Class 7 Maths Fractions Questions and Solutions
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Questions and Answers

What is the definition of a fraction in mathematics?

  • A whole number
  • A part of a whole thing (correct)
  • A decimal number
  • An odd number

    • How is a proper fraction defined?

  • A number representing a part of a whole (correct)
  • A combination of whole number and proper fraction
  • Numerator greater than denominator
  • A number where the denominator is greater than the numerator

    • What type of fraction is a combination of a whole number and a proper fraction?

  • Proper fraction
  • Mixed fraction (correct)
  • Improper fraction
  • Equivalent fraction

    • What is the product of 5/129 and its reciprocal?

    <p>$1$</p> Signup and view all the answers

    What does the numerator and denominator of a fraction represent?

    <p>The ratio of the fraction</p> Signup and view all the answers

    Which type of fraction has the numerator greater than the denominator?

    <p>Improper fraction</p> Signup and view all the answers

    What is the reciprocal of 5/129?

    <p>129/5</p> Signup and view all the answers

    If Sunita has 3/4 m of cloth and gives 1/3 of it to Rehana, how much cloth does Rehana have?

    <p>1/4 m</p> Signup and view all the answers

    In 6 hours, what part of a work can Anuradha do?

    <p>1/6</p> Signup and view all the answers

    What is the product of (⅖) and 5 ¼?

    <p>21/10</p> Signup and view all the answers

    What is the result of dividing 3/10 by (1/4 of 3/5)?

    <p>3/20</p> Signup and view all the answers

    What is the value of 1/(4 2/7) + 1/(3 11/13) + 1/(5/9)?

    <p>172/75</p> Signup and view all the answers

    What is the result of 3 ½ ÷ 4?

    <p>7/8</p> Signup and view all the answers

    What does 1/8 of a number equal to?

    <p>(2/5) ÷ (1/20)</p> Signup and view all the answers

    If Raj travels 360 km on three-fifths of his petrol tank, how far would he travel at the same rate with a full tank of petrol?

    <p>600 km</p> Signup and view all the answers

    What is the result of 2/3 ÷ 4?

    <p>1/6</p> Signup and view all the answers

    If a cake weighs 5 kg, how many 1/4 kg pieces can be cut from it?

    <p>20</p> Signup and view all the answers

    What is the reciprocal of 7/8?

    <p>8/7</p> Signup and view all the answers

    If 3/4 of a cake is eaten, what fraction of the cake remains?

    <p>1/4</p> Signup and view all the answers

    What is the sum of 1/6 and 2/9?

    <p>5/18</p> Signup and view all the answers

    If a cake weighs 6 kg and 1/3 kg pieces are cut from it, how many pieces can be cut?

    <p>18</p> Signup and view all the answers

    What is the product of 5/129 and its reciprocal?

    <p>1</p> Signup and view all the answers

    If Sunita has 3/4 m of cloth and gives 1/3 of it to Rehana, how much cloth does Rehana have?

    <p>2/3 m</p> Signup and view all the answers

    What part of the work can Anuradha do in 1 hour?

    <p>1/6</p> Signup and view all the answers

    What is the result of multiplying (⅖) by 5 ¼?

    <p>21/10</p> Signup and view all the answers

    What is the result of dividing 3/10 by (1/4 of 3/5)?

    <p>9/10</p> Signup and view all the answers

    What is the value of rac{1}{4rac{2}{7}}+rac{1}{3rac{11}{13}}+rac{1}{rac{5}{9}}?

    <p>rac{172}{75}</p> Signup and view all the answers

    What is the result of dividing 3 ½ by 4?

    <p>rac{7}{8}</p> Signup and view all the answers

    What does 1/8 of a number equal to if it is equal to 2/5 ÷ 1/20?

    <p>rac{64}{5}</p> Signup and view all the answers

    If Raj travels 360 km on three-fifths of his petrol tank, how far would he travel at the same rate with a full tank of petrol?

    <p>600 km</p> Signup and view all the answers

    Study Notes

    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 ).

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    Description

    Test your understanding of arithmetic operations on fractions with these questions and solutions based on the latest NCERT curriculum. Explore the concept of fractions, their representation, and practical applications through this quiz.

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