Resources tagged with: Ratio and proportion

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

Ratio Sudoku 1

Age 11 to 16
Challenge Level

A Sudoku with clues as ratios.

Orbiting Billiard Balls

Age 14 to 16
Challenge Level

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

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. . . .

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. . . .

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. . . .

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. . . .

Retiring to Paradise

Age 11 to 14
Challenge Level

When Charlie retires, he's looking forward to the quiet life, whereas Alison wants a busy and exciting retirement. Can you advise them on where they should go?

Triathlon and Fitness

Age 11 to 14
Challenge Level

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

A Shade Crossed

Age 14 to 16
Challenge Level

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?

Ratio Sudoku 3

Age 11 to 16
Challenge Level

A Sudoku with clues as ratios or fractions.

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.

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?

Pent

Age 14 to 18
Challenge Level

The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.

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.

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?

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?

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?

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?

Roasting Old Chestnuts 3

Age 11 to 16

Mainly for teachers. More mathematics of yesteryear.

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?

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?

Wedge on Wedge

Age 14 to 16
Challenge Level

Two right-angled triangles are connected together as part of a structure. An object is dropped from the top of the green triangle where does it pass the base of the blue triangle?

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. . . .

Make Your Own Solar System

Age 7 to 16
Challenge Level

Making a scale model of the solar system

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. . . .

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?

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?

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?

Gift of Gems

Age 14 to 16
Challenge Level

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

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?

Straw Scaffold

Age 11 to 14
Challenge Level

Build a scaffold out of drinking-straws to support a cup of water

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. . . .

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.

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?

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?

Two Ladders

Age 14 to 16
Challenge Level

Two ladders are propped up against facing walls. The end of the first ladder is 10 metres above the foot of the first wall. The end of the second ladder is 5 metres above the foot of the second. . . .

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?

Investigating the Dilution Series

Age 14 to 16
Challenge Level

Which dilutions can you make using only 10ml pipettes?

Pi, a Very Special Number

Age 7 to 14

Read all about the number pi and the mathematicians who have tried to find out its value as accurately as possible.

Toad in the Hole

Age 11 to 14
Challenge Level

Is it cheaper to cook a meal from scratch or to buy a ready meal? What difference does the number of people you're cooking for make?

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

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?

Nutrition and Cycling

Age 14 to 16
Challenge Level

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

Eight Ratios

Age 14 to 16
Challenge Level

Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.

Mixing Lemonade

Age 11 to 14
Challenge Level

Can you work out which drink has the stronger flavour?

Mixed up Mixture

Age 14 to 16
Challenge Level

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

Exact Dilutions

Age 14 to 16
Challenge Level

Which exact dilution ratios can you make using only 2 dilutions?

Dilution Series Calculator

Age 14 to 16
Challenge Level

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

Tin Tight

Age 14 to 16
Challenge Level

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