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!