Section B Section B Checkpoint

Problem 1

Select all expressions that are equivalent to 58\frac{5}{8}.

A
 18+18+18+18+18\frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8}
B
 38+28+28\frac{3}{8} + \frac{2}{8} + \frac{2}{8}
C
 28+28+18\frac{2}{8} + \frac{2}{8} + \frac{1}{8}
D
 48+18\frac{4}{8} + \frac{1}{8}
E
 35+23\frac{3}{5} + \frac{2}{3}

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Solution
A, C, D
Show Sample Response
Sample Response
A, C, D

Problem 2

Find the value of each expression. Explain or show your reasoning. Use the number line if it is helpful.

  1.  325+453\frac{2}{5} + \frac{4}{5}

    Number line. Scale 0 to 5. Evenly spaced by fifths.

  2.  2−182 - \frac{1}{8}

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Solution

  1. 215\frac{21}{5}. Sample response: Each whole is 55\frac{5}{5}, so there are 155\frac{15}{5} in 3 and 175\frac{17}{5} in 3253 \frac{2}{5}. Then 45\frac{4}{5} more makes 215\frac{21}{5}.

  2. 158\frac{15}{8}. Sample response: Each whole is 88\frac{8}{8}, so 2 is equivalent to 168\frac{16}{8}, and subtracting 18\frac{1}{8} gives 158\frac{15}{8}.

Show Sample Response
Sample Response

  1. 215\frac{21}{5}. Sample response: Each whole is 55\frac{5}{5}, so there are 155\frac{15}{5} in 3 and 175\frac{17}{5} in 3253 \frac{2}{5}. Then 45\frac{4}{5} more makes 215\frac{21}{5}.

  2. 158\frac{15}{8}. Sample response: Each whole is 88\frac{8}{8}, so 2 is equivalent to 168\frac{16}{8}, and subtracting 18\frac{1}{8} gives 158\frac{15}{8}.

Problem 3

The line plot shows the weights of some puppies at a pet store.

Dot plot from 0 to 5
Dot plot from 0 to 5 by 1’s. Hash marks at eighths. Horizontal axis, weight, in pounds. Beginning at 5 eighths, the number of X’s above each eighth increment is 2, 0, 1, 1, 0, 1, 0, 1, 0, 0, 3, 0, 0, 1, 0, 1, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1.
  1. What is the difference between the weights of the heaviest puppy and the lightest puppy? Explain or show your reasoning.
  2. How much did the 5 heaviest puppies weigh all together? Explain or show your reasoning.
Show Solution
Solution
  1. 4184\frac {1}{8} pounds. Sample response: 468−58=4184\frac {6}{8} - \frac {5}{8} = 4\frac {1}{8}
  2. 184818 \frac {4}{8} pounds. Sample response: I first added the whole numbers of pounds which was 4+3+3+3+34 + 3 + 3+ 3 + 3 or 16. Then I added the eighths which was 68+78+78 = 208\frac {6}{8} + \frac{7}{8} + \frac{7}{8}  =  \frac{20}{8}, which is the same as 2482\frac{4}{8}. 16+248=184816 + 2\frac {4}{8} = 18\frac {4}{8}
Show Sample Response
Sample Response
  1. 4184\frac {1}{8} pounds. Sample response: 468−58=4184\frac {6}{8} - \frac {5}{8} = 4\frac {1}{8}
  2. 184818 \frac {4}{8} pounds. Sample response: I first added the whole numbers of pounds which was 4+3+3+3+34 + 3 + 3+ 3 + 3 or 16. Then I added the eighths which was 68+78+78 = 208\frac {6}{8} + \frac{7}{8} + \frac{7}{8}  =  \frac{20}{8}, which is the same as 2482\frac{4}{8}. 16+248=184816 + 2\frac {4}{8} = 18\frac {4}{8}