Question

1. Explain how you would model 5 x 2/32. When you multiply 2/3 by a fraction less than one, how does the product compare to the factors? Explain.3. There is 5/6 of an apple pie left from dinner. Tomorrow, Victor plans to eat 1/6 of the pie that was left. How much of the whole pie will he eat tomorrow?A. 1/36B. 5/36C. 1/3D. 2/34. Matt made the model below to help him solve his math problem. Which of the expressions could he have been working out? (Yes, I made the model which emojis.) Blue Heart: Green SquareYellow Heart: Yellow Square Broken Heart: Blank Squareexplain how you can model 5 x 2/3A. 3/12 x 3/4B. 3/4 x 3C. 3/12 x 3/12D. 1/3 x 3/45. If an angle measures 100 degrees, through what fraction of a circle does the angle turn?A. 1/100B. 1/4C. 100/360D. 1/2

Answer 1

We need find the value of "5 times 2/3" using model.

2/3 can be represented by a rectangle in which 2 out of 3 parts are colored.

When we find 5 times 2/3, then the total colored parts are 10

5 times 2/3 is the same that Add 2/3 five times, that is:

5 x 2/3 = 2/3 + 2/3 + 2/3 + 2/3 + 2/3

take into account that the sum of fractions with the same denominators is equal to the sum of the numerators, over the common denominator, as follow:

2/3 + 2/3 + 2/3 + 2/3 + 2/3 = 10/3

The model is shown below:

You can notice that each rectangle has 2 blue parts of the total three parts, that is, 2/3. And due to there are other five rectangles with 2/3 of blue parts, then, you have 5 times 2/3, or 5 x 2/3 = 10/3.