Year 8 Maths: Fractions and Mixed Numbers

Understanding Fractions

What is a Fraction?

A fraction represents a part of a whole. It consists of two numbers:

• The numerator (the top number) tells us how many parts we have.
• The denominator (the bottom number) 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).

Types of Fractions

1. Proper Fractions: The numerator is less than the denominator. Example: $$\frac{2}{5}$$ .
2. Improper Fractions: The numerator is equal to or greater than the denominator. Example: $$\frac{5}{4}$$ .
3. Mixed Numbers: A whole number combined with a proper fraction. Example: $$1 \frac{1}{2}$$ (which means 1 whole and half).

Mixed Numbers

What is a Mixed Number?

A mixed number has both a whole part and a fractional part. For example, in $$1 \frac{2}{3}$$ :

• The whole number is 1.
• The fraction is $$\frac{2}{3}$$ .

How to Convert Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, follow these steps:

1. Multiply the whole number by the denominator of the fraction.
2. Add the numerator to this result.
3. Place the answer over the original denominator.

Example: Convert $$1 \frac{2}{3}$$ to an improper fraction.

1. Multiply: $$1 \times 3 = 3$$ .
2. Add: $$3 + 2 = 5$$ .
3. So, $$1 \frac{2}{3} = \frac{5}{3}$$ .

How to Convert Improper Fractions to Mixed Numbers

To convert an improper fraction back to a mixed number, follow these steps:

1. Divide the numerator by the denominator.
2. The quotient is the whole number.
3. The remainder is the new numerator, and the denominator stays the same.

Example: Convert $$\frac{7}{4}$$ to a mixed number.

1. Divide: $$7 ÷ 4 = 1$$ remainder $$3$$ .
2. So, $$\frac{7}{4} = 1 \frac{3}{4}$$ .

Key Rules and Tips

• Always simplify fractions to their lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD).
• When adding or subtracting fractions, make sure they have the same denominator. If not, find a common denominator first.
• When multiplying fractions, multiply the numerators together and the denominators together. Example: $$\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$$ .
• When dividing fractions, flip the second fraction (take the reciprocal) and multiply. Example: $$\frac{2}{3} ÷ \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$$ after simplification.

Questions

Easy Level Questions (20)

1. What is the numerator in $$\frac{3}{5}$$ ?
2. What is the denominator in $$\frac{2}{8}$$ ?
3. Convert $$1 \frac{2}{3}$$ to an improper fraction.
4. Convert $$\frac{9}{4}$$ to a mixed number.
5. Simplify $$\frac{4}{8}$$ .
6. What type of fraction is $$\frac{3}{7}$$ ?
7. What is $$\frac{1}{2} + \frac{1}{2}$$ ?
8. What is $$\frac{1}{3} – \frac{1}{3}$$ ?
9. Multiply $$\frac{2}{5} \times \frac{1}{2}$$ .
10. Divide $$\frac{3}{4} ÷ \frac{1}{2}$$ .
11. Is $$\frac{5}{5}$$ a proper or improper fraction?
12. What is $$\frac{2}{6}$$ simplified?
13. What is $$\frac{3}{8} + \frac{1}{8}$$ ?
14. What is the whole number in $$2 \frac{1}{4}$$ ?
15. What is the numerator in the mixed number $$2 \frac{3}{5}$$ ?
16. What is $$\frac{6}{8}$$ simplified?
17. What is $$\frac{5}{6} – \frac{1}{6}$$ ?
18. What type of fraction is $$\frac{10}{10}$$ ?
19. Simplify $$\frac{12}{16}$$ .
20. What is $$\frac{7}{10} + \frac{3}{10}$$ ?

Medium Level Questions (20)

1. Convert $$2 \frac{1}{2}$$ to an improper fraction.
2. Convert $$\frac{11}{3}$$ to a mixed number.
3. What is $$\frac{5}{12} + \frac{1}{4}$$ ?
4. Simplify $$\frac{15}{20}$$ .
5. What is $$\frac{3}{5} – \frac{1}{10}$$ ?
6. Multiply $$\frac{5}{6} \times \frac{2}{3}$$ .
7. Divide $$\frac{4}{5} ÷ \frac{2}{3}$$ .
8. What is $$1 \frac{1}{3} + 2 \frac{2}{3}$$ ?
9. What is $$3 \frac{1}{4} – 1 \frac{1}{2}$$ ?
10. Simplify $$\frac{18}{24}$$ .
11. What is $$\frac{7}{8} + \frac{1}{4}$$ ?
12. What is the GCD of 12 and 16?
13. What is $$\frac{9}{10} – \frac{1}{5}$$ ?
14. Convert $$\frac{5}{2}$$ to a mixed number.
15. What is $$\frac{8}{9} + \frac{1}{3}$$ ?
16. What is $$\frac{7}{12} – \frac{1}{4}$$ ?
17. Multiply $$\frac{3}{4} \times \frac{4}{5}$$ .
18. Divide $$\frac{6}{7} ÷ \frac{2}{3}$$ .
19. What is $$2 \frac{2}{5} – 1 \frac{1}{5}$$ ?
20. What is $$\frac{14}{15} + \frac{1}{3}$$ ?

