Question

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a. name the fraction that corresponds to point a.b. name the fraction that corresponds to point b.5. a. determine the fractions that correspond to points a, b, and c on the number line.b. explain how you knew what fractions to write in the boxes.6. fill in the boxes with the fractions that correspond to points a and b.

Explanation:

Step1: Analyze first number line

The line from 0 to 1 is split into 2 equal parts. Point A is at the 1st part: $\frac{1}{2}$
Point B is at the end, so it is $1$

Step2: Analyze second number line

The line from 0 to 1 is split into 4 equal parts.
Point A is at the 1st part: $\frac{1}{4}$
Point B is at the 2nd part: $\frac{2}{4}=\frac{1}{2}$
Point C is at the 3rd part: $\frac{3}{4}$

Step3: Explain fraction selection

Count equal segments from 0 to the point. The denominator is total segments between 0 and 1, numerator is the number of segments to the point.

Step4: Analyze third number line

Each segment between marked points is $\frac{1}{3}$ (since $\frac{4}{3}-\frac{3}{3}=1-\frac{2}{3}=\frac{1}{3}$).
Point A is 1 segment from 0: $\frac{1}{3}$
Point B is 2 segments from 0: $\frac{2}{3}$

Answer:

1. Point A: $\frac{1}{2}$, Point B: $1$
2. a. Point A: $\frac{1}{4}$, Point B: $\frac{1}{2}$, Point C: $\frac{3}{4}$

b. Count the number of equal segments from 0 to each point; the denominator is the total number of equal parts between 0 and 1, and the numerator is the number of parts to the point.

1. Point A: $\frac{1}{3}$, Point B: $\frac{2}{3}$