Section C Section C Checkpoint

Problem 1

For each diagram, write an expression for the area of the shaded region. Then find the area.

  1.  
    Area diagram. Length, 5. Width, 1 third. 

  2.  
    Area diagram. Length, 3. Width, 2 fourths. 

  3.  
    Area diagram, Length, 4. Width, 1 and 2 thirds.

Show Solution
Solution

  1. Expression: 13×5\frac{1}{3} \times 5 or 5×135 \times \frac{1}{3} (or equivalent). Area: 53\frac{5}{3} square units

  2. Expression: 24×3\frac{2}{4} \times 3 or 12×3\frac{1}{2} \times 3 (or equivalent). Area: 64\frac{6}{4} square units

  3. Expression: 53×4\frac{5}{3} \times 4 (or equivalent). Area: 13\frac{1}{3} square units

Show Sample Response
Sample Response

  1. Expression: 13×5\frac{1}{3} \times 5 or 5×135 \times \frac{1}{3} (or equivalent). Area: 53\frac{5}{3} square units

  2. Expression: 24×3\frac{2}{4} \times 3 or 12×3\frac{1}{2} \times 3 (or equivalent). Area: 64\frac{6}{4} square units

  3. Expression: 53×4\frac{5}{3} \times 4 (or equivalent). Area: 13\frac{1}{3} square units

Problem 2

Clare made a flag that is 2 meters long and 35\frac{3}{5} meter wide. What is the area of the flag? Explain or show your reasoning.

Show Solution
Solution
65\frac{6}{5} m. Sample response:  2×35=652 \times \frac{3}{5} = \frac{6}{5}
Show Sample Response
Sample Response
65\frac{6}{5} m. Sample response:  2×35=652 \times \frac{3}{5} = \frac{6}{5}

Problem 3

Find the value of each expression.

  1. 15×10\frac{1}{5} \times 10

  2. 523×45\frac{2}{3} \times 4

  3. 134×5\frac{13}{4} \times 5

Show Solution
Solution
  1. 105\frac{10}{5} or 2 (or equivalent)
  2. 208320 \frac{8}{3} or 683\frac{68}{3} (or equivalent)
  3. 654\frac{65}{4} (or equivalent)
Show Sample Response
Sample Response
  1. 105\frac{10}{5} or 2 (or equivalent)
  2. 208320 \frac{8}{3} or 683\frac{68}{3} (or equivalent)
  3. 654\frac{65}{4} (or equivalent)