Mathematics Questions

Order from smallest to largest the following items based on their number in a stack 1 ft high:

• Number of pennies

• Number of books

• Number of dollar bills

• Number of bread slices

Answer explanation

The number of pennies is the largest because they are small and numerous, fitting more in a 1 ft stack than books, dollar bills, or bread slices, which take up more space. Thus, the order is: pennies, dollar bills, bread slices, books.

Tags

CCSS.6.RP.A.1

Use the numbers 4, 40, and 4000 to complete the sentence. a. (a)   ÷ 40.01 is close to 1.

Answer explanation

To find a number that, when divided by 40.01, is close to 1, we need a number close to 40.01. The number 40 is the only option that fits this criterion, as 40 ÷ 40.01 is approximately 1.

Tags

CCSS.6.NS.B.2

CCSS.6.NS.B.3

Use the numbers 4, 40, and 4000 once to complete the sentence.
b. The value of (a)   ÷ 40.01 is much less than 1.

Answer explanation

To find a value that, when divided by 40.01, is much less than 1, we can use 4. Since 4 ÷ 40.01 = 0.099, which is less than 1, it is the correct choice. Using 40 or 4000 would yield values greater than 1.

Tags

CCSS.6.NS.B.2

Use each of the numbers 4, 40, and 4000 once to complete the sentence. c. The value of (a)   ÷ 40.01 is much greater than

Answer explanation

Using 4000 in the sentence, 4000 ÷ 40.01 is much greater than 100, while using 4 or 40 would yield much smaller results. Thus, 4000 is the correct choice to complete the sentence.

Tags

CCSS.6.NS.B.2

Without computing, decide whether the value of the expression 100 ÷ (1/1000) is:

• Much smaller than 1

• Close to 1

• Much greater than 1

Answer explanation

Dividing 100 by 1/1000 is equivalent to multiplying 100 by 1000, which equals 100000. This value is much greater than 1, confirming the correct choice.

Tags

CCSS.6.NS.A.1

Without computing, decide whether the value of 4.7 ÷ 5.2 is:

• Much smaller than 1

• Close to 1

• Much greater than 1

Answer explanation

4.7 is slightly less than 5, and 5.2 is slightly more than 5. Thus, 4.7 ÷ 5.2 is a fraction where the numerator and denominator are close in value, making the result close to 1.

Tags

CCSS.6.NS.B.3

Without computing, decide whether the value of the expression 2 ÷ 7335 is:

• much smaller than 1

• close to 1

• much greater than 1

Answer explanation

The expression 2 ÷ 7335 represents a division of a small number by a much larger number. Therefore, the result will be much smaller than 1, confirming the correct choice.

Tags

CCSS.6.NS.C.7

CCSS.6.NS.C.6

Without computing, decide whether the value of the expression 2,000,001 ÷ 9 is:

• Much smaller than 1

• Close to 1

• Much greater than 1

Answer explanation

The expression 2,000,001 ÷ 9 results in a value greater than 1 because 2,000,001 is significantly larger than 9. Thus, the correct choice is 'Much greater than 1'.

Tags

CCSS.6.NS.B.2

Without computing, decide whether the value of the expression 0.002 ÷ 2,000 is:

• Much smaller than 1

• Close to 1

• Much greater than 1

Answer explanation

The expression 0.002 ÷ 2,000 involves dividing a small number (0.002) by a much larger number (2,000). This results in a value that is much smaller than 1, confirming the correct choice.

Tags

CCSS.6.NS.B.3

A garden hose emits 9 quarts of water in 6 seconds. At this rate, how long will it take the hose to emit 12 quarts?

• 8 seconds

• 7 seconds

• 6 seconds

• 5 seconds

Answer explanation

The hose emits 9 quarts in 6 seconds, which is 1.5 quarts per second. To find the time for 12 quarts, divide 12 by 1.5, resulting in 8 seconds. Thus, it will take 8 seconds to emit 12 quarts.

Tags

CCSS.6.RP.A.2

CCSS.6.RP.A.3