Practice/Review 1

Which fraction is equivalent to a repeating decimal?

• 4/9

• 3/8

• 1/5

• 1/10

Answer explanation

The fraction 4/9 is equivalent to the repeating decimal 0.444..., while 3/8, 1/5, and 1/10 are terminating decimals. Thus, 4/9 is the correct choice for a repeating decimal.

Which situation involves opposite quantities combining to make 0?

• a deposit of $76 followed by a withdrawal of $152

• a deposit of $76 followed by another deposit of $76

• a withdrawal of $152 followed by a deposit of $152

• a withdrawal of $152 followed by another withdrawal of $76

Answer explanation

The correct choice is 'a withdrawal of $152 followed by a deposit of $152' because these two opposite quantities cancel each other out, resulting in a total of 0.

Which term describes -7/11

• integer

• positive number

• whole number

• rational number

Answer explanation

-7/11 is a fraction, which is a type of rational number. Rational numbers are defined as numbers that can be expressed as the quotient of two integers, where the denominator is not zero. Thus, the correct term is 'rational number'.

A cyclist rides 2 1/2​ miles in 3/4 hour. What is the cyclist's speed in miles per hour?

• 3 1/3 miles per hour

• 2 2/3​ miles per hour

• 3 3/4​ miles per hour

• 2 1/4 miles per hour

Answer explanation

To find the speed, divide the distance by the time. The cyclist rides 2.5 miles in 0.75 hours. Speed = 2.5 / 0.75 = 3.33 miles per hour, which is 3 1/3 miles per hour.

Which equation represents the relationship?

• A. y=48x

• B. y=12x

• C. y=8x

• D. y=6x

Answer explanation

The equation y=12x indicates a direct proportionality where y increases by 12 for every unit increase in x. This matches the relationship described in the question, making B the correct choice.

Last year, 150 students participated in a math club, and 200 students participated in a science club. This year, the number of students in the math club increased by 10%, and the number of students in the science club increased by 15%. How many total students are in the math and science clubs this year?

• A. 380 students

• B. 385 students

• C. 395 students

• D. 400 students

Answer explanation

The math club has 150 students, increasing by 10% to 165. The science club has 200 students, increasing by 15% to 230. Total this year: 165 + 230 = 395 students. Thus, the correct answer is C.

This year, 220 students are in a drama club, and 264 students are in a debate club. The number of students in the drama club increased by 10% from last year, and the number of students in the debate club increased by 20% from last year.

How many total students were in the drama and debate clubs last year?

• A. 400 students
  

• B. 420 students
  

• C. 430 students
  

• D. 440 students

Answer explanation

Let x be last year's drama club students. Then, x * 1.1 = 220, so x = 200. For the debate club, y * 1.2 = 264, so y = 220. Total last year = 200 + 220 = 420. Thus, the answer is B.

A baker frosts 4 1/2 cakes in 3/4 hour. At this rate, how many cakes can the baker frost in 1 hour?

• 8 cakes

• 6 cakes

• 3 cakes

• 1 cake

Answer explanation

The baker frosts 4 1/2 cakes in 3/4 hour. To find the rate per hour, multiply by 4/3: (4.5 cakes) * (4/3) = 6 cakes. Thus, the baker can frost 6 cakes in 1 hour.

A student measures the water level of a pond that contains

10 centimeters of water and records how the water level changes each week. The student writes the expression 10+(−4)+5 to describe the changes in the water level over two weeks.

• A. The water level decreases by 10 cm, then increases by 4 cm, and finally decreases by 5 cm.

• B. The initial water level is 10 cm. The water level decreases by 4 cm in the first week and then increases by 5 cm in the second week.

• C. The initial water level is 10 cm. The water level increases by 4 cm in the first week and then decreases by 5 cm in the second week.

• The initial water level is 10 cm. The water level decreases by 5 cm in the first week and increases by 4 cm in the second week.

Answer explanation

The expression 10+(−4)+5 indicates the water level starts at 10 cm, decreases by 4 cm in the first week, and then increases by 5 cm in the second week, confirming choice B as correct.

A car travels 7/8​ mile in 1/4​ hour at a constant speed. What is the speed of the car in miles per hour?

• 7/2 miles per hour

• 7/32 miles per hour

• 8/7 miles per hour

• 3/8 miles per hour

Answer explanation

To find the speed, divide the distance by time. The car travels 7/8 mile in 1/4 hour. Speed = (7/8) / (1/4) = (7/8) * (4/1) = 7/2 miles per hour. Thus, the correct answer is 7/2 miles per hour.