Hard Level Questions (20)

1. Convert $$3 \frac{3}{8}$$ to an improper fraction.
2. Convert $$\frac{17}{4}$$ to a mixed number.
3. What is $$\frac{7}{8} + \frac{3}{16}$$ ?
4. What is $$\frac{5}{9} – \frac{1}{3}$$ ?
5. Multiply $$\frac{2}{3} \times \frac{3}{7}$$ .
6. Divide $$\frac{5}{6} ÷ \frac{1}{4}$$ .
7. What is $$2 \frac{1}{6} + 3 \frac{1}{2}$$ ?
8. What is $$4 \frac{2}{5} – 1 \frac{3}{10}$$ ?
9. Simplify $$\frac{24}{36}$$ .
10. What is $$\frac{12}{5} + \frac{4}{15}$$ ?
11. What is $$\frac{11}{12} – \frac{1}{6}$$ ?
12. Find the LCM of 4 and 6.
13. What is $$\frac{13}{15} + \frac{4}{5}$$ ?
14. Convert $$\frac{29}{6}$$ to a mixed number.
15. What is $$\frac{9}{10} – \frac{1}{5}$$ ?
16. What is $$\frac{5}{8} \times \frac{2}{3}$$ ?
17. Divide $$\frac{3}{4} ÷ \frac{5}{6}$$ .
18. What is $$3 \frac{1}{4} + 2 \frac{2}{3}$$ ?
19. What is $$\frac{8}{15} – \frac{1}{5}$$ ?
20. What is $$\frac{10}{12} + \frac{8}{12}$$ ?

Answers and Explanations

Easy Level Answers

1. 3
2. 8
3. $$\frac{5}{3}$$
4. $$1 \frac{1}{4}$$
5. $$\frac{1}{2}$$
6. Proper
7. 1
8. 0
9. $$\frac{1}{5}$$
10. $$\frac{3}{2}$$
11. Improper
12. $$\frac{1}{3}$$
13. $$\frac{4}{8}$$
14. 2
15. 3
16. $$\frac{3}{4}$$
17. $$\frac{4}{6} = \frac{2}{3}$$
18. 1
19. $$\frac{3}{4}$$
20. 1

Medium Level Answers

1. $$\frac{5}{2}$$
2. $$5 \frac{2}{3}$$
3. $$\frac{11}{12}$$
4. $$\frac{3}{4}$$
5. $$\frac{1}{2}$$
6. $$\frac{10}{18} = \frac{5}{9}$$
7. $$\frac{6}{5} = 1 \frac{1}{5}$$
8. $$3 \frac{3}{6} = 4 \frac{1}{6}$$
9. $$1 \frac{3}{4}$$
10. $$\frac{3}{4}$$
11. $$\frac{1}{3}$$
12. 4
13. $$\frac{11}{15}$$
14. $$4 \frac{1}{2}$$
15. $$\frac{11}{15}$$
16. $$\frac{5}{12}$$
17. $$\frac{9}{8} = 1 \frac{1}{8}$$
18. $$\frac{10}{12} = \frac{5}{6}$$
19. $$1 \frac{1}{5}$$
20. $$\frac{18}{12} = \frac{3}{2} = 1 \frac{1}{2}$$

Hard Level Answers

1. $$\frac{27}{8}$$
2. $$4 \frac{1}{4}$$
3. $$\frac{13}{16}$$
4. $$\frac{2}{9}$$
5. $$\frac{2}{7}$$
6. $$\frac{10}{3}$$
7. $$5 \frac{2}{3}$$
8. $$2 \frac{1}{10}$$
9. $$\frac{2}{3}$$
10. $$\frac{38}{15}$$
11. $$\frac{2}{12} = \frac{1}{6}$$
12. 12
13. $$\frac{13}{15}$$
14. $$4 \frac{5}{6}$$
15. $$\frac{7}{10}$$
16. $$\frac{5}{12}$$
17. $$\frac{9}{10}$$
18. $$5 \frac{5}{12}$$
19. $$\frac{11}{15}$$
20. $$\frac{3}{2}$$

Feel free to ask questions if anything is unclear! Let’s practice and improve our understanding of fractions and mixed numbers together.