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Fractions and Proportionality Test Questions
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| Below are sample questions from the
TIMSS achievement tests in Science administered to twenty-six countries.
TIMSS is a research project sponsored by the International Association for
the Evaluation of Educational Achievement (IEA). These questions may be
used in the classroom, as a tool for evaluation, or to provide examples
of test-question writing. The sample questions are grouped by grades
3 and 4 and by grades 7 and 8. |
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| |
| Grades
3 and 4 |
| 1. 0.4 is the same as |
| A. four |
| B. four tenths |
| C. four hundredths |
|
D. one-fourth
Answer: B
|
|
2. Mario uses five tomatoes to make half a liter of tomato sauce. How much
sauce can he make from 15 tomatoes? |
| A. a liter and half |
| B. two liters |
| C. two liters and half |
|
D. three liters
Answer: A
|
|
3. There are 54 marbles, and they are put into 6 bags, so that the same
number of marbles is in each bag. How many marbles would two bags contain? |
| A. 108 marbles |
| B. 18 marbles |
| C. 15 marbles |
| D. 12 marbles |
|
E. 9 marbles
Answer: B
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4. Julie put a box on a shelf that is 96.4 centimeters long. The box is
33.2 centimeters long. What is the longest box she could put on the rest
of the shelf? Show all your work. |
| |
| Answer:_______________ |
|
.
Answer: 63.2
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5. A teacher marks 10 of her pupils' tests every half hour. It takes her
one and half hours to mark all her pupils' tests. How many pupils are in
her class? |
| |
| Answer:_______________ |
|
Answer: 30
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6. There are 10 girls and 20 boys in Juanita's class. Juanita said that
there is one girl for every two boys. Her friend Amanda said that means
1/2 of all the students in the class are girls. |
| How many student are there in Juanita's
class?. Answer:______________ |
| Is Juanita right? Answer:______________ |
| Use words or picture to explain why. |
|
Is Amanda right? Answer:___________
Answer: Yes. 20 is twice as much as 10 or 10 is half as much as 20.
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Answer: No. 10 is not half of 30
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7. Write a fraction that is larger than 2/7. |
| Answer:______________ |
|
Answer: A fraction with numerator greater then 2 and denominator equal
to 7. A fraction with numerator equal to 2 and denominator less than 7.
3/8
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|
8. Maria and her sister Louisa leave home at the same time and ride their
bicycles to school 9 kilometers away. |
| Maria rides at a rate of 3 kilometers
in 10 minutes. How long will it take her to get to school? |
| Answer:_________________ |
| Louisa rides at a rate of 1 kilometer
in 3 minutes. How long will it take her to get to school? |
| Answer:_____________ |
| Who Arrives at school first? |
|
Answer:_______________
Answer: 30
|
| Answer: 27 |
| Answer: Louisa |
| |
| Grades
7 and 8 |
|
1.
Two groups of tourists each have 60 people. If 3/4 of the first group
and 2/3 of the second group board buses to travel to a museum, how many
more people in the first group board buses than in the second group?
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A.
2
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B.
4
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C.
5
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D.
40
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E.
45
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Answer:
C
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2.
In a discus-throwing competition, the winning throw was 61.60m. The second
place throw was 59.72 m. How much longer was the winning throw than the
second-place throw?
|
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A.
1.18m
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B.
1.88m
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C.
1.98m
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D.
2.18m
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Answer:
B
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3.
Write a fraction that is larger than 2/7.
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Answer:__________________
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Answer:
A fraction with a numerator greater than 2 and a denominator equal to
7.
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4.
Divide 8/35 by 4/15=
|
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Answer:
___________________
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Answer:
33761
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5.
Divide: 24.56 by 0.004
|
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A.
0.614
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B.
6.14
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C.
61.4
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D.
614
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E.
6140
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Answer:
E
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6.
