Fractions (OCR GCSE Maths): Revision Notes

Example: In the fraction $\frac{3}{4}$:

• $3$ is the numerator.
• $4$ is the denominator.

Example 1: Finding a Fraction of a Quantity

• Problem: What is $\frac{3}{4}$ of $24$?
• Steps:

1. Divide by the denominator:

2. Multiply by the numerator:

• Result: $\frac{3}{4}$ of $24$ is 18.

Example 2: Fraction of a Quantity with Units

• Problem: Find $\frac{5}{7}$ of $2436$ grammes.
• Steps:

3. Divide by the denominator:

4. Multiply by the numerator:

• Result: $\frac{5}{7}$ of $2436$ grammes is 1740 grammes

Example 1: Creating an Equivalent Fraction

• Problem: Find an equivalent fraction for $\frac{2}{7}$ with a denominator of $21$.
• Steps:

5. Ask yourself: "What has been done to the $7$ to make it $21$?"

• Answer: $7×3=21.$

6. Do the same to the numerator:

• Multiply $2$ by $3$:

7. Result: The equivalent fraction is $\frac{6}{21}$.

Example 2: Identifying an Equivalent Fraction

• Problem: Identify what $\frac{49}{70}$ is equivalent to when the numerator is reduced to $7$.
• Steps:

8. Ask yourself: "What has been done to the $49$ to make it $7$?"

• Answer: $49÷7=7$.

9. Do the same to the denominator:

• Divide $70$ by $7$:

10. Result: The equivalent fraction is $\frac{7}{10}$.

Example 3: Simplifying a Fraction

• Problem: Simplify the fraction $\frac{48}{54}$.
• Steps:

11. Find a common factor that divides both the numerator and the denominator. Start by dividing by $2$:

12. Now, divide both by $3$:

13. Result: The simplified fraction is $\frac{8}{9}$.

Example 1: Convert $\frac{22}{5}$ to a Mixed Number

• Step 1: Divide the numerator by the denominator: $22÷5=4$ with a remainder of $2$

• The quotient ($4$) represents the whole number.

• The remainder ($2$) becomes the numerator of the proper fraction.

• Step 2: Write the remainder over the original denominator:

• Result: The improper fraction $\frac{22}{5}$ is equivalent to the mixed number $4 \frac{2}{5}$.

Example 2: Convert $3 \frac{5}{8}$ to an Improper Fraction

• Step 1: Multiply the whole number by the denominator:

• Step 2: Add the result to the numerator:

• The sum becomes the numerator of the improper fraction.
• Step 3: Write the result over the original denominator:

• Result: The mixed number $3 \frac{5}{8}$ is equivalent to the improper fraction $\frac{29}{8}$.

Example 1: Adding Fractions

Example 2: Subtracting Fractions

• Problem: $\frac{4}{15} - \frac{1}{5}$
• Steps:

1. Find a common denominator:

• The LCM of $15$ and $5$ is $15$.
• Convert $\frac{1}{5}$ to $\frac{3}{15}$.

2. Subtract the numerators:

3. Result: The difference is $\frac{1}{15}$.

Example 1: Multiplying Fractions

• Problem: $\frac{2}{3} × \frac{4}{7}$
• Steps:

4. Multiply the numerators:

5. Multiply the denominators:

6. Result: The product is $\frac{8}{21}$.

Example 2: Dividing Fractions

• Problem: $\frac{3}{7} ÷ \frac{2}{5}$
• Steps:

7. Flip the second fraction:

8. Change to multiplication:

9. Multiply the numerators:

10. Multiply the denominators:

11. Result: The quotient is $\frac{15}{14}$.

• Example: Convert $0.364$ to a percentage.
• Steps:

14. Multiply the decimal by $100$:

15. Result: $0.364$ as a percentage is 36.4%.

• Example: Convert $8.3$ to a decimal.
• Steps:

16. Divide the percentage by $100$:

17. Result: $8.3$ as a decimal is 0.083.

• Example: Convert $0.16$ to a fraction.
• Steps:

18. Write the decimal as a fraction with the denominator as $100$ (since there are two decimal places):

19. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is $4$ in this case:

20. Result: $0.16$ as a fraction is $\frac{4}{25}$.

• Example: Convert $\frac{13}{20}$ to a decimal.
• Steps:

21. Adjust the fraction so that the denominator is $100$ (multiply both the numerator and the denominator by $5$):

22. Convert the fraction to a decimal by dividing the numerator by the denominator:

23. Result: $\frac{13}{20}$ as a decimal is 0.65.

• Example: Convert $\frac{5}{8}$ to a percentage.
• Steps:

24. First, convert the fraction to a decimal by dividing the numerator by the denominator:

25. Then, convert the decimal to a percentage by multiplying by $100$:

26. Result: $\frac{5}{8}$ as a percentage is 62.5%.

• Example: Convert $12.5$ to a fraction.
• Steps:

27. Start by writing the percentage as a fraction over $100$:

28. To remove the decimal, multiply both the numerator and the denominator by $10$:

29. Simplify the fraction by dividing both the numerator and the denominator by their GCD, which is $25$:

30. Result: $12.5$ as a fraction is $\frac{1}{8}$.