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Additional resources for Quantum Probability and Related Topics: Proceedings of the 30th Conference

Example text

1 2 3 NUMBER OF GARDENERS Vans Days 1 8 2 4 4 2 1:8 ×2 ÷2 1 van takes 8 days to deliver the parcels 8 6 2:4 ×2 ÷2 2 vans take 4 days to deliver the parcels TIME DAYS if the number of vans doubles then it takes half the time to deliver the parcels 2 2 1 3:6 ▷ Delivering parcels The number of vans used to deliver parcels determines how many days it takes to deliver the parcels. Twice as many vans means half as many days to deliver. 1 4 the ratio is always the same when reduced to its simplest terms, in this case 1 : 2 1 van takes 8 days to deliver some parcels Trees 2 gardeners can plant 4 trees in a day 6 TREES PLANTED IN A DAY ▷Planting trees The number of gardeners used to plant trees determines how many trees can be planted in a day: twice as many gardeners means twice as many trees can be planted.

56 NUMBERS : Ratio and proportion SEE ALSO RATIO COMPARES THE SIZE OF QUANTITIES. PROPORTION COMPARES THE RELATIONSHIP BETWEEN TWO SETS OF QUANTITIES. Multiplication  18–21 22–25  48–55 Division  Fractions Ratios show how much bigger one thing is than another. Two things are in proportion when a change in one causes a related change in the other. Writing ratios Ratios are written as two or more numbers with a colon between each. For example, a fruit bowl in which the ratio of apples to pears is 2 : 1 means that there are 2 apples for every 1 pear in the bowl.

Multiply whole number by denominator 10 1 10 × 3 + 1 31 = = 3 3 3 denominator Multiply the whole number by the denominator—in this case, 10 × 3 = 30. Then add the numerator. The result is the top-heavy fraction 31⁄3, with a numerator (31) greater than the denominator (3). FRACTIONS 51 Equivalent fractions The same fraction can be written in different ways. These are known as equivalent (meaning “equal”) fractions, even though they look different. 3 highlighted sectors take up same space as 9 highlighted sectors in circle on left = numerator ÷3 9 12 3 4 = ÷3 denominator 2 highlighted rectangles take up same space as 4 highlighted rectangles on left = divide numerator and denominator by same number ÷2 4 6 2 3 = ÷2 cancellation results in equivalent fraction with smaller numerator and denominator △ Cancellation Cancellation is a method used to find an equivalent fraction that is simpler than the original.

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