \frac {1\,+\,6}{8}\)
= \(\large \frac {7}{8}\)
∴ \(\large \frac {1}{8}\) + \(\large \frac {3}{4}\) = \(\large \frac {7}{8}\)
(2) \(\large \frac {2}{21}\) + \(\large \frac {3}{7}\)
Ans:
\(\large \frac {2}{21}\) + \(\large \frac {3}{7}\)
= \(\large \frac {2}{21}\) + \(\large \frac {3\,×\,3}{7\,×\,3}\)
= \(\large \frac {2}{21}\) + \(\large \frac {9}{21}\)
= \(\large \frac {2\,+\,9}{21}\)
= \(\large \frac {11}{21}\)
∴ \(\large \frac {2}{21}\) + \(\large \frac {3}{7}\) = \(\large \frac {11}{21}\)
(3) \(\large \frac {2}{5}\) + \(\large \frac {1}{3}\)
Ans:
\(\large \frac {2}{5}\) + \(\large \frac {1}{3}\)
= \(\large \frac {2\,×\,3}{5\,×\,3}\) + \(\large \frac {1\,×\,5}{3\,×\,5}\)
= \(\large \frac {6}{15}\) + \(\large \frac {5}{15}\)
= \(\large \frac {6\,+\,5}{15}\)
= \(\large \frac {11}{15}\)
∴ \(\large \frac {2}{5}\) + \(\large \frac {1}{3}\) = \(\large \frac {11}{15}\)
(4) \(\large \frac {2}{7}\) + \(\large \frac {1}{2}\)
Ans:
\(\large \frac {2}{7}\) + \(\large \frac {1}{2}\)
= \(\large \frac {2\,×\,2}{7\,×\,2}\) + \(\large \frac {1\,×\,7}{2\,×\,7}\)
= \(\large \frac {4}{14}\) + \(\large \frac {7}{14}\)
= \(\large \frac {4\,+\,7}{14}\)
= \(\large \frac {11}{14}\)
∴ \(\large \frac {2}{7}\) + \(\large \frac {1}{2}\) = \(\large \frac {11}{14}\)
(5) \(\large \frac {3}{9}\) + \(\large \frac {3}{5}\)
Ans:
\(\large \frac {3}{9}\) + \(\large \frac {3}{5}\)
= \(\large \frac {3\,×\,5}{9\,×\,5}\) + \(\large \frac {3\,×\,9}{5\,×\,9}\)
= \(\large \frac {15}{45}\) + \(\large \frac {27}{45}\)
= \(\large \frac {15\,+\,27}{45}\)
= \(\large \frac {42}{45}\)
∴ \(\large \frac {3}{9}\) + \(\large \frac {3}{5}\) = \(\large \frac {42}{45}\)
2. Subtract
(1) \(\large \frac {3}{10}\) – \(\large \frac {1}{20}\)
Ans:
\(\large \frac {3}{10}\) – \(\large \frac {1}{20}\)
= \(\large \frac {3\,×\,2}{10\,×\,2}\) – \(\large \frac {1}{20}\)
= \(\large \frac {6}{20}\) – \(\large \frac {1}{20}\)
= \(\large \frac {6\,–\,1}{20}\)
= \(\large \frac {5}{20}\)
= \(\large \frac {5\,×\,1}{5\,×\,4}\)
= \(\large \frac {1}{4}\)
∴ \(\large \frac {3}{10}\) – \(\large \frac {1}{20}\) = \(\large \frac {1}{4}\)
(2) \(\large \frac {3}{4}\) – \(\large \frac {1}{2}\)
Ans:
\(\large \frac {3}{4}\) – \(\large \frac {1}{2}\)
= \(\large \frac {3}{4}\) – \(\large \frac {1\,×\,2}{2\,×\,2}\)
= \(\large \frac {3}{4}\) – \(\large \frac {2}{4}\)
= \(\large \frac {3\,–\,2}{4}\)
= \(\large \frac {1}{4}\)
∴ \(\large \frac {3}{4}\) – \(\large \frac {1}{2}\) = \(\large \frac {1}{4}\)
(3) \(\large \frac {6}{14}\) – \(\large \frac {2}{7}\)
Ans:
\(\large \frac {6}{14}\) – \(\large \frac {2}{7}\)
= \(\large \frac {6}{14}\) – \(\large \frac {2\,×\,2}{7\,×\,2}\)
