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Final review: ratio and proportion
Textbook, p. 228
GoalReview ratio, proportion, direct and inverse proportionality and scale.
New words
ratio · nisbatproportion · proporsiyaproportionality · proporsionallikscale · masshtab
Explanation
A ratio is the quotient of two numbers. A proportion is the equality of two ratios a : b = c : d; its basic property is a · d = b · c. We find an unknown term with this property. In directly proportional quantities, when one grows several times the other grows the same number of times (price and amount); in inverse proportion the other shrinks the same number of times (number of workers and time) and the product is constant. To divide a number in the ratio m : n, split it into m + n equal parts. A scale 1 : n means 1 unit on the drawing is n units in reality.
Worked examples
Divide 40 in the ratio 3 : 2: 3 + 2 = 5 parts, 40 : 5 = 8; the shares are 24 and 16.
From 12 : 8 = 15 : x we get x = 8 · 15 : 12 = 10.
Class activity
“Which relation?”: cards with problems. The team decides whether the relation is direct or inverse, solves it and explains why the answer makes sense.
Practice
1
Find the ratio of 45 minutes to 1.5 hours (in the same unit).
1:2
2
In x : 6 = 14 : 21, find x.
4
3
A map has scale 1 : 25,000. How many km is 4 cm on the map?
1
4
6 pumps fill a pool in 10 hours. In how many hours do 4 pumps fill it? Why must the answer be more than 10?
15 hours (6 · 10 : 4). Fewer pumps need more time: inverse proportionality.