Section B Section B Checkpoint

Problem 1

An artist is making a paste for a sculpture. She uses 85\frac{8}{5} kilograms of flour to make 23\frac{2}{3} of a batch. How much flour is needed to make a full batch?

  1. Draw a diagram and label it to represent the situation.
  2. Find the answer and show your reasoning.
Show Solution
Solution
  1. Sample response:

  2. 125\frac{12}{5} or 2252\frac{2}{5} kilograms. Sample reasoning: If there are 85\frac{8}{5} kilograms in 23\frac{2}{3} of a batch, then there is 45\frac{4}{5} kilogram in 13\frac{1}{3} of a batch and 125\frac{12}{5} kilograms in 1 whole batch.
Show Sample Response
Sample Response
  1. Sample response:

  2. 125\frac{12}{5} or 2252\frac{2}{5} kilograms. Sample reasoning: If there are 85\frac{8}{5} kilograms in 23\frac{2}{3} of a batch, then there is 45\frac{4}{5} kilogram in 13\frac{1}{3} of a batch and 125\frac{12}{5} kilograms in 1 whole batch.

Problem 2

For each experiment, a scientist needs 310\frac{3}{10} liter of a liquid. If the scientist has 4124 \frac{1}{2} liters of the liquid, how many experiments can be done?

  1. Write a multiplication equation and a division equation to represent the question. Use a “?” for the unknown value.
  2. Explain or show that the answer is 15 experiments.
Show Solution
Solution
  1. ?⋅310=412{?} \boldcdot \frac{3}{10} = 4\frac{1}{2} and 412÷310=?4\frac{1}{2} \div \frac{3}{10} = {?}
  2. Sample response: 
    • 15⋅310=451015 \boldcdot \frac{3}{10} = \frac{45}{10}, which is 4124\frac{1}{2}.
    • Ten experiments can be done with 3 liters (10⋅310=310 \boldcdot \frac{3}{10} = 3) and 5 more can be done with 1121\frac{1}{2} liters.
    • There are 45 tenths in 4124\frac{1}{2} and there are 15 groups of 3 tenths in 45 tenths.
Show Sample Response
Sample Response
  1. ?⋅310=412{?} \boldcdot \frac{3}{10} = 4\frac{1}{2} and 412÷310=?4\frac{1}{2} \div \frac{3}{10} = {?}
  2. Sample response: 
    • 15⋅310=451015 \boldcdot \frac{3}{10} = \frac{45}{10}, which is 4124\frac{1}{2}.
    • Ten experiments can be done with 3 liters (10⋅310=310 \boldcdot \frac{3}{10} = 3) and 5 more can be done with 1121\frac{1}{2} liters.
    • There are 45 tenths in 4124\frac{1}{2} and there are 15 groups of 3 tenths in 45 tenths.