Problem solving with advanced algebraic fractions

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Lesson details

Learning outcome

I can use my knowledge of advanced algebraic fractions to solve problems.

Key learning points

Real world formula can be complex and contain multiple variables.
When rearranging, you can sometimes check equivalence numerically.
Algebraic fractions follow the same rules as fractions.

Keywords

Compound interest - Compound interest is the interest calculated on the original amount and the interest accumulated over the previous period.
Tree diagrams - Tree diagrams are a representation used to model statistical/probability questions. Branches represent different possible events or outcomes.
Probability tree - Each branch of a probability tree shows a possible outcome from an event or from a stage of a trial, along with the probability of that outcome happening.

Common misconception

Thinking the multiplier for a 2% increase is either 0.02 or 1.2

A 2% increase is 100% + 2% of the original amount. 102% is equivalent to 1.02 as a decimal.

Teacher tip

Discuss types of loans that pupils have heard of. Pupils may wish to look at how the formula for multiple repayments is derived. They could compare this to the core maths formula. This lesson can be used to increase pupils' awareness of some of the skills they will develop if they study Core Maths.

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0

except where otherwise stated. See Oak's terms & conditions

(Collection 2).

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Worksheet

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Prior knowledge starter quiz

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6 Questions

Q1.
An Oak teacher invests £1000 with 5% compound interest a year. After 4 years they will have £ to the nearest penny.

Correct Answer: 1215.51, £1215.51

Q2.
The solution to the equation $$\frac{5}{2} + \frac{x}{4}=10$$ is when $$x=$$

Correct Answer: 30

Q3.
Write $$\frac{x}{a} + \frac{x}{b}$$ as a single fraction.

$$\frac{x^2}{ab}$$

$$\frac{2x}{a+b}$$

$$\frac{bx+b}{a}$$

Correct answer: $$\frac{bx+ax}{ab}$$

Q4.
Make $$x$$ the subject of $$\frac{x}{a} + \frac{x}{b}=c$$ .

$$x=ab+ac$$

$$x=\frac{a(c+b)}{2}$$

Correct answer: $$x=\frac{abc}{a+b}$$

$$x=\frac{abc-a}{b}$$

$$x=\frac{abc-bx}{a}$$

Q5.
Lucas rolls a fair 6 sided die and flips a fair coin. What is the probability Lucas gets a 2 on the die and a heads on the coin?

Correct answer: $$\frac{1}{12}$$

$$\frac{1}{6}$$

$$\frac{1}{4}$$

$$\frac{2}{3}$$

$$\frac{5}{6}$$

Q6.
Use the probability tree to match each event to its probability.

Correct Answer:P(A and C),$$\frac{1}{4}$$

$$\frac{1}{4}$$

Correct Answer:P(A and D),$$\frac{1}{12}$$

$$\frac{1}{12}$$

Correct Answer:P(B and C),$$\frac{1}{2}$$

$$\frac{1}{2}$$

Correct Answer:P(B and D),$$\frac{1}{6}$$

$$\frac{1}{6}$$

Assessment exit quiz

Download exit quiz questions (PDF)

6 Questions

Q1.
Sofia borrows $$(C)$$ from her brother. Her brother charges her 2% compound interest a week. After 3 weeks, Sofia owes her brother £20. To the nearest penny, Sofia borrowed £ .

Correct Answer: £18.85, 18.85

Q2.
A money lending firm charges 3% compound interest each month. £100 is borrowed over 2 months and £60 paid back after 1 month. After 2 months the final repayment should be £ .

Correct Answer: £44.29, 44.29

Q3.
A money lending firm charges 3% compound interest each month. £100 is borrowed over 2 months and repaid in two equal monthly repayments. In total £ is paid back.

Correct Answer: £104.52, 104.52

Q4.
There are $$n$$ counters in a bag. 3 are red and the rest are blue. A counter is picked , put back in the bag and another is picked. What is the probability of getting 2 red counters?

$$\frac{1}{3}$$

$$\frac{6}{n}$$

Correct answer: $$\frac{9}{n^2}$$

$$\frac{n^2-6n+9}{n^2}$$

Q5.
There are $$n$$ counters in a bag. 3 are red and the rest are blue. A counter is picked, put back in the bag and another is picked. What is the probability of getting two counters the same colour?

$$\frac{9}{n^2}$$

$$\frac{3n-9}{n^2}$$

$$\frac{6n-18}{n^2}$$

$$\frac{n^2-6n+9}{n^2}$$

Correct answer: $$\frac{n^2-6n+18}{n^2}$$

Q6.
There are $$n$$ counters in a bag, 3 are red and the rest blue. Jun picks one, puts it back and picks another. The probability of getting two the same colour is $${5\over 8}$$. Calculate $$n$$.

