No. 1.4.1 - Composing And Decomposing Numbers

1.

Which expression is not equal to 160,785?.

A.

100,000 + 60,000 + 700 + 85
B.

80,000 + 80,000 + 500 + 200 + 85
C.

150,000 + 10,000 + 700 + 80 + 5
D.

160,000 + 70 + 80 + 5

Correct Answer
D. 160,000 + 70 + 80 + 5

2.

The population of Hobbville is 10,082. What is another way to write this amount?

A.

1000 + 80 + 2
B.

5000 +5000 + 82
C.

10,000 + 800 + 2
D.

500 + 500 + 80 + 2

Correct Answer
B. 5000 +5000 + 82

Explanation
The given amount, 10,082, can be written as 5000 + 5000 + 82.

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3.

Communicating through letters is very popular in Russia. They have 93,076 post offices. What is another way to represent the number of post offices in Russia?

A.

93,000 + 70 + 6
B.

9,300 + 70 + 6
C.

930 + 70 + 6
D.

930 + 10,000 + 700 + 6

Correct Answer
A. 93,000 + 70 + 6

Explanation
The given answer, 93,000 + 70 + 6, is another way to represent the number of post offices in Russia. It breaks down the number 93,076 into its individual place values - 90,000 (representing the thousands place), 70 (representing the tens place), and 6 (representing the ones place). By adding these values together, we get the total number of post offices in Russia.

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4.

Bo likes to use decomposing to solve math problems. How could he decompose the following number? 57, 842

A.

50,000 + 7,000 + 80 + 40 + 2
B.

50,000 + 7,000 + 800 + 40 + 2
C.

40,000 + 17,000 + 80 + 40 + 2
D.

40,000 + 7,000 + 800 + 40 + 2

Correct Answer
B. 50,000 + 7,000 + 800 + 40 + 2

Explanation
Bo can decompose the number 57,842 by breaking it down into its place values. The number 57,842 can be decomposed as 50,000 + 7,000 + 800 + 40 + 2. This means that the number can be expressed as the sum of its place values, where the first digit represents the value in the ten thousands place, the second digit represents the value in the thousands place, the third digit represents the value in the hundreds place, the fourth digit represents the value in the tens place, and the fifth digit represents the value in the ones place.

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5.

Penny scored 484,675 points playing pinball at the arcade. Which of the following is not a correct representation of her score?

A.

400,000 + 80,000 + 4,000 + 600 + 75
B.

200,000 + 200,000 + 80,000 + 4,000 + 600 + 75
C.

400,000 + 80 + 40 + 600 + 7 + 5
D.

400,000 + 84,000 + 670 + 5

Correct Answer
C. 400,000 + 80 + 40 + 600 + 7 + 5

Explanation
The given representation of Penny's score as "400,000 + 80 + 40 + 600 + 7 + 5" is not correct because it does not account for the 80,000 points she scored playing pinball at the arcade.

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6.

The boys were playing “Represent the Number”. Bill turned over the following card. Each of the players wrote Bill’s number in a different way. Who did not correctly represent Bill's number?

A.

George500,000 + 80,000 + 100 + 43
B.

Juan400,000 + 180,000 + 143
C.

Calvin580,000 + 50 + 50 + 30 + 13
D.

Hakeem500,000 + 80,000 + 1,000 + 400 + 30

Correct Answer
D. Hakeem500,000 + 80,000 + 1,000 + 400 + 30

Explanation
Hakeem did not correctly represent Bill's number because he added an extra 1,000 and 400 to the number. The correct representation should only include 500,000, 80,000, and 30.

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7.

Matt is a whiz at mental math! He loves to calculate a string of numbers to impress his friends. What should Matt state as the correct sum to the list of numbers below?

A.

164,250
B.

22,250
C.

16,425
D.

2,500

Correct Answer
D. 2,500

8.

Jacob wanted to represent the number 54,789. So far he has written: 25,000 + 25,000 + 700 + 50 + 39 What is missing from his representation?

A.

4,000
B.

400
C.

40
D.

4

Correct Answer
A. 4,000

Explanation
Jacob's representation of the number 54,789 is missing the value of 4,000.

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9.

Ms. Brooks' 4th grade class is playing a game in which each team completes a puzzle. To place the final piece, John must pull a number that will finish the following equation: 6,000 + 6,000 + n + 200 + 9 = 12,709 Which of the following numbers does he need to pull?

A.

N = 500
B.

N = 700
C.

N = 2,000
D.

n = 7,000

Correct Answer
A. N = 500

Explanation
In order to find the value of n, we need to solve the equation. By combining like terms, we have 12,709 = 12,209 + n. To isolate n, we subtract 12,209 from both sides of the equation, giving us n = 500. Therefore, John needs to pull the number 500 to complete the puzzle.

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10.

Which of the following is equivalent to 1,500 +1,500 + 500 + 400 + 50 + 30?

A.

3,453
B.

3,980
C.

5,543
D.

15,453

Correct Answer
B. 3,980

Explanation
The given expression is a sum of several numbers. To find the equivalent value, we can simply add all the numbers together. Adding 1,500 + 1,500 + 500 + 400 + 50 + 30 gives us a total of 3,980. Therefore, the correct answer is 3,980.

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