*This Math quiz is called 'Solving Problems 4' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.*

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You should have learned a few methods for solving real life problems from the previous three middle school Math quizzes: see how well you can apply your skills to these problems.

1.

If a wheel rotates (turns) at a speed of 6,000 revolutions (complete turns) in 5 minutes, how many revolutions does it make in 1 minute?

3,000

12,000

30,000

1,200

6,000 ÷ 5 = 1,200. You have to divide 6,000 by 5 because you want to find out how many 'lots' of 5 there are in 6,000 : each 'lot' equals the number of revolutions in 1 minute

2.

It takes 4 men 128 hours to complete a certain engineering maintenance job. How long will it take 16 men to complete the same job if they work at the same speed?

64 hr

16 hr

32 hr

8 hr

It takes 4 men 128 hours to complete the job, so it will take 1 man four times that amount of time = 4 x 128 = 512 hr. Now a group of 16 men is 16 times more than one man, so they will complete the job in ^{1}⁄_{16} of the time it takes one man: 512 ÷ 16 = 32 hr. ALTERNATIVELY, a group of 16 men is 4 times that of a group of 4 men, so they will do the job in quarter of the time: 128 ÷ 4 = 32 hr

3.

If you lose a half of an eighth of all your money, what fraction of your money have you lost?

The word 'of' means multiply, so ^{1}⁄_{2} x ^{1}⁄_{8} = ^{1}⁄_{16}

4.

Mike lives five times further way from London than Tom. If Mike lives 75 miles away from London, how far away does Tom live?

375 miles

37.5 miles

15 miles

13 miles

If Mike lives five times further way from London than Tom, then Tom lives one fifth of that distance away from London: 75 ÷ 5 = 15 miles

5.

The temperature of a substance in a chemistry experiment is -6°C. If the temperature is increasing at the rate of 2°C per minute, what will the temperature of the substance be in 8 minutes?

16°C

22°C

-4°C

10°C

If the temperature is increasing at the rate of 2°C per minute, the temperature of the substance at the end of 8 minutes = 8 x 2 = 16°C BUT it was initially at -6°C, so the final temperature will be -6°C + 16°C = 10°C

6.

At the end of a rugby match, 125 people left the grounds every 3 minutes. If there were 2,500 spectators at the match, how long did it take for the grounds to empty?

60 min

30 min

120 min

20 min

2,500 ÷ 125 = 20. You have to divide 2,500 by 125 because you want to find out how many 'lots' of 125 there are in 2,500 : each 'lot' equals 3 minutes. So 20 'lots' of 3 minutes means it took 20 x 3 = 60 minutes to empty the grounds. How fast or how slow something is happening is called a 'rate'. In this case: the spectators are leaving at a rate of 125 people per 3 minute period

7.

Farmer Jones is spraying his crops with a pesticide. If 10 ml of pesticide is required for each square meter, how many liters of pesticide will be required to spray 1,000 m^{2}?

100 L

1 L

10 L

1,000 L

1 m^{2} requires 10 ml therefore 1,000 m^{2} requires 1,000 times more pesticide: 1,000 x 10 = 10,000 ml. Now 1 L = 1,000 ml therefore 10,000 ml = 10 L because 10,000 ml is 10 times more than 1,000 ml

8.

Small toy cars are packed in toy boxes whose volume is 120 cm^{3}. There are 6,000 toy boxes. If the toy boxes are to be packed into larger packing boxes, each of whose volume is 1,200 cm^{3}, how many packing boxes will be required to pack all the toy boxes?

60

600

120

60,000

1,200 ÷ 120 = 10. You have to divide 1,200 by 120 because you want to find out how many 'lots' of 120 there are in 1,200: each 'lot' equals the number of toy boxes that can be put into each packing box. Each packing box can hold ten toy boxes, so 6,000 toy boxes require 6,000 ÷ 10 = 600 packing boxes: You have to divide 6,000 by 10 because you want to find out how many 'lots' of 10 there are in 6,000: each 'lot' equals the number of packing boxes that are required

9.

The temperature changed from -8°C to 3°C and then to -14°C over the last two day period. How many degrees below 3°C was the final temperature?

-14°C

14°C

-17°C

17°C

From 3°C to -14°C is a temperature movement of 17°C BUT it is not -17°C

10.

The height of the Towers building is three times taller than the Spire building. If the Spire building is 18 m high, how high is the Towers building?

6 m

54 m

36 m

27 m

The height of the Towers building is three times the height of the Spire building = 3 x 18 = 54

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