Correct answer: $$n=4$$

$$n=6$$

$$n=8$$

$$n=10$$

Correct answer: $$n=12$$

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Problem solving with advanced algebraic fractions

Lesson slides

Lesson details

Learning outcome

Key learning points

Keywords

Common misconception

Teacher tip

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.An Oak teacher invests £1000 with 5% compound interest a year. After 4 years they will have £ to the nearest penny.

Q2.The solution to the equation $$\frac{5}{2} + \frac{x}{4}=10$$ is when $$x=$$

Q3.Write $$\frac{x}{a} + \frac{x}{b}$$ as a single fraction.

Q4.Make $$x$$ the subject of $$\frac{x}{a} + \frac{x}{b}=c$$ .

Q5.Lucas rolls a fair 6 sided die and flips a fair coin. What is the probability Lucas gets a 2 on the die and a heads on the coin?

Q6.Use the probability tree to match each event to its probability.

Assessment exit quiz

6 Questions

Q1.Sofia borrows $$(C)$$ from her brother. Her brother charges her 2% compound interest a week. After 3 weeks, Sofia owes her brother £20. To the nearest penny, Sofia borrowed £ .

Q2.A money lending firm charges 3% compound interest each month. £100 is borrowed over 2 months and £60 paid back after 1 month. After 2 months the final repayment should be £ .

Q3.A money lending firm charges 3% compound interest each month. £100 is borrowed over 2 months and repaid in two equal monthly repayments. In total £ is paid back.

Q4.There are $$n$$ counters in a bag. 3 are red and the rest are blue. A counter is picked , put back in the bag and another is picked. What is the probability of getting 2 red counters?

Q5.There are $$n$$ counters in a bag. 3 are red and the rest are blue. A counter is picked, put back in the bag and another is picked. What is the probability of getting two counters the same colour?

Q6.There are $$n$$ counters in a bag, 3 are red and the rest blue. Jun picks one, puts it back and picks another. The probability of getting two the same colour is $${5\over 8}$$. Calculate $$n$$.

How to plan a lesson using our resources

Q1.
An Oak teacher invests £1000 with 5% compound interest a year. After 4 years they will have £ to the nearest penny.

Q2.
The solution to the equation $$\frac{5}{2} + \frac{x}{4}=10$$ is when $$x=$$

Q3.
Write $$\frac{x}{a} + \frac{x}{b}$$ as a single fraction.

Q4.
Make $$x$$ the subject of $$\frac{x}{a} + \frac{x}{b}=c$$ .

Q5.
Lucas rolls a fair 6 sided die and flips a fair coin. What is the probability Lucas gets a 2 on the die and a heads on the coin?

Q6.
Use the probability tree to match each event to its probability.

Q1.
Sofia borrows $$(C)$$ from her brother. Her brother charges her 2% compound interest a week. After 3 weeks, Sofia owes her brother £20. To the nearest penny, Sofia borrowed £ .

Q2.
A money lending firm charges 3% compound interest each month. £100 is borrowed over 2 months and £60 paid back after 1 month. After 2 months the final repayment should be £ .

Q3.
A money lending firm charges 3% compound interest each month. £100 is borrowed over 2 months and repaid in two equal monthly repayments. In total £ is paid back.

Q4.
There are $$n$$ counters in a bag. 3 are red and the rest are blue. A counter is picked , put back in the bag and another is picked. What is the probability of getting 2 red counters?

Q5.
There are $$n$$ counters in a bag. 3 are red and the rest are blue. A counter is picked, put back in the bag and another is picked. What is the probability of getting two counters the same colour?

Q6.
There are $$n$$ counters in a bag, 3 are red and the rest blue. Jun picks one, puts it back and picks another. The probability of getting two the same colour is $${5\over 8}$$. Calculate $$n$$.