What are Fractions?

Fractions are numbers that show parts of a whole. They have two parts: the numerator (the top number) and the denominator (the bottom number).

  • The numerator tells us how many parts we have.
  • The denominator tells us how many equal parts the whole is divided into.

What is a Proper Fraction?

A proper fraction is a fraction where the numerator is less than the denominator. This means you have fewer parts than the whole.

Example of Proper Fractions:

  • \frac{1}{2}
    (one part out of two)
  • \frac{3}{4}
    (three parts out of four)

What is an Improper Fraction?

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. This means you have more parts than the whole or exactly one whole.

Example of Improper Fractions:

  • \frac{5}{4}
    (five parts out of four, which is more than one whole)
  • \frac{3}{3}
    (three parts out of three, which is exactly one whole)

Key Rules

  1. Proper Fractions: The numerator is always smaller than the denominator. For example, \frac{2}{5}
    is proper because 2 < 5.
  2. Improper Fractions: The numerator is greater than or equal to the denominator. For example, \frac{7}{6}
    is improper because 7 > 6.
  3. Mixed Numbers: Sometimes, we can also express improper fractions as mixed numbers. A mixed number has a whole number and a proper fraction. For example, \frac{5}{4}
    can be expressed as 1\frac{1}{4}
    (one whole and one quarter).

Tips and Tricks

  • To remember which is which, think about proper (like ‘proper’ behaviour), which means less than a whole, and improper (like ‘improper’ behaviour), which means more than a whole.
  • When you have an improper fraction, you can convert it to a mixed number to make it easier to understand.

Questions

Easy Level Questions

  1. Is \frac{3}{5}
    a proper or improper fraction?
  2. Is \frac{4}{4}
    a proper or improper fraction?
  3. What is the numerator of \frac{2}{7}
    ?
  4. What is the denominator of \frac{5}{2}
    ?
  5. Convert \frac{9}{8}
    to a mixed number.
  6. Is \frac{1}{3}
    a proper fraction?
  7. Write a proper fraction using the numbers 2 and 6.
  8. Write an improper fraction using the numbers 7 and 4.
  9. Is \frac{5}{5}
    proper or improper?
  10. Which is larger: \frac{2}{3}
    or \frac{4}{5}
    ?

Medium Level Questions

  1. Convert \frac{11}{4}
    to a mixed number.
  2. Is \frac{8}{10}
    proper or improper?
  3. Write a fraction that is improper with a denominator of 7.
  4. How many equal parts are in \frac{6}{4}
    ?
  5. What is the mixed number for \frac{13}{5}
    ?
  6. Is \frac{7}{8}
    a proper or improper fraction?
  7. Write a proper fraction with a numerator of 1.
  8. Can \frac{6}{6}
    be considered proper or improper?
  9. Compare \frac{3}{8}
    and \frac{2}{6}
    . Which is greater?
  10. What type of fraction is \frac{10}{10}
    ?

Hard Level Questions

  1. Convert the improper fraction \frac{17}{6}
    to a mixed number.
  2. How would you express \frac{9}{3}
    as a mixed number?
  3. Is \frac{15}{14}
    proper or improper?
  4. Write an improper fraction that is equivalent to the proper fraction \frac{2}{3}
    .
  5. What is the sum of \frac{1}{2}
    and \frac{1}{2}
    ?
  6. If \frac{7}{4}
    is improper, what is its mixed number?
  7. Convert \frac{28}{6}
    to a mixed number.
  8. Is \frac{2}{2}
    a proper or improper fraction?
  9. Which is larger: \frac{5}{4}
    or \frac{3}{3}
    ?
  10. Create a proper fraction with a numerator of 3 and a denominator of 10.

Answers

Easy Level Answers

  1. Proper
  2. Improper
  3. 2
  4. 4
  5. 1\frac{1}{8}
  6. Yes
  7. \frac{2}{6}
  8. \frac{7}{4}
  9. Improper
  10. \frac{4}{5}
    is larger

Medium Level Answers

  1. 2\frac{3}{4}
  2. Proper
  3. \frac{7}{5}
  4. 6
  5. 2\frac{3}{5}
  6. Proper
  7. \frac{1}{5}
  8. Improper
  9. \frac{3}{8}
    is greater
  10. Proper

Hard Level Answers

  1. 2\frac{5}{6}
  2. 3\frac{0}{3}
  3. Improper
  4. \frac{4}{6}
  5. 1
  6. 1\frac{3}{4}
  7. 4\frac{2}{3}
  8. Improper
  9. \frac{5}{4}
    is larger
  10. \frac{3}{10}

This structured approach to understanding proper and improper fractions should help you learn and enjoy maths even more!