A chemist mixes 3.75 milliliter of solution A with 5.625 milliliter of solution
B to form a new solution. How many milliliter does this new solution contain? |
|
Answer:_____________________________
|
|
|
Answer:
9.375
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7. Last
year there were 1172 students at Beaton High School. This year there are
15 percent more students than last year. Approximately how many students
are at Beaton High School this year? |
| A.
1800 |
| B.
1600 |
| C.
1500 |
| D.
1400 |
| E.
1200 |
|
| Answer:
D |
8. 3/4+8/3+11/8=
|
| A.
22/15 |
| B.
43/24 |
| C.
91/24 |
| D.
115/24 |
|
| Answer:
D |
9. Which
number is five hundred four and seven-tenths? |
| A.
54.7 |
| B.
504.7 |
| C.
547 |
| D.
5004.7 |
|
| Answer:
B |
10.
What is the value of 2/3-1/4-1/12? |
| A.
1/16 |
| B.
1/3 |
| C.
3/8 |
| D.
5/12 |
| E.
1/2 |
|
| Answer:
B |
11.
Which is the largest number? |
| A.
4/5 |
| B.
3/4 |
| C.
5/8 |
| D.
7/10 |
|
| Answer:
A |
12.
Multiply: 0.203 by 0.56= |
| Answer:__________________
|
|
| Answer:
0.11368 |
13.
A newspaper reported that about 18 200 trees had been planted in the park.
The number was rounded to the nearest hundred. Which of these could have
been the actual number planted? |
| A.
18 043 |
| B.
18 189 |
| C.
18 289 |
| D.
18 328 |
|
| Answer:
B |
14.
In which list of fractions are all of the fractions equivalent? |
| A.
3/4,6/8,12/14 |
| B.
3/5,5/7,9/15 |
| C.
3/8,6/16,12/32 |
| D.
5/10,10/15,1/2 |
|
| Answer:
C |
15.
Han had a bag of marbles. She gave half of them to James and then a third
of the marbles still in the bag to Pat. She then had 6 marbles left. How
many marbles were in the bag to start with? |
| A.
18 |
| B.
24 |
| C.
30 |
| D.
36 |
|
| Answer:
A |
16.
A car has a fuel tank that holds 35 L of fuel. The car consumes 7.5 L of
fuel for each 100 km driven. A trip of 250 km was started with a full tank
of fuel. How much fuel remained in the tank at the end of the trip? |
| A.
16.25 L |
| B.
17.65 L |
| C.
18.75 L |
| D.
23.75 L |
|
| Answer:
A |
17.
If the price of a can of beans is raised from 60 cents to 75 cents, what
is the percentage increase in the price? |
| A.
15% |
| B.
20% |
| C.
25% |
| D.
30% |
|
| Answer:
C |
18.
Which of these is 89.0638 rounded to the nearest hundredth? |
| A.
100 |
| B.
90 |
| C.
89.1 |
| D.
89.06 |
| E.
89.064 |
|
| Answer:
D |
19.
Luis exercises by running 5 km each day. The course he runs is 1/4 km long.
How many times through the course does he run each day? |
|
| Answer:___________________________ |
| |
| Answer:20 |
|
| 20. Mark's garden has 84 rows of
cabbages. There are 57 cabbages in each row. Which of these gives the BEST
way to estimate how many cabbages there are altogether? |
| A. 100 times 50=5000 |
| B. 90 times 60=5400 |
| C. 80 times 60= 4800 |
| D. 80 times 50=4000 |
| |
| Answer: C |
|
| 21. A person's heart is beating 72
times a minute. At this rate, about how many times does it beat in one hour? |
| A. 420 000 |
| B. 42 000 |
| C. 4 200 |
| D. 420 |
| |
| Answer: C |
|
| 22. Janis, Maija, and their mother
were eating a cake. Janis ate 1/2 of the cake. Maija ate 1/4 of the cake.
