# Resources tagged with: Ratio and proportion

Filter by: Content type:
Age range:
Challenge level:

### There are 72 results

Broad Topics > Fractions, Decimals, Percentages, Ratio and Proportion > Ratio and proportion

### Ratio Sudoku 3

##### Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios or fractions.

### Ratio Sudoku 1

##### Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios.

### Ratio Sudoku 2

##### Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios.

### Circuit Training

##### Age 14 to 16 Challenge Level:

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .

### Hello Again

##### Age 11 to 14 Challenge Level:

Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?

### Pythagoras’ Comma

##### Age 14 to 16 Challenge Level:

Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.

##### Age 14 to 16 Challenge Level:

Four jewellers share their stock. Can you work out the relative values of their gems?

### Number Lines in Disguise

##### Age 7 to 14 Challenge Level:

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

### Rati-o

##### Age 11 to 14 Challenge Level:

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

### Six Notes All Nice Ratios

##### Age 14 to 16 Challenge Level:

The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.

### Contact

##### Age 14 to 16 Challenge Level:

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

### Fractions Rectangle

##### Age 11 to 14 Challenge Level:

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

### Mixing More Paints

##### Age 14 to 16 Challenge Level:

Can you find an efficent way to mix paints in any ratio?

### Mixing Paints

##### Age 11 to 14 Challenge Level:

Can you work out how to produce different shades of pink paint?

### Racing Odds

##### Age 11 to 14 Challenge Level:

In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?

### Equal Temperament

##### Age 14 to 16 Challenge Level:

The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.

### Around and Back

##### Age 14 to 16 Challenge Level:

A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .

### How Big?

##### Age 11 to 14 Challenge Level:

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

### A Chance to Win?

##### Age 11 to 14 Challenge Level:

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

### Speeding Boats

##### Age 14 to 16 Challenge Level:

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

### One and Three

##### Age 14 to 16 Challenge Level:

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

### Semi-square

##### Age 14 to 16 Challenge Level:

What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?

### Do Unto Caesar

##### Age 11 to 14 Challenge Level:

At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won \$1 200. What were the. . . .

### Oh for the Mathematics of Yesteryear

##### Age 11 to 14 Challenge Level:

A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45. . . .

### Roasting Old Chestnuts 3

##### Age 11 to 16

Mainly for teachers. More mathematics of yesteryear.

### Rule of Three

##### Age 11 to 14 Challenge Level:

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

### Golden Thoughts

##### Age 14 to 16 Challenge Level:

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

### Washing Elephants

##### Age 11 to 14 Short Challenge Level:

How long will it take Mary and Nigel to wash an elephant if they work together?

### Ratio or Proportion?

##### Age 7 to 14

An article for teachers which discusses the differences between ratio and proportion, and invites readers to contribute their own thoughts.

### Burning Down

##### Age 14 to 16 Challenge Level:

One night two candles were lit. Can you work out how long each candle was originally?

### Same Height

##### Age 14 to 16 Challenge Level:

A trapezium is divided into four triangles by its diagonals. Can you work out the area of the trapezium?

### Star Gazing

##### Age 14 to 16 Challenge Level:

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

### Rhombus in Rectangle

##### Age 14 to 16 Challenge Level:

Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.

### Mixed up Mixture

##### Age 14 to 16 Challenge Level:

Can you fill in the mixed up numbers in this dilution calculation?

### Cereal Mix

##### Age 11 to 14 Challenge Level:

A farmer is supplying a mix of seeds, nuts and dried apricots to a manufacturer of crunchy cereal bars. What combination of ingredients costing £5 per kg could he supply?

### Sitting Pretty

##### Age 14 to 16 Challenge Level:

A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?

### Points in Pairs

##### Age 14 to 16 Challenge Level:

Move the point P to see how P' moves. Then use your insights to calculate a missing length.

### Dilution Series Calculator

##### Age 14 to 16 Challenge Level:

Which dilutions can you make using 10ml pipettes and 100ml measuring cylinders?

### Bus Stop

##### Age 14 to 16 Challenge Level:

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .

### Triangle in a Triangle

##### Age 14 to 16 Challenge Level:

Can you work out the fraction of the original triangle that is covered by the inner triangle?

### Slippage

##### Age 14 to 16 Challenge Level:

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .

### Tin Tight

##### Age 14 to 16 Challenge Level:

What's the most efficient proportion for a 1 litre tin of paint?

### Tray Bake

##### Age 11 to 14 Challenge Level:

My recipe is for 12 cakes - how do I change it if I want to make a different number of cakes?

### Temperature

##### Age 11 to 14 Challenge Level:

Is there a temperature at which Celsius and Fahrenheit readings are the same?

##### Age 11 to 14 Challenge Level:

Can you work out which drink has the stronger flavour?

### Ratios and Dilutions

##### Age 14 to 16 Challenge Level:

Scientists often require solutions which are diluted to a particular concentration. In this problem, you can explore the mathematics of simple dilutions

### Zin Obelisk

##### Age 11 to 14 Challenge Level:

In the ancient city of Atlantis a solid rectangular object called a Zin was built in honour of the goddess Tina. Your task is to determine on which day of the week the obelisk was completed.

### Arrh!

##### Age 14 to 16 Challenge Level:

Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. . . .

### Square Pegs

##### Age 11 to 14 Challenge Level:

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

### Half a Triangle

##### Age 14 to 16 Challenge Level:

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.