Section A Practice Problems

Problem 1

Round each number to the nearest 10 and to the nearest 100.

  1. 63

  2. 350

  3. 485

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Solution
  1. 60 and 100
  2. 350 and 400
  3. 490 and 500

Problem 2

A point P is located on the number line and represents a number.

Number line. Scale 600 to 800, by 100's. Point P, over halfway between 600 and 700.
  1. Round P to the nearest multiple of 100. Explain your reasoning.
  2. Can you tell what P is if the value is rounded to the nearest multiple of 10? Explain your reasoning.
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Solution
  1. 700. Sample response: The number is closer to 700 than to 600, so it is 700 when rounded to the nearest 100.
  2. No. Sample response: It is more than halfway to 700 from 600, so it is more than 650. I can not tell exactly but would guess 670 or 680.

Problem 3

Find the value of each expression. Show your thinking. Organize it so it can be followed by others.

  1. 523+278523 + 278
  2. 418−235418 - 235
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Solution
  1. 801. Sample response: I added the hundreds, tens, and ones and got 700+101700 + 101, which is 801.
  2. 183. Sample response: I broke up a hundred to make 10 tens and then subtracted to get 1 hundred, 8 tens, and 3 ones.

Problem 4

Here are three numbers: 265, 652, and 526. For each question, explain your reasoning.

  1. Does the digit 6 have a greater value in 265 or 652?
  2. Does the digit 5 have a greater value in 265 or 652?
  3. In which number does the digit 2 have the greatest value? In which number does the digit 2 have the least value?
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Solution
Sample responses:
  1. The value of 6 in 652 is 600, which is more than 60, the value of 6 in 265.
  2. The value of 5 in 652 is 50, which is more than 5, the value of 5 in 265.
  3. The 2 has the greatest value in 265 where its value is 200. The 2 has the least value in 652, where its value is 2. 

Problem 5

Each large square represents 1.

  1. Write the number that represents the shaded part of the large square as a fraction and in decimal notation.

    Hundreds diagram. Fifty three of one hundred shaded.


    Fraction: __________

    Decimal Notation: __________

  2. Shade part of each square to represent the given number. Then write the number in the format that is not given.

    Hundreds diagram. 


    Fraction: 13100\frac{13}{100}

    Decimal Notation: __________

    Hundredths grid. 0 square shaded.


    Fraction: __________

    Decimal Notation: 0.44

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Solution
  1. 53100\frac{53}{100} and 0.53
  2. First diagram: 13 of the 100 small squares in the diagram are shaded. The decimal is 0.13.
    Second diagram: 44 of the 100 small squares in the diagram are shaded. The fraction is 44100\frac{44}{100}.

Problem 6

Select all the numbers equivalent to 210\frac{2}{10}.

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Solution
B,C,E

Problem 7

  1. Locate and label 0.6 and 0.35 on the number line.

    Number line. 10 evenly spaced tick marks. First tick mark, 0 and second tick mark ,1 tenth. 

  2. Compare 0.6 and 0.35 using < or >.
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Solution
  1. Number line.
  2. 0.6>0.350.6 > 0.35

Problem 8

Order the numbers from least to greatest.

5.90

9.05

5.95

0.59

5.59

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Solution
0.59, 5.59, 5.90, 5.95, 9.05

Problem 9

Order the numbers from least to greatest.

1310\frac{13}{10}

1.25

1.46

75\frac{7}{5}

155100\frac{155}{100}

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Solution
1.25, 1310\frac{13}{10}, 75\frac{7}{5}, 1.46, 155100\frac{155}{100}

Problem 10

The table shows the distances, in miles, some students walked during the school week.

Order the numbers from least to greatest.

student distance (miles)
Han 5345\frac{3}{4}
Tyler 5785\frac{7}{8}
Mai 5.95
Elena 58105\frac{8}{10}
Andre 5.79
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Solution
5345\frac{3}{4}, 5.79, 58105\frac{8}{10}, 5785\frac{7}{8}, 5.95

Problem 11

In an earlier lesson, you learned about the lengths of the jumps made by Carl Lewis and other athletes.

Create and label a number line to show the distances of all 10 jumps made by the athletes.

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Solution

Sample response:

Number line.