Question

Draw rectangular fraction models of 3 x 1/4 and 1/3 x 1/4. Compare multiplying a number by 3 and by 1 third.

Answer 1

Answer:

In the file are the rectangular fraction models.

In the second draw, you can observe that the result of multiply $\frac{1}{3}\times\frac{1}{4}$ is obtained the following form:

1. Draw a rectangle and divide it into four pieces.

2. Then create the fraction by coloring one column of pink.

3. We split the rectangle in thirds by drawing horizontal lines that divide the rectangle into three equal rows.

4. Then we color one row with green to show one third of one quarter

5.  So the answer (product) is the area of the rectangle where both of the shadings overlap each other. The denominator corresponds to the total of squares and the numerator of the product is the number of small rectangles where the shadings overlap.

When we multiply a number by 3 the result is a number greater that the number that we multiply, but when we multiply by $\frac{1}{3}$ the result is a number smaller that the number that we multiply.