Their mother ate 1/4 of the cake. How much of the cake is left? |
| A. 3/4 |
| B. 1/2 |
| C. 1/4 |
| D. None |
| |
| Answer: D |
|
| 23. Write 0.28 as a fraction reduced
to it's lowest terms. |
| Answer:______________________________ |
| |
| Answer: 7/25 |
|
| 24. The Smith family uses about 6000
L of water per week. Approximately how many liters of water do they use
per year? |
| A. 30 000 |
| B. 240 000 |
| C. 300 000 |
| D. 2 400 000 |
| E. 3 000 000 |
| |
| Answer: C |
|
| 25. Which list shows the numbers
from smallest to largest? |
| A. 0.345, 0.19, 0.8, 1/5 |
| B. 0.19, 1/5, 0.345, 0.8 |
| C. 0.8, 0.19, 1/5, 0.345 |
| D. 1/5, 0.8, 0.345, 0.19 |
| |
| Answer: B |
|
| 26. 3/4 + (2/3 times 1/4)= |
| A. 1/8 |
| B. 5/16 |
| C. 17/48 |
| D. 5/6 |
| E. 11/12 |
| |
| Answer: E |
|
| 27. Subtract: 2.201-0.753= |
| A. 1.448 |
| B. 1.458 |
| C. 1.548 |
| D. 1.558 |
| |
| Answer: A |
|
| 28. A stack of 200 identical sheets
of paper is 2.5 cm thick. What is the thickness of one sheet of paper? |
| A. 0.008 cm |
| B. 0.0125 cm |
| C. 0.05 cm |
| D. 0.08 cm |
| |
| Answer: B |
|
| 29. Subtract: 6000-2369= |
| A. 4369 |
| B. 3742 |
| C. 3631 |
| D. 3531 |
| |
| Answer: C |
|
| 30. Mr. Lewis had $360. He spent
7/9 of it. How much money did he have left? |
| Answer: ________________________________________ |
| |
| Answer: 80 |
|
| 31. Teresa wants to record 5 songs
on tape. The length of time each song plays for is shown in the table. |
| Song |
Amount of Time |
| 1 |
2 minutes 41 seconds |
| 2 |
3 minutes 10 seconds |
| 3 |
2 minutes 51 seconds |
| 4 |
3 minutes |
| 5 |
3 minutes 32 seconds |
|
| ESTIMATE to the nearest minute the
total time taken for all five songs to play and explain how this estimate
was made. |
| |
| Estimate:_______________________ |
| |
| Explain: |
| |
| Answer: 15 minutes, by rounding each
amount of time to whole minutes |
|
| 32. Rounded to the nearest 10 kg
the weight of a dolphin was reported as 170 kg. Write down a weight that
might have been the actual weight of the dolphin. |
| |
| Answer: |
| |
| Answer: A number between 165 and
170. |
|
| 1. The table shows the values of
x and y where x is proportional to y. |
|
|
| What are the values of P and Q? |
| A. P=14 and Q=31 |
| B. P=10 and Q=14 |
| C. P=10 and Q=31 |
| D. P=14 and Q=15 |
| E. P=15 and Q=14 |
| |
| Answer: E |
|
| 2. A class has 28 students. The ratio
of girls to boys is 4:3. How many girls are in the class? |
| Answer:________________________ |
| |
| Answer: 16 |
|
| 3. Three-fifths of the students in
a class are girls. If 5 girls and 5 boys are added to the class, which statement
is true of the class? |
| A. There are more girls than boys. |
| B. There are the same number of girls
as there are boys. |
| C. There are more boys than girls. |
| D. You cannot tell whether there
are more girls or boys from the information given. |
| |
| Answer: A |
|
| 4. Peter bought 70 items and Sue
bought 90 items. Each item costs the same and the items cost $800 altogether.
How much did Sue pay? |
| Answer: Sue paid_________________________ |
| |
| Answer: 450 |
|
| 5. To mix a certain color of paint,
Alana combines 5 liters of red paint, 2 liters of blue paint, and 2 liters
of yellow paint. What is the ratio of red paint to the total amount of paint? |
| A. 5/2 |
| B. 9/4 |
| C. 5/4 |
| D. 5/9 |
| |
| Answer: D |
| |
