Fractions and Proportionality Test Questions


Below are sample questions from the TIMSS achievement tests in Science administered to twentysix 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 testquestion writing. The sample questions are grouped by grades 3 and 4 and by grades 7 and 8.  
Grades 3 and 4  
1. 0.4 is the same as  
A. four  
B. four tenths  
C. four hundredths  
D. onefourth 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 

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 

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 

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. 

Answer: No. 10 is not half of 30 

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 

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? 

A. 2 

B. 4 

C. 5 

D. 40 

E. 45 

Answer: C 

2. In a discusthrowing competition, the winning throw was 61.60m. The second place throw was 59.72 m. How much longer was the winning throw than the secondplace throw? 

A. 1.18m 

B. 1.88m 

C. 1.98m 

D. 2.18m 



Answer: B 

3. Write a fraction that is larger than 2/7. 

Answer:__________________ 

Answer: A fraction with a numerator greater than 2 and a denominator equal to 7. 

4. Divide 8/35 by 4/15= 

Answer: ___________________ 



Answer: 33761 

5. Divide: 24.56 by 0.004 

A. 0.614 

B. 6.14 

C. 61.4 

D. 614 

E. 6140 



Answer: E 

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 

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 seventenths? 

A. 54.7  
B. 504.7  
C. 547  
D. 5004.7  
Answer: B  
10. What is the value of 2/31/41/12? 

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: 2.2010.753=  
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: 60002369=  
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.  


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. Threefifths 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  