Section A Practice Problems

Problem 1

Write a multiplication expression represented by each diagram.

  1.  
  2.  
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Solution
  1. 4×54 \times 5 or 5×45 \times 4
  2. 5×45 \times 4 or 4×54 \times 5

Problem 2

Each bottle contains 2 liters of water. How many liters of water are there in 6 bottles?

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Solution

Sample response: 12 liters

Problem 3

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

  1. 5×185 \times \frac{1}{8}

  2. 5×385 \times \frac{3}{8}

  3. 4×7124 \times \frac{7}{12}
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Solution
  1. 58\frac{5}{8}. Sample response: That's 5 pieces, and each piece is 18\frac{1}{8} of the whole.
  2. 158\frac{15}{8}. Sample response: That's 5 groups of 38\frac{3}{8}, which is 15 groups of 18\frac{1}{8} in all.
  3. 2812\frac{28}{12}. Sample response: 712\frac{7}{12} is 7 groups of 112\frac{1}{12}, and 4×7124 \times \frac{7}{12} is 4 groups of that, which means 28 groups of 112\frac{1}{12}.

Problem 4

Find the value of each expression.

  1. 25+45\frac{2}{5} + \frac{4}{5}
  2. 158−481\frac{5}{8} - \frac{4}{8}
  3. 216+1562\frac{1}{6} + 1\frac{5}{6}
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Solution
  1. 65\frac{6}{5} or equivalent
  2. 1181\frac{1}{8} or equivalent
  3. 3663\frac{6}{6} or 4 or equivalent

Problem 5

Here are some connecting cubes.

connecting cube tower, 2.

Select all pictures that show 4 times as many connecting cubes.

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Solution
B,C

Problem 6

Han read 4 books during the summer. Priya read 3 times as many books as Han.

  1. Draw a diagram that represents the situation.
  2. Write an equation that represents the situation.
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Solution

  1. Sample response:

    3 groups of 4 dots

  2. 3×4=123 \times 4 = 12

Problem 7

Mai exercised 3 times as many hours as Tyler last week. Mai exercised for 15 hours.

  1. Write an equation to represent the situation.
  2. How many hours did Tyler exercise last week?
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Solution
  1. 3×?=153 \times {?} = 15 or ?×3=15{?} \times 3 = 15
  2. 5 hours

Problem 8

Diego has 8 songs on his playlist. Mai has 3 times as many songs as Diego.

  1. Write an equation that represents the situation.

  2. Draw a diagram that represents the situation.
  3. Explain how the diagram and the equation are related.

  4. How many songs are on Mai’s playlist?

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Solution
  1. 3×8=?3 \times 8 = {?} or 8×3=?8 \times 3 = {?}
  2. See diagram.
  3. The equation and the tape show three 8s and the total is unknown.
  4. 24
diagram

Problem 9

Lin scored 6 points in her basketball game on Saturday. She scored 3 times as many points in her basketball game on Sunday. How many points did Lin score altogether in the two games? Explain or show your reasoning.

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Solution

24. Sample response: She scored 3×63 \times 6 or 18 points in the Sunday game, so that's 6+186 + 18 or 24 points total.

Problem 10

  1. If Diagram A represents 15, what does Diagram B represent? Explain your reasoning.

    diagram. two rectangles. Bottom rectangle, B. partitioned into 5 equal parts. Top rectangle, A. Same size as one of the 5 parts of bottom rectangle.

  2. If Diagram B represents 100, what does Diagram A represent? Explain your reasoning.
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Solution
  1. 75. Sample response: The amount in Diagram B is 5 times as much as in A, and 5×15=755 \times 15 = 75.
  2. 20. Sample response: 5×20=1005 \times 20 = 100

Problem 11

For each question, explain or show your reasoning.

diagram. two rectangles.
diagram. two rectangles. top rectangle, Lin's books. partitioned into 5 equal parts. Bottom rectangle, Diego's books. Partitioned into 7 equal parts. The partitioned parts on the top and bottom are the same size.

  1. If Lin brought 10 books, how many books did Diego bring?
  2. If Diego brought 21 books to the fair, how many books did Lin bring?
  3. If Lin and Diego brought 60 books altogether, how many did they each bring?
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Solution
  1. 14. Sample response: Each box in the diagram represents 2 books.
  2. 15. Sample response: Each box in the diagram represents 3 books.
  3. Lin brought 25 books and Diego brought 35 books. Sample response: There are 12 boxes altogether in the diagrams. If they represent 60 books, then each box is 5 books.

Problem 12

Write a comparison story problem.

Trade problems with a partner.

  1. Draw a diagram and write an equation to represent the situation.
  2. Solve the story problem.
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Solution
Sample response: I have 65 cents in my pocket. That's 5 times as much as my sister. How many cents does she have in her pocket?
  1. 5×?=655 \times {?} = 65 or ?×5=65{?} \times 5 = 65 or 5×13=655 \times 13 = 65 or 13×5=6513 \times 5 = 65
  2. My sister has 13 cents.

diagram. two rectangles.
diagram. two rectangles. bottom rectangle, my pocket. partitioned into 5 equal parts. Top rectangle, My sister's pocket. Same size as one small rectangle on the bottom