There are **101** NRICH Mathematical resources connected to **Ratio and proportion**, you may find related items under Fractions, Decimals, Percentages, Ratio and Proportion.

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

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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?

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

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

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

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A new problem posed by Lyndon Baker who has devised many NRICH problems over the years.

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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.

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The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

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

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

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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?

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The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

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Can you decide whose drink has the strongest blackcurrant flavour from these pictures?

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A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?

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Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?

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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. . . .

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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?

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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. . . .

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

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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. . . .

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Do you have enough information to work out the area of the shaded quadrilateral?

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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.

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

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

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

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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?

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Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

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

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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?

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

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

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A brief introduction to PCR and restriction mapping, with relevant calculations...

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Ever wondered what it would be like to vaporise a diamond? Find out inside...

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Do each of these scenarios allow you fully to deduce the required facts about the reactants?

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What does the empirical formula of this mixture of iron oxides tell you about its consituents?

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Investigate some of the issues raised by Geiger and Marsden's famous scattering experiment in which they fired alpha particles at a sheet of gold.

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

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In this question we push the pH formula to its theoretical limits.

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

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Which dilutions can you make using only 10ml pipettes?

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

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

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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.

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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.

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The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

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The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?