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
$\frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}$
$\frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18}$
$\frac{15}{18} > \frac{14}{18} \Rightarrow \frac{5}{6} > \frac{7}{9}$
ADDITION AND SUBTRACTION OF FRACTION
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} $
Answer:
$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}$
Ch 2 - Decimals - Multiplication and Division (Worksheet)
Ch 2 - Fractions and Decimals - NCERT Exercise Answers 2.6
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