4. The Grade 8 students went on a 40 km canoe trip.

a) The number line for the trip shows 10% of 40 km as 4 km. Explain how to determine 10% when you know 100%.

b) Explain how to use 10% to determine 40%.

c) Complete the number line for the trip

Go here for the number line photo: http://msparvu.pbworks.com/w/file/fetch/80005256/CHAPTER%2012.pdf   (Go to page 373)
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(a) You can use a ruler to draw a line ten centimetres long. This represents 100%. Now mark off each centimetre division, so that's at 1cm, 2cm, 3cm, and so on. You can make the line into a box (rectangle) of length 10cm and width 1cm so that the divisions are easier to see. The box now has 10 divisions. Each division represents 10%, because 10 times 10% equals 100%.

Now as it happens 4 inches is close to 10cm. That means the number line can also be used to represent 40km. There are 10 divisions so each division also represents 40/10=4km, just as on the 10cm line, representing 100%, 10% was represented by 10/10=1cm divisions. If you use a ruler to measure the division in inches, you will see that each division is about four tenths of an inch.

(b) 40% on the 10cm line is 4 divisions (4cm). The number of divisions remaining is 6, meaning that 60% of the line is left, because 6×10%=60%.

(c) On the trip when the students have canoed 10% of the trip, they still have 90% to go (9 divisions of the number line). We know that 10% of the number line is 4km of the trip, so they have 9 more divisions to go. Each division is 4km, so 9 divisions is 9×4=36km. And when we add 36km to 4km we get 40km, the full length of the trip.

When the students have canoed 40% of the trip, they will have gone 4×4=16km, with 60% remaining, that is, 6 divisions of 4km per division, making 24km. 16km+24km=40km, the full length of the trip.

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