# CBSE Class 7 - Maths - Fractions - Solved Problems

A fraction is a part of whole.

Fractions are of various types. Commonly used fractions are mixed fractions, proper fractions

e.g. $\frac{13}{4}, 2\frac{3}{4}, \frac{1}{2}$ etc.

COMPARE FRACTIONS

We can compare two or more fractions by taking the L.C.M of the denominators of the given fractions. Fraction with a greater denominator is bigger and vice versa.

Q1: Compare $\frac{23}{52} \textrm{ and } \frac{19}{22}$

Answer: $\frac{23}{52} > \frac{19}{22}$

Q2: Compare $\frac{5}{6} \textrm{ and } \frac{7}{9}$

Answer: LCM of 6 and 9 is 18

$\frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}$

$\frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18}$

$\frac{15}{18} > \frac{14}{18} \Rightarrow \frac{5}{6} > \frac{7}{9}$

To add or subtract two or more fractions there are three simple steps.

1. Make The Denominator Same

2. Add or Subtract The Numerators

3. Simplify The Fraction

Q3: Add $6\frac{1}{3} + 7\frac{3}{4}$

$6\frac{1}{3} = \frac{19}{3}+$7\frac{3}{4} = \frac{31}{4}$L.C.M of 3 and 4 is 12$\therefore \frac{19}{3} = \frac{19 \times 4}{3 \times 4} = \frac{76}{12}\frac{31}{4} = \frac{31 \times 3}{4 \times 3} = \frac{93}{12}$Now,$\frac{76}{12} + \frac{93}{12}= \frac{169}{12}= 14\frac{1}{12}$MULTIPLICATION OF A PROPER OR IMPROPER FRACTION BY A WHOLE NUMBER To multiply a whole number with a proper or improper fraction, we multiply the whole number with the numerator of the fraction, keeping the denominator same. Q4: Multiply$\frac{5}{7}$by 3 Answer:$\frac{5}{7} \times 3 = \frac{15}{7}$MULTIPLICATION OF A MIXED FRACTION BY A WHOLE NUMBER To multiply a whole number with a mixed fraction, we first convert the mixed fraction to an improper fraction and then multiply. Q5: Solve$6 \times 4\frac{2}{5}$Answer:$6 \times 4\frac{2}{5}  = 6 \times \frac{22}{5}  = \frac{6 \times 22}{5}= \frac{132}{5} = 26\frac{2}{5}$MULTIPLICATION OF A FRACTION BY A FRACTION We multiply two fractions as$ \frac{\textrm{Product of Numerators}}{\textrm{Product of Denominators}}$Q6: Solve$\frac{5}{3} \times \frac{2}{7} $Answer:$\frac{5}{3} \times \frac{2}{7} = \frac{5 \times 2}{3 \times 7} = \frac{10}{21}$Note: - Fraction as an operator ʻof ʼ represents multiplication. - The non-zero numbers whose product with each other is 1, are called the reciprocals of each other Q7: In a class, there are 60 students. One-third of them are girls. How many girls are there in the class? Answer: Total Girl students are =$\frac{1}{3}\textrm{ of } 60= \frac{1}{3} \times  60$= 20 DIVISION OF A PROPER OR IMPROPER FRACTION BY A WHOLE NUMBER While dividing a fraction by a whole number, we multiply the fraction by the reciprocal of the whole number. Q8: Solve$\frac{5}{3} \div 6$Answer:$ \frac{5}{3} \div 6  = \frac{5}{3} \times \frac{1}{6}  = \frac{5}{18} $DIVISION OF A WHOLE NUMBER BY A FRACTION While dividing a whole number by a fraction, we multiply the whole number by the reciprocal of the fraction. Q9: Solve$6 \div \frac{5}{3}$Answer:$6 \div \frac{5}{3}= 6 \times \frac{3}{5}= \frac{18}{5}$Q10: Solve$6 \div \frac{3}{5}$Answer:$6 \div \frac{3}{5}= 6 \times \frac{5}{3}= 10$DIVISION OF A FRACTION BY ANOTHER FRACTION While dividing by another fraction, we multiply the first fraction by the reciprocal a fraction of the other. Q11: Solve$\frac{4}{3} \div \frac{3}{5}$Answer:$\frac{4}{3} \div \frac{3}{5} = \frac{4}{3} \times \frac{5}{3} = \frac{20}{9}\$