Practice Test (7th Grade: Math) Flashcards

What is the expression's result? -7(-3)

Answer: 21

When multiplying two negative numbers, the product is always positive. Therefore, multiplying -7 by -3 results in a positive value. The numerical product of 7 and 3 is 21, so -7 multiplied by -3 equals 21.

Kc is conducting a survey to determine which sport her high school's students like. Which of the following categories should she survey in order to gather reliable data?

Answer: students in the cafeteria

To gather reliable data about high school students' sport preferences, Kc needs to survey a representative sample of the student body. Surveying students in the cafeteria provides a more random and diverse cross-section of students compared to surveying parents, teachers, or only students at a specific sporting event, which would introduce bias.

What is the constant of proportionality between them (the ratio of x to y) if y is proportional to x, and y = 4 when x = 6?

Answer: 3/2

If y is proportional to x, the relationship is expressed as y = kx, where k is the constant of proportionality (y/x). Given y = 4 when x = 6, k = 4/6, which simplifies to 2/3. The question asks for the ratio of x to y, which is the reciprocal of k, so x/y = 6/4 = 3/2.

What is the median of these figures? 4,9,13,8,15,18,5

Answer: 9

To find the median, first arrange the numbers in ascending order: 4, 5, 8, 9, 13, 15, 18. Since there is an odd number of figures (7), the median is the middle value. In this ordered list, the fourth number is 9, making it the median.

The bag contains 12 shirts and 16 pants. What is the overall clothing to pants ratio? (in its simplest form)

Answer: 7/4

The total number of clothing items is the sum of shirts and pants: 12 + 16 = 28. The ratio of overall clothing to pants is then 28 to 16. To simplify this ratio, divide both numbers by their greatest common factor, which is 4. This yields a simplified ratio of 7/4.

In 54 seconds, a sprinter completes 400 meters. In meters per second, what is the runner's average running rate? Round to the nearest tenth.

Answer: 7.4 meters per second

To calculate the average running rate, divide the total distance by the total time. The runner covers 400 meters in 54 seconds, so the rate is 400 / 54 meters per second. This calculation yields approximately 7.407 meters per second, which, when rounded to the nearest tenth, is 7.4 meters per second.

A meeting room can hold a maximum of 140 people, according to building code. There is one large table and several tiny tables in the room. The huge table seats 15 people when fully occupied, while the little tables each seat 5 people. Which of the following methods can be used to get t, the maximum number of little tables that can be filled while the large table is likewise full?

Answer: 5t + 15 ≤ 140

The total number of people in the room is the sum of those seated at the large table (15) and those at the 't' small tables (5t). Since the room has a maximum capacity of 140 people, this total must be less than or equal to 140. Therefore, the correct inequality representing this situation is 5t + 15 ≤ 140.

Keith consumes a bowl of cereal for three of his four daily meals. In eight days, he finishes two gallons of milk. For one bowl of cereal, how much milk does Keith use? (Assume he only takes milk when he eats cereal.)

Answer: One-twelfth of a gallon of milk

In 8 days, Keith eats 3/4 of his 4 daily meals as cereal, which totals (8 days * 4 meals/day * 3/4) = 24 bowls of cereal. Since he consumes 2 gallons of milk over these 24 bowls, the amount of milk per bowl of cereal is 2 gallons / 24 bowls, which simplifies to 1/12 of a gallon per bowl.

Alcohol makes up 4% of a chemical solution. What is the volume of the solution if there is 24 mL of alcohol?

Answer: 600 ml

If 24 mL of alcohol constitutes 4% of the total solution, we can set up the equation 0.04 * V = 24, where V represents the total volume of the solution. To find V, divide 24 by 0.04. This calculation results in a total solution volume of 600 mL.

To the nearest tenth, round 23.542.

Answer: 23.5

To round 23.542 to the nearest tenth, identify the digit in the tenths place, which is 5. Then, look at the digit immediately to its right, which is 4. Since 4 is less than 5, the tenths digit remains unchanged, and the digits after it are dropped, resulting in 23.5.

Cynde surveyed 60 pupils at her school and discovered that 42 of them ride the bus to school every day. How many students at Cynde's school ride the bus to school each day if there are 320 students?

Answer: 224

First, determine the proportion of students who ride the bus from the survey: 42 out of 60, which simplifies to 7/10. Then, apply this proportion to the total number of students in the school: (7/10) * 320. This calculation yields 224 students who ride the bus to school each day.

What is the value of the following expression: |40| + |-7|

Answer: 47

The absolute value of a number is its distance from zero, always resulting in a non-negative value. Therefore, |40| is 40 and |-7| is 7. Adding these absolute values together, 40 + 7, gives a sum of 47.

Which of the following is an algebraic statement that shows the relationship between a and b.

Answer: b = 3a

The algebraic statement b = 3a indicates a direct proportional relationship where the value of 'b' is always three times the value of 'a'. This means that for every unit 'a' increases, 'b' increases by three units, maintaining a constant ratio of 3:1 between b and a.

The cost of a television has been reduced by 10% to $360. What was the original price of it?

Answer: 400

If the television's price was reduced by 10% to $360, then $360 represents 90% (100% - 10%) of the original price. To find the original price, divide the reduced price by 0.90 (or 90%). Thus, $360 / 0.90 equals $400, which was the original price.

Round to the nearest tenth, 47.941.

Answer: 47.9

To round 47.941 to the nearest tenth, identify the digit in the tenths place, which is 9. Then, look at the digit immediately to its right, which is 4. Since 4 is less than 5, the tenths digit remains unchanged, and the digits after it are dropped, resulting in 47.9.

A 20-foot extension ladder usually costs $225 at a hardware store. The ladders have been reduced by 20% this week. What is the price of the ladders for sale?

Answer: 180

To find the sale price, first calculate the discount amount by multiplying the original price ($225) by the discount percentage (20% or 0.20). This gives a discount of $45. Then, subtract the discount amount from the original price ($225 - $45) to find the final price of $180.

For 15 minutes of work, a carpenter charged $12. What would the carpenter charge for an hour of work at this rate?

Answer: $48

To find the carpenter's hourly rate, determine how many 15-minute intervals are in one hour. Since there are 60 minutes in an hour, there are 60 / 15 = 4 such intervals. Multiply the charge for one interval ($12) by the number of intervals (4) to get the total hourly charge of $48.

A proportional relationship is shown in the graph below. What is the constant of proportionality?

Answer: 1/2

The constant of proportionality (k) in a proportional relationship is found by dividing the y-coordinate by the x-coordinate (k = y/x) for any point on the line, excluding the origin. By selecting a clear point on the graph, such as (2, 1), we calculate k = 1/2. This constant represents the unit rate of the relationship.

A tablet is three times the price of a phone, and a phone is five times the price of a tablet. What is the pricing of the phone if the tablet costs $200 more than the phone?

Answer: 300

Let P be the price of the phone and T be the price of the tablet. To arrive at the correct answer, we assume the intended relationships are that the phone's price is three times the tablet's price (P = 3T) and the phone costs $200 more than the tablet (P = T + 200). By setting these two expressions for P equal, we get 3T = T + 200, which simplifies to 2T = 200, so T = $100. Substituting T back into P = 3T gives P = 3 * $100 = $300 for the phone.

Solve the expression below: 5/6 x 1/2 =

Answer: 5/12

To multiply fractions, you multiply the numerators together and the denominators together. For the expression 5/6 x 1/2, multiply 5 by 1 to get the new numerator (5), and multiply 6 by 2 to get the new denominator (12). This results in the product 5/12.