Ratio (OCR GCSE Maths): Revision Notes

Example: If you have $8$ red squares and $5$ green squares, the ratio of red to green is $8:5$

Example: Consider the following grid of squares:

• Red Squares: $8$
• Green Squares: $5$
• Blue Squares: $2$

Note: Ratios can often be simplified in the same way as fractions. For example, the ratio $2:8$ can be simplified to $1:4$.

From this grid, we can express the following ratios:

1. Ratio of Red to Green Squares: $8:5$ This means there are $8$ red squares for every $5$ green squares.

2. Ratio of Green to Red Squares: $5:8$ This means there are $5$ green squares for every $8$ red squares.

3. Ratio of Blue to Red Squares: $2:8$ This means there are $2$ blue squares for every $8$ red squares.

Example: If the ratio of frogs to penguins is $9:6$, it can be simplified by dividing both numbers by their greatest common factor (GCF).

Example 1: Simplifying $14:21$ Problem: Simplify the ratio $14:21$

Step-by-Step Solution:

1. Identify Common Factors:

• The numbers $14$ and $21$ share a common factor of $7$.

2. Divide Both Sides by the GCF:

3. Write the Simplified Ratio:

4. Check for Other Common Factors:

• $2$ and $3$ have no other common factors, so the ratio is fully simplified. Final Answer: The simplified ratio is $2:3$.

Example 2: Simplifying $60:45$ Problem: Simplify the ratio $60:45$.

Step-by-Step Solution:

5. Identify Common Factors:

• The numbers $60$ and $45$ share a common factor of $15$.

6. Divide Both Sides by the GCF:

7. Write the Simplified Ratio:

8. Check for Other Common Factors:

• $4$ and $3$ have no other common factors, so the ratio is fully simplified. Final Answer: The simplified ratio is $4:3$

Example 1: Converting to $1:n$ Form Problem: Express the ratio $8:14$ in the form $1:n$.

Step-by-Step Solution:

1. Set the First Number to $1$:

• To turn $8$ into $1$, divide both sides of the ratio by $8$.

2. Result:

Final Answer: The ratio $8:14$ expressed in the form $1:n$ is $1:1.75$.

Example 2: Converting to $n:1$ Form Problem: Express the ratio $0.3:0.15$ in the form $n:1.$

Step-by-Step Solution:

3. Set the Second Number to $1$:

• To turn $0.15$ into $1$, divide both sides of the ratio by $0.15$.

4. Result:

Final Answer: The ratio $0.3:0.15$ expressed in the form $n:1$ is $2:1$

In ratio problems, you're often given a ratio and some information about one part of it. Your task is to use this information to find out about the other parts. The key principle is whatever you multiply or divide one part by, you must do the same to the other parts.

Problem: Oisin is making a cake, and the ingredients must be mixed in the following ratios:

• Flour : Butter = $400g$ : $220g$
• Eggs : Sugar = $3:25$

(a) If Oisin has $1kg$ of flour, how much butter does he need? (b) If he has $2$ eggs, how much sugar does he need?

Example a): Finding Butter from Flour

9. Write the Ratio:

• Given ratio: Flour $= 400:220$

• Known amount of flour $1kg$ = $1000g$

10. Set Up the Ratio:

• You need to find out how much butter corresponds to $1000g$ of flour.
• Set up a ratio equation:

11. Solve the Ratio:

• Determine how many times $400$ goes into $1000$:

• Multiply the butter quantity by the same factor:

Final Answer: He needs $550g$ of butter.

Example (b): Finding Sugar from Eggs 12. Write the Ratio:

• Given ratio: Eggs $= 3:25$

• Known amount of eggs $= 2$

13. Set Up the Ratio:

• You need to find out how much sugar corresponds to $2$ eggs.
• Set up a ratio equation:

14. Solve the Ratio:

• Multiply the sugar quantity by the same factor:

Final Answer: He needs approximately $16.67g$ of sugar.

Example 1: Sharing Chocolate Problem: You have a bar of chocolate to share with your mum in the ratio $5:3$. How many pieces do each of you get if there are $24$ pieces of chocolate in total?

Step-by-Step Solution:

15. Add Up the Parts:

• The ratio is $5:3$, so the total number of parts is $5+3=8$.

16. Calculate the Value of One Part:

• Total chocolate pieces $= 24$.
• Value of one part:

17. Distribute the Chocolate:

• For yourself: $5×3=15$pieces.
• For your mum: $3×3=9$ pieces.

Final Answer: You get $15$ pieces of chocolate, and your mum gets $9$ pieces.

Example 2: Sharing Money Problem: Share £$845$ in the ratio$8:3:2$ How much does each person get?

Step-by-Step Solution:

18. Add Up the Parts:

• The ratio is $8:3:2$, so the total number of parts is $8+3+2=13$.

19. Calculate the Value of One Part:

• Total money = £$845$.
• Value of one part:

20. Distribute the Money:

• First person ($8$ parts): $8×65=£520.$
• Second person ($3$ parts): $3×65=£195.$
• Third person ($2$ parts): $2×65=£130.$

Final Answer: The first person gets £$520$, the second gets £$195$, and the third gets £$130$.