Class 7 Maths Fractions Questions and Solutions

Definitions and Types of Fractions

• A fraction is a numerical representation indicating parts of a whole, expressed as a quotient of two integers: the numerator over the denominator.
• A proper fraction has a numerator that is smaller than the denominator, indicating a value less than one.
• A mixed number is a combination of a whole number and a proper fraction (e.g., 3 ¼).
• An improper fraction has a numerator greater than the denominator, indicating a value greater than or equal to one.

Operations with Fractions

• The reciprocal of a fraction ( a/b ) is ( b/a ). For ( 5/129 ), the reciprocal is ( 129/5 ).
• The product of ( 5/129 ) and its reciprocal ( 129/5 ) equals 1.
• To calculate how much cloth Rehana receives if Sunita gives ( 1/3 ) of ( 3/4 ) m:
  • ( 1/3 \times 3/4 = 1/4 ) m.
• If Anuradha completes work in 6 hours, her work rate for 1 hour can be determined based on the total work expected.

Work and Distance Calculations

• If Raj travels ( 360 ) km on three-fifths of his petrol tank, then with a full tank, he would cover ( 360 / (3/5) = 600 ) km.
• To find what part of the work Anuradha can do in 1 hour, divide the total work by 6.
• The result of ( 3/10 \div (1/4 \times 3/5) ) can be calculated as follows:
  • Find ( 1/4 \times 3/5 = 3/20 ), then divide ( 3/10 ) by ( 3/20 ) which equals ( 2/1 ) or 2.

Fraction Operations and Conversions

• The product of ( \frac{2}{5} ) and ( 5 \frac{1}{4} ) is calculated by converting ( 5 \frac{1}{4} ) to an improper fraction and multiplying.
• To find the result of ( 3 \frac{1}{2} \div 4 ):
  • Convert to an improper fraction and divide accordingly.
• To find the sum of ( 1/6 ) and ( 2/9 ), convert both fractions to a common denominator and then add.

Practical Applications

• From a cake weighing ( 5 ) kg, the number of ( 1/4 ) kg pieces is calculated by dividing ( 5 ) kg by ( 1/4 ), which yields ( 20 ) pieces.
• If ( 3/4 ) of a cake is eaten, ( 1/4 ) of the cake remains.
• If ( 6 ) kg of a cake is cut into ( 1/3 ) kg pieces, the number of pieces is ( 6 / (1/3) = 18 ) pieces.
• The result of ( \frac{1}{4 \frac{2}{7}} + \frac{1}{3 \frac{11}{13}} + \frac{1}{\frac{5}{9}} ) involves finding a common denominator for calculation.

Interesting Fraction Values

• Finding what ( 1/8 ) of a number equates to can be solved by determining the number first from given operations such as ( \frac{2/5}{1/20} ) which yields a specific total.
• The reciprocal of ( 7/8 ) is ( 8/7 ).