Understanding Fractions

Hello, Year 4! Today, we’re going to learn about fractions, specifically the simplest formal fractions. A fraction tells us how many parts of a whole we have.

What is a Fraction?

A fraction is made up of two numbers:

  • The top number is called the numerator. It tells us how many parts we have.
  • The bottom number is called the denominator. It tells us how many equal parts the whole is divided into.

For example, in the fraction $$\frac{3}{4}$$:

  • The numerator is 3 (we have 3 parts).
  • The denominator is 4 (the whole is divided into 4 equal parts).

Simplest Form of a Fraction

A fraction is in its simplest form when the numerator and the denominator have no common factors other than 1. This means they cannot be divided by the same number anymore.

For example:

  • The fraction $$\frac{4}{8}$$ can be simplified. Both 4 and 8 can be divided by 4:$$\frac{4 \div 4}{8 \div 4} = \frac{1}{2}$$

So, $$\frac{1}{2}$$ is the simplest form of $$\frac{4}{8}$$.

Key Rules for Simplifying Fractions

  1. Find Common Factors: Look for numbers that can divide both the numerator and the denominator.
  2. Divide: Divide both numbers by their greatest common factor (GCF).
  3. Check: Make sure that the new fraction cannot be simplified further.

Tips and Tricks for Simplifying Fractions

  • List the Factors: Write down the factors of the numerator and denominator to find the greatest common factor.
  • Use Visuals: Drawing a circle or using blocks can help you see how fractions work.
  • Practice: The more you practice simplifying fractions, the easier it will become!

Practice Questions

Easy Level Questions

  1. Simplify $$\frac{2}{4}$$.
  2. Simplify $$\frac{6}{12}$$.
  3. Simplify $$\frac{3}{9}$$.
  4. Simplify $$\frac{8}{10}$$.
  5. Simplify $$\frac{5}{15}$$.
  6. What is the simplest form of $$\frac{10}{20}$$?
  7. Simplify $$\frac{4}{16}$$.
  8. What is the simplest form of $$\frac{12}{16}$$?
  9. Simplify $$\frac{9}{27}$$.
  10. What is the simplest form of $$\frac{14}{21}$$?

Medium Level Questions

  1. Simplify $$\frac{15}{25}$$.
  2. What is the simplest form of $$\frac{18}{24}$$?
  3. Simplify $$\frac{20}{30}$$.
  4. What is the simplest form of $$\frac{9}{36}$$?
  5. Simplify $$\frac{28}{42}$$.
  6. What is the simplest form of $$\frac{45}{60}$$?
  7. Simplify $$\frac{12}{36}$$.
  8. What is the simplest form of $$\frac{30}{45}$$?
  9. Simplify $$\frac{21}{28}$$.
  10. What is the simplest form of $$\frac{50}{100}$$?

Hard Level Questions

  1. Simplify $$\frac{64}{80}$$.
  2. What is the simplest form of $$\frac{36}{48}$$?
  3. Simplify $$\frac{81}{108}$$.
  4. What is the simplest form of $$\frac{72}{90}$$?
  5. Simplify $$\frac{99}{121}$$.
  6. What is the simplest form of $$\frac{56}{84}$$?
  7. Simplify $$\frac{44}{88}$$.
  8. What is the simplest form of $$\frac{63}{81}$$?
  9. Simplify $$\frac{100}{250}$$.
  10. What is the simplest form of $$\frac{88}{132}$$?

Answers and Explanations

Easy Level Answers

  1. $$\frac{1}{2}$$
  2. $$\frac{1}{2}$$
  3. $$\frac{1}{3}$$
  4. $$\frac{4}{5}$$
  5. $$\frac{1}{3}$$
  6. $$\frac{1}{2}$$
  7. $$\frac{1}{4}$$
  8. $$\frac{3}{4}$$
  9. $$\frac{1}{3}$$
  10. $$\frac{2}{3}$$

Medium Level Answers

  1. $$\frac{3}{5}$$
  2. $$\frac{3}{4}$$
  3. $$\frac{2}{3}$$
  4. $$\frac{1}{4}$$
  5. $$\frac{2}{3}$$
  6. $$\frac{3}{4}$$
  7. $$\frac{1}{3}$$
  8. $$\frac{2}{3}$$
  9. $$\frac{3}{4}$$
  10. $$\frac{1}{2}$$

Hard Level Answers

  1. $$\frac{4}{5}$$
  2. $$\frac{3}{4}$$
  3. $$\frac{3}{4}$$
  4. $$\frac{4}{5}$$
  5. $$\frac{9}{11}$$
  6. $$\frac{2}{3}$$
  7. $$\frac{1}{2}$$
  8. $$\frac{7}{9}$$
  9. $$\frac{2}{5}$$
  10. $$\frac{2}{3}$$

Now, practice these questions, and remember to simplify your fractions whenever you can! Happy learning!