Problem solving with advanced algebraic fractions | Maths

Starter quiz

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

'1215.51' ✓
The solution to the equation $\frac{5}{2} + \frac{x}{4}=10$ is when $x=$ ______

'30' ✓
Write $\frac{x}{a} + \frac{x}{b}$ as a single fraction.

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

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

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

$\frac{bx+ax}{ab}$ ✓
Make $x$ the subject of $\frac{x}{a} + \frac{x}{b}=c$ .

$x=ab+ac$

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

$x=\frac{abc}{a+b}$ ✓

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

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

$\frac{1}{12}$ ✓

$\frac{1}{6}$

$\frac{1}{4}$

$\frac{2}{3}$

$\frac{5}{6}$
Use the probability tree to match each event to its probability.

P(A and C)

⇔

$\frac{1}{4}$ ✓

P(A and D)

⇔

$\frac{1}{12}$ ✓

P(B and C)

⇔

$\frac{1}{2}$ ✓

P(B and D)

⇔

$\frac{1}{6}$ ✓

Exit quiz

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 £______.

'£18.85' ✓
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 £______.

'£44.29' ✓
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.

'£104.52' ✓
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?

$\frac{1}{3}$

$\frac{6}{n}$

$\frac{9}{n^2}$ ✓

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

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

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

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

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

$\frac{n^2-6n+18}{n^2}$ ✓
$There are <Math>n</Math> counters in a bag, 3 are red and the rest blue. Jun picks one, puts it back and picks another. The probability of getting two the same colour is <Math>{5\over 8}</Math>. Calculate <Math>n</Math>.$

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 $n$ .

$n=4$ ✓

$n=6$

$n=8$

$n=10$

$n=12$ ✓

Worksheet

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Lesson Details

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.

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.

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.