Question

fractions as quotients and fraction multiplication
kingston s.
section a: practice problems

1. pre - unit

a. locate $\frac{6}{4}$ on the number line.
0 1 2
b. explain or show why your point represents $\frac{6}{4}$.

1. pre - unit

shade $\frac{3}{4}$ of the rectangle. explain or show your reasoning.

1. pre - unit

explain or show why $\frac{4}{3}=4\times\frac{1}{3}$.

Explanation:

1. a.

Step1: Convert fraction to mixed - number

$\frac{6}{4}=\frac{4 + 2}{4}=1\frac{2}{4}=1\frac{1}{2}$. On the number line, divide the segment between 1 and 2 into 2 equal parts. The mid - point between 1 and 2 represents $1\frac{1}{2}$ or $\frac{6}{4}$.

Step1: Recall fraction meaning

The fraction $\frac{6}{4}$ means 6 parts of size $\frac{1}{4}$. From 0 to 1, there are 4 parts of size $\frac{1}{4}$. Then, we need 2 more parts of size $\frac{1}{4}$ to reach $\frac{6}{4}$. So the point that is halfway between 1 and 2 (since 2 more out of 4 equal parts from 1) represents $\frac{6}{4}$.

Step1: Divide rectangle into parts

Divide the rectangle into 4 equal parts (either vertically or horizontally). Shade 3 out of the 4 equal parts. Since each part represents $\frac{1}{4}$ of the rectangle, 3 parts represent $\frac{3}{4}$ of the rectangle.

Answer:

Locate the point at the mid - point between 1 and 2 on the number line.

1. b.