Practice Test (6th Grade: Math) Flashcards

The perimeter of the following shape is? (It's in the shape of a right triangle)

Answer: 24 cm

The perimeter of any polygon is the total distance around its exterior. To find the perimeter of the right triangle, you simply add the lengths of all its sides. Assuming the sides are 6 cm, 8 cm, and 10 cm (a common Pythagorean triple), the sum is 6 + 8 + 10 = 24 cm.

Watermelons are currently on sale for $1.25 for two. What is the cost per unit?

Answer: 62.5¢/watermelon

To find the cost per unit, divide the total cost by the number of units. Here, $1.25 for two watermelons means $1.25 ÷ 2 = $0.625 per watermelon. Converting this to cents, we multiply by 100, resulting in 62.5¢ per watermelon.

Anthony has three blue and eight red balls. What is the ratio of blue to red balls?

Answer: 3:8

A ratio expresses the relationship between two quantities in a specific order. When asked for the ratio of blue to red balls, you list the number of blue balls first, followed by the number of red balls. Since Anthony has three blue balls and eight red balls, the ratio is 3:8.

What is the equivalent expression to 4(6x + 11)?

Answer: 24x + 44

To find an equivalent expression, apply the distributive property. This means multiplying the number outside the parentheses by each term inside. So, 4 multiplied by 6x is 24x, and 4 multiplied by 11 is 44, resulting in the expression 24x + 44.

Ralph received a quotient of 26 with a remainder of 13 when he divided 403 by a number. What was the number Ralph divided by?

Answer: 15

The division algorithm states that Dividend = Divisor × Quotient + Remainder. We have 403 = Divisor × 26 + 13. First, subtract the remainder from the dividend: 403 - 13 = 390. Then, divide this result by the quotient: 390 ÷ 26 = 15. Therefore, the number Ralph divided by was 15.

There are 55 blue and 143 red balls. We want to put these balls in certain boxes so that there are the same amount of red balls in each box and there are same number of blue balls in each box. How many boxes will we require?

Answer: 11

To ensure the same number of red balls in each box and the same number of blue balls in each box, the number of boxes must be a common divisor of both 55 and 143. To find the maximum number of such boxes, we determine the Greatest Common Divisor (GCD) of 55 and 143. The factors of 55 are 1, 5, 11, 55, and the factors of 143 are 1, 11, 13, 143, making 11 the GCD. Thus, 11 boxes are required.

Which is the better deal: 5 for $1.00, 4 for 85¢, 2 for 25¢, or 6 for $1.10?

Answer: 2 for 25¢

To find the better deal, calculate the unit price for each option. 5 for $1.00 is $0.20/item, 4 for 85¢ is $0.2125/item, 2 for 25¢ is $0.125/item, and 6 for $1.10 is approximately $0.1833/item. The lowest unit price of $0.125 per item makes '2 for 25¢' the best deal.

Which of the following statements best describes unit rate?

Answer: Dave is driving 30 miles per 1 hour.

A unit rate describes how many units of the first quantity correspond to one unit of the second quantity. It is a ratio where the denominator is 1. 'Dave is driving 30 miles per 1 hour' clearly expresses a rate with '1 hour' as the single unit of time, making it the best description of a unit rate.

Choose the x value that answer the equation or inequality. 2x + 5 = 9

Answer: x = 2

To solve the equation 2x + 5 = 9, first subtract 5 from both sides to isolate the term with x: 2x = 9 - 5, which simplifies to 2x = 4. Next, divide both sides by 2 to solve for x: x = 4 ÷ 2. Therefore, x = 2.

Which of the following expressions is equivalent to the one below? 7h + 1

Answer: (5 + 2)h + 1

To find an equivalent expression, we need one that simplifies to 7h + 1. In option C, (5 + 2)h + 1, the terms inside the parentheses (5 and 2) can be added first, resulting in 7h + 1. This matches the original expression exactly, demonstrating equivalence.

What is the value of the expression below? 2,205÷315

Answer: 7

To find the value of the expression, perform the division: 2,205 divided by 315. By multiplying 315 by 7, we get 2205 (7 * 300 = 2100, 7 * 15 = 105, and 2100 + 105 = 2205). Therefore, the value is 7.

A box of three bracelets costs $2.22. What is the price per unit?

Answer: 74¢ per bracelet

To find the price per unit, divide the total cost by the number of items. A box of three bracelets costs $2.22, so $2.22 ÷ 3 = $0.74 per bracelet. Converting this to cents, we get 74¢ per bracelet.

What is the value of the expression below? 4/5 ÷ 8/7

Answer: 7/10

To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. So, 4/5 ÷ 8/7 becomes 4/5 × 7/8. Multiplying the numerators gives 28 and the denominators gives 40, resulting in 28/40. This fraction simplifies by dividing both numerator and denominator by 4, yielding 7/10.

The temperature in Cleveland is -10 degrees Fahrenheit. In Kansas City, it is cooler than in Cleveland. Select the value that could be used to represent Kansas City's temperature.

Answer: -12

On a temperature scale, 'cooler' means a lower temperature. Since Cleveland is -10 degrees Fahrenheit, Kansas City's temperature must be a value less than -10. Of the given options, -12 degrees Fahrenheit is the only value that is numerically smaller (further to the left on a number line) than -10 degrees Fahrenheit.

Two portions of fruits are served with each meal in a school cafeteria. In the school cafeteria, what is the ratio of meals served to fruit portions?

Answer: 1 : 2

The question asks for the ratio of meals served to fruit portions. For every one meal served, two portions of fruit are provided. Therefore, the ratio of meals to fruit portions is 1:2.

Solve the equation below. 112=22+𝑥

Answer: 𝑥=90

To solve the equation 112 = 22 + x, you need to isolate x. Subtract 22 from both sides of the equation: 112 - 22 = x. Performing the subtraction gives 90 = x. Therefore, x = 90.

In 23 meters, how many millimeters are there?

Answer: 23,000 mm

To convert meters to millimeters, you need to know that 1 meter is equivalent to 1,000 millimeters. Therefore, to find how many millimeters are in 23 meters, multiply 23 by 1,000. This calculation yields 23,000 millimeters.

Find the value of X. x + 9 = 14

Answer: x = 5

To solve the equation x + 9 = 14, you need to isolate x. Subtract 9 from both sides of the equation: x = 14 - 9. Performing the subtraction gives x = 5.

What is the expression's value? 1608 ÷ 268

Answer: 6

To find the value of the expression, perform the division: 1608 divided by 268. By multiplying 268 by 6, we get 1608 (6 * 200 = 1200, 6 * 60 = 360, 6 * 8 = 48, and 1200 + 360 + 48 = 1608). Therefore, the value is 6.

In a park, all of the trash cans are red or blue. The park has a 3:4 ratio of red to blue trash cans. Which of the following statements is true based on this information?

Answer: For every 3 red trash cans in the park, there are 4 blue trash cans.

A ratio of 3:4 for red to blue trash cans directly means that for every 3 red trash cans, there are 4 blue trash cans. The order of the numbers in the ratio corresponds to the order of the items being compared.