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Introduction Quiz - CBSE Class 7 Mathematics

Free practice quiz: Introduction (CBSE Class 7 Mathematics). 18 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 7 Mathematics practice quiz has 18 multiple-choice questions on Introduction, and 18 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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What a fraction means

  • A fraction shows equal parts of a whole or a collection.
  • The bottom number (denominator) tells how many equal parts the whole is divided into.
  • The top number (numerator) tells how many of those equal parts are taken.
General fraction
\[\frac{a}{b},\quad b \neq 0\]
Part of a total
\[\text{Fraction} = \frac{\text{part}}{\text{total}}\]

Common mistake: Mixing up numerator and denominator. The numerator is always on top, and the denominator is always below the line.

Types of fractions

  • Proper fraction: numerator smaller than denominator, so its value is less than one.
  • Improper fraction: numerator greater than or equal to denominator, so its value is one or more.
  • A unit fraction has numerator one. Any nonzero number over itself equals one.
Proper fraction
\[\frac{a}{b},\ a < b\]
Improper fraction
\[\frac{a}{b},\ a \geq b\]
Same numerator and denominator
\[\frac{a}{a} = 1,\ a \neq 0\]

Common mistake: Calling a fraction with a larger numerator 'proper'. A larger numerator than denominator makes it improper, not proper.

Equivalent fractions and simplest form

  • Multiplying or dividing the top and bottom by the same nonzero number gives an equal fraction.
  • To simplify, divide both numbers by their HCF until no common factor except one remains.
  • Two fractions are equal if their cross products are equal.
Making equivalent fractions
\[\frac{a}{b} = \frac{a \times n}{b \times n},\ n \neq 0\]
Simplifying using HCF h
\[\frac{a}{b} = \frac{a \div h}{b \div h}\]
Cross-multiplication check
\[\frac{a}{b} = \frac{c}{d} \iff a \times d = b \times c\]

Common mistake: Dividing only the numerator or only the denominator. You must do the same operation to both, or the value changes.

Comparing fractions

  • With the same denominator, the fraction with the bigger numerator is bigger.
  • With the same numerator, the fraction with the smaller denominator is bigger, because its parts are larger.
  • Otherwise, cross-multiply or rewrite both fractions with a common denominator (LCM).
Unit fractions
\[\frac{1}{m} > \frac{1}{n} \text{ when } m < n\]
Cross-multiplication compare
\[\frac{a}{b} > \frac{c}{d} \iff a \times d > b \times c \quad (b, d > 0)\]

Common mistake: Thinking a bigger denominator means a bigger fraction. More pieces means each piece is smaller.

Decimals, percentages and measuring

  • To change a decimal to a fraction, write the digits over 10, 100 or 1000, then simplify.
  • To change a fraction to a percentage, multiply it by 100.
  • To find how many small measures make a bigger amount, divide the amount by the measure.
Decimal with k digits after the point
\[\text{decimal} = \frac{\text{digits without the point}}{10^{k}}\]
Fraction to percentage
\[\frac{a}{b} = \left(\frac{a}{b} \times 100\right)\%\]
How many measures fit (same denominator)
\[\frac{a}{b} \div \frac{c}{b} = \frac{a}{c}\]

Common mistake: Forgetting to simplify after writing a decimal over a power of 10, or forgetting to multiply by 100 when finding a percentage.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. What is a fraction?

    Show answer

    Answer: A. A part of a whole

    A fraction represents a part of a whole number, typically expressed as one number over another.

  2. Which fraction is bigger: 1/2 or 1/3?

    Show answer

    Answer: A. 1/2

    1/2 is greater than 1/3 because each half is larger than each third of the same whole.

  3. If a fraction's numerator is equal to its denominator, what is the fraction equal to?

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    Answer: A. 1

    When the numerator and denominator of a fraction are equal, the fraction represents a whole, or 1.

  4. Which of these fractions is equivalent to 3/9?

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    Answer: A. 1/3

    The fraction 3/9 simplifies to 1/3 by dividing both terms by 3, which is their greatest common divisor.

  5. How would you express 1/5 as a percentage?

    Show answer

    Answer: A. 20%

    To find the percentage, multiply the fraction by 100: (1/5)*100 = 20%.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. Which of the following is a correct fraction representation?
  2. If you divide a pizza into 2 equal parts, what is the fraction for one part?
  3. What is the numerator in the fraction 5/8?
  4. Which part of 3/7 is the denominator?
  5. When you simplify the fraction 10/20, what is the result?
  6. A student scores 15 out of 30 in a test. What fraction of the total marks does this represent?
  7. If you have a fraction 7/14, what two actions can simplify it directly?
  8. How do you convert 0.75 to a fraction?
  9. How can you check if two fractions, 2/4 and 1/2, are equivalent?
  10. A recipe requires 1/3 cup of oil, but you only have a 1/6 cup measure. How many times do you need to use the 1/6 cup to equal 1/3 cup?
  11. Compare: Which is larger, 4/5 or 5/6?
  12. If a fraction has a numerator larger than its denominator, what type of fraction is it?
  13. If you need 3/4 cup of sugar but only have a 1/4 cup measure, how many times will you fill it?

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