= \(\large \frac {6}{14}\) – \(\large \frac {4}{14}\)
= \(\large \frac {6\,–\,4}{14}\)
= \(\large \frac {2}{14}\)
= \(\large \frac {2\,×\,1}{2\,×\,7}\)
= \(\large \frac {1}{7}\)
∴ \(\large \frac {6}{14}\) – \(\large \frac {2}{7}\) = \(\large \frac {1}{7}\)
(4) \(\large \frac {4}{6}\) – \(\large \frac {3}{5}\)
Ans:
\(\large \frac {4}{6}\) – \(\large \frac {3}{5}\)
= \(\large \frac {4\,×\,5}{6\,×\,5}\) – \(\large \frac {3\,×\,6}{5\,×\,6}\)
= \(\large \frac {20}{30}\) – \(\large \frac {18}{30}\)
= \(\large \frac {20\,–\,18}{30}\)
= \(\large \frac {2}{30}\)
= \(\large \frac {2\,×\,1}{2\,×\,15}\)
= \(\large \frac {1}{15}\)
∴ \(\large \frac {4}{6}\) – \(\large \frac {3}{5}\) = \(\large \frac {1}{15}\)
(5) \(\large \frac {2}{7}\) – \(\large \frac {1}{4}\)
Ans:
\(\large \frac {2}{7}\) – \(\large \frac {1}{4}\)
= \(\large \frac {2\,×\,4}{7\,×\,4}\) – \(\large \frac {1\,×\,7}{4\,×\,7}\)
= \(\large \frac {8}{28}\) – \(\large \frac {7}{28}\)
= \(\large \frac {8\,–\,7}{28}\)
= \(\large \frac {1}{28}\)
∴ \(\large \frac {2}{7}\) – \(\large \frac {1}{4}\) = \(\large \frac {1}{28}\)
Practice set 23
1. What is \(\large \frac {1}{3}\) of each of the collections given below?
(1) 15 pencils
Ans:
\(\large \frac {1}{3}\) × 15
= 15 ÷ 3
= 5 pencils
(2) 21 balloons
Ans:
\(\large \frac {1}{3}\) × 21
= 21 ÷ 3
= 7 balloons
(3) 9 children
Ans:
\(\large \frac {1}{3}\) × 9
= 9 ÷ 3
= 3 children
(4) 18 books
Ans:
\(\large \frac {1}{3}\) × 18
= 18 ÷ 3
= 6 books
2. What is \(\large \frac {1}{5}\) of each of the following ?
(1) 20 rupees
Ans:
\(\large \frac {1}{5}\) × 20
= 20 ÷ 5
= 4 rupees
(2) 30 km
Ans:
\(\large \frac {1}{5}\) × 30
= 30 ÷ 5
= 6 km
(3) 15 litres
Ans:
\(\large \frac {1}{5}\) × 15
= 15 ÷ 5
= 3 litres
(4) 25 cm
Ans:
\(\large \frac {1}{5}\) × 25
= 25 ÷ 5
= 5 cm
3. Find the part of each of the following numbers equal to the given fraction.
(1) \(\large \frac {2}{3}\) of 30
Ans:
We’ll take \(\large \frac {1}{3}\) of 30 and take it twice
∴ \(\large \frac {1}{3}\) × 30
= 30 ÷ 3
= 10
Now,
2 × 10 = 20
∴ \(\large \frac {2}{3}\) of 30 = 20
(2) \(\large \frac {7}{11}\) of 22
Ans:
We’ll take \(\large \frac {1}{11}\) of 22 and take it seven times
∴ \(\large \frac {1}{11}\) × 22
= 22 ÷ 11
= 2
Now,
7 × 2 = 14
∴ \(\large \frac {2}{3}\) of 30 = 14
(3) \(\large \frac {3}{8}\) of 64
Ans:
We’ll take \(\large \frac {1}{8}\) of 64 and take it thrice
∴ \(\large \frac {1}{8}\) × 64
= 64 ÷ 8
= 8
Now,
3 × 8 = 24
∴ \(\large \frac {3}{8}\) of 64 = 24
(4) \(\large \frac {5}{13}\) of 65
Ans:
We’ll take \(\large \frac {1}{13}\) of 65 and take it five times
∴ \(\large \frac {1}{13}\) × 65
= 65 ÷ 13
= 5
Now,
5 × 5 = 25
∴ \(\large \frac {5}{13}\) of 65 = 25