Section A Section A Checkpoint

Problem 1

Clare makes glitter glue by mixing 78\frac78 pound of glitter with 13\frac13 gallon of glue. At this rate,

  1. How much glitter would she mix with 1 gallon of glue?
  2. How much glue would she mix with 3 pounds of glitter?
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Solution
  1. 218\frac{21}{8} pounds (or equivalent)
  2. 87\frac87 gallons (or equivalent)
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Sample Response
  1. 218\frac{21}{8} pounds (or equivalent)
  2. 87\frac87 gallons (or equivalent)

Problem 2

Farm A harvested xx bales of cotton. Farm B harvested 35\frac35 more than that.

Select all the expressions that represent how much cotton Farm B harvested.

A
35x\frac35 x
B
85x\frac85 x
C
1+351 + \frac35
D
x+35xx + \frac35 x
E
0.6x0.6x
F
1.35x1.35x
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Solution
B, D
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Sample Response
B, D

Problem 3

What is the decimal representation of 512\frac{5}{12}? Show your reasoning.
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Solution
0.416‾0.41\overline{6}, because

\requireenclose0.4166 12\encloselongdiv5.1000−0‾.100050.100−48‾.10020.00−12‾.0080.0−72‾.080.−72‾.8.\displaystyle \require{enclose} \begin{array}{rll} 0.4166 \\[-3pt] 12 \enclose{longdiv}{5\phantom{.1000}} \\[-3pt] \underline{-0}\phantom{.1000} \\[-3pt] 50\phantom{.100} \\[-3pt] \underline{-48}\phantom{.100} \\[-3pt] 20\phantom{.00} \\[-3pt] \underline{-12}\phantom{.00} \\[-3pt] 80\phantom{.0}\\[-3pt] \underline{-72}\phantom{.0} \\[-3pt] 80\phantom{.}\\[-3pt] \underline{-72}\phantom{.}\\[-3pt] 8\phantom{.} \end{array}

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Sample Response
0.416‾0.41\overline{6}, because

\requireenclose0.4166 12\encloselongdiv5.1000−0‾.100050.100−48‾.10020.00−12‾.0080.0−72‾.080.−72‾.8.\displaystyle \require{enclose} \begin{array}{rll} 0.4166 \\[-3pt] 12 \enclose{longdiv}{5\phantom{.1000}} \\[-3pt] \underline{-0}\phantom{.1000} \\[-3pt] 50\phantom{.100} \\[-3pt] \underline{-48}\phantom{.100} \\[-3pt] 20\phantom{.00} \\[-3pt] \underline{-12}\phantom{.00} \\[-3pt] 80\phantom{.0}\\[-3pt] \underline{-72}\phantom{.0} \\[-3pt] 80\phantom{.}\\[-3pt] \underline{-72}\phantom{.}\\[-3pt] 8\phantom{.} \end{array}