Section D Practice Problems

Problem 1

  1. Find the value of 1÷0.011 \div 0.01. Use the diagram if it is helpful.

    Diagram, square. Partitioned into 10 rows of 10 of the same size squares. No squares shaded.

  2. Jada says there are 100 hundredths in 1, so 1÷0.011 \div 0.01 is 100. Do you agree? Explain or show or explain your reasoning.
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Solution
  1. 100. Sample response: If the large square represents 1, then each small square is 0.01 and there are 100 of them in the large square.
  2. Yes. Sample response: 0.01 is a hundredth and there are 100 hundredths in a whole as I can see in the square divided into 100 small squares.

Problem 2

  1. Find the value of 2÷0.22 \div 0.2. Use the diagram if it is helpful.

    <p>Two diagrams. Each squares. Each partitioned into 10 rows of 10 of the same size squares. No squares shaded. </p>

  2. Find the value of 21÷0.221 \div 0.2.
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Solution

  1. 10. Sample response:

    2 diagrams. hundredths square grids.

  2. 105. Sample response: There are five 0.2s in each whole and 21×5=10521 \times 5 = 105.

Problem 3

Here is a diagram.

Two diagrams. Each squares.
Two diagrams. Each squares. Each partitioned into 10 rows of 10 of the same size squares. All squares shaded. For each 25 squares, shading alternates, blue, orange.

  1. Explain or show how the diagram shows 200÷25200 \div 25. What is the value of the expression?

  2. Explain or show how the diagram shows 2÷0.252 \div 0.25. What is the value of the expression?
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Solution

Sample responses:

  1. There are 200 small squares and 8 groups of 25. So, 200÷25=8200 \div 25 = 8.
  2. There are 2 large squares and 8 groups of 0.25. So, 2÷0.25=82 \div 0.25 = 8.

Problem 4

Find the value of each expression. Explain or show your reasoning.

  1. 0.2÷50.2 \div 5. Use the diagram if it is helpful.

    ​​​​​

    Diagram, square. Length and width, 1. Partitioned into 10 rows of 10 of the same size squares. No squares shaded.<strong> </strong>

  2. 6÷36 \div 3
  3. 6÷0.36 \div 0.3
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Solution
  1. 0.04. Sample response:

    diagram. hundredths square grid.

  2. 2. Sample response: There are 2 3s in 6.
  3. 20. Sample response: There are 10 times as many 0.3s in 6 as 3s.

Problem 5

Find the value of each expression. Explain or show your reasoning.

  1. 0.5÷0.10.5 \div 0.1
  2. 0.5÷0.010.5 \div 0.01
  3. 3.5÷0.013.5 \div 0.01
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Solution
  1. 5. Sample response: 0.5 means 5 tenths.
  2. 50. Sample response: there are 50 hundredths in 5 tenths.
  3. 350. Sample response: There are an additional 300 hundredths in 3 along with the 50 in 0.5.

Problem 6

Noah has a scale that weighs to the nearest ounce. The table shows the weights of different numbers of paper clips Noah found using the scale.

How many ounces do you think each paper clip weighs? Explain or show your reasoning.

number of paper clips weight (ounces)
1 0
10 0
20 1
25 1
50 2
100 3

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Solution

Sample response: The non-zero weights give these values for each paper clip when I perform division.

number of paper clips weight of each paper clip
20 0.05
25 0.04
50 0.02
100 0.03

These values cannot all be correct. The scale only reads to the nearest ounce. So if 100 paper clips weigh 3 ounces then the 100 paper clips are between 2.5 and 3.4 ounces. I think the best guess for their weight is 0.03 ounces. This would make sense with all of the measurements.

Problem 7

The daily recommended allowance of vitamin C for a 5th grader is 0.045 gram.

  1. One vitamin C tablet has 1 gram of vitamin C. Approximately how many times the daily recommended allowance of vitamin C is 1 tablet? Use the diagram if it is helpful.

    Diagram, square. Partitioned into 10 rows of 10 of the same size squares. No squares shaded.

  2. A large orange has 0.18 gram of vitamin C. Approximately how many times the daily recommended allowance of vitamin C is in a large orange? Use the diagram if it is helpful.

    Diagram, square. Partitioned into 10 rows of 10 of the same size squares. No squares shaded.

Show Solution
Solution
  1. 20 times the daily recommended allowance. Sample response: 1÷0.051 \div 0.05 is 20. I used a hundredths grid and 0.05 is half of each column and there are 10 columns in the hundredths grid.
  2. 3353 \frac{3}{5} time the daily recommended allowance. Sample response: There are more than 3 and less than 4. If I multiply both numbers by 100, then I get 18÷518 \div 5 and that is the same as 3353 \frac{3}{5}.