Exercise: 4-G
Q1: Represent \(\frac{2}{3}\) on the number line
Step 1: Identify the fraction \(\frac{2}{3}\). The denominator 3 means the whole number 1 is divided into 3 equal parts.
Step 2: Since numerator is 2, count 2 parts from 0 towards 1 on the number line.
Step 3: Mark the point at \(\frac{2}{3}\).
Answer: \(\frac{2}{3}\) is located two-thirds of the way from 0 to 1 on the number line.
Number line representation: |--------|---------Φ---------|------ 0 1/3 2/3 1
Q2: Represent \(-\frac{5}{7}\) on the number line
Step 1: Identify the fraction \(-\frac{5}{7}\). The denominator 7 means the whole number 1 is divided into 7 equal parts.
Step 2: Since numerator is 5, count 5 parts from 0 towards -1 on the number line because the fraction is negative.
Step 3: Mark the point at \(-\frac{5}{7}\).
Answer: \(-\frac{5}{7}\) is located five-sevenths of the way from 0 to -1 on the number line, to the left of zero.
Number line representation: |----|----Φ----|----|----|----|----|----|----- -1 -6/7 -5/7 -4/7 -3/7 -2/7 -1/7 0 1/7
Q3: Represent \(\frac{1}{6}\) on the number line
Step 1: Identify the fraction \(\frac{1}{6}\). The denominator 6 means the whole number 1 is divided into 6 equal parts.
Step 2: Since numerator is 1, count 1 part from 0 towards 1 on the number line.vStep 3: Mark the point at \(\frac{1}{6}\).
Answer: \(\frac{1}{6}\) is located one-sixth of the way from 0 to 1 on the number line, to the right of zero.
Number line representation: |----Φ----|----|----|----|----|----- 0 1/6 2/6 3/6 4/6 5/6 1
Q4: Represent \(-\frac{3}{8}\) on the number line
Step 1: Identify the fraction \(-\frac{3}{8}\). The denominator 8 means the whole number 1 is divided into 8 equal parts.
Step 2: Since the numerator is 3 and the sign is negative, count 3 parts from 0 towards -1 on the number line (to the left of zero).
Step 3: Mark the point at \(-\frac{3}{8}\).
Answer: \(-\frac{3}{8}\) is located three-eighths of the way from 0 to -1 on the number line, to the left of zero.
Number line representation: |----|----|----|----|----Φ----|----|----|----- -1 -7/8 -6/8 -5/8 -4/8 -3/8 -2/8 -1/8 0
Q5: Represent \(\frac{22}{7}\) on the number line
Step 1: Convert the improper fraction \(\frac{22}{7}\) into a mixed number.\[
\frac{22}{7} = 3 \frac{1}{7}
\]Step 2: The denominator 7 means 1 is divided into 7 equal parts. So each whole number interval is divided into 7 parts.
Step 3: Since \(\frac{22}{7} = 3 \frac{1}{7}\), move 3 whole units to the right of 0, then 1 part out of 7 more units.
Step 4: Mark the point at \(3 \frac{1}{7}\) on the number line.
Answer: \(\frac{22}{7}\) lies a little beyond 3 on the number line, exactly 1/7th of the distance between 3 and 4.
Number line representation:
------|------Φ------|------|------|------|------|------|------|------
3 3 1/7 3 2/7 3 2/7 3 3/7 3 4/7 3 5/7 3 6/7 4
Q6: Represent \(\frac{23}{-5}\) on the number line
Step 1: Convert the improper fraction \(\frac{23}{-5}\) into a mixed number.
\[
-\frac{23}{5} = -4 \frac{3}{5}
\]Step 3: Since it’s negative, we move to the left of 0.
Break the interval between -5 and -4 into 5 equal parts and count 3 parts from -5 towards -4.
Step 4: Mark the point at \(-4 \frac{3}{5}\) on the number line.
Answer: \(\frac{23}{-5} = -4\frac{3}{5}\) lies between -5 and -4 on the number line.
Number line representation:
------|--------|--------Φ--------|--------|--------|------
-5 -4 4/5 -4 3/5 -4 2/5 -4 1/5 -4
Q7: Represent \(-\frac{3}{4}\) on the number line
Step 1: The rational number is already in its simplest form:
\[
-\frac{3}{4}
\]Step 2: Since it is negative, it lies to the left of 0.
To represent \(-\frac{3}{4}\), divide the interval between 0 and -1 into 4 equal parts.
Step 3: Move 3 parts from 0 towards -1 and mark the point.
Answer: \(-\frac{3}{4}\) lies between -1 and 0 on the number line, 3 parts from 0 towards -1.
Number line representation:
----|--------Φ--------|--------|--------|------
-1 -3/4 -2/4 -1/4 0
Q8: Represent \(\frac{-12}{5}\) on the number line
Step 1: Convert to mixed fraction:
\[
\frac{-12}{5} = -2\frac{2}{5}
\]Step 2: Since the number is negative, it lies to the left of 0.
Step 3: We will mark the number line from -3 to 0.
Divide each unit into 5 equal parts to represent fifths.
Step 4: Move to -2 and then 2 parts more to the left to get \(-2\frac{2}{5}\).
Answer: \(\frac{-12}{5}\) lies between -3 and -2 on the number line, 2 parts right from -3 or 2 parts left from -2.
Number line representation:
----|--------|--------|--------Φ--------|--------|---
-3 -2 4/5 -2 3/5 -2 2/5 -2 1/5 2
Q9: Represent \(\frac{13}{6}\) on the number line
Step 1: Convert to mixed fraction:
\[
\frac{13}{6} = 2\frac{1}{6}
\]Step 2: Since the number is positive, it lies to the right of 0.
It lies between 2 and 3 on the number line.
Step 3: Divide each unit into 6 equal parts to represent sixths.
Move to 2 and then 1 part more to the right to reach \(2\frac{1}{6}\).
Answer: \(\frac{13}{6}\) lies between 2 and 3 on the number line, 1 part right from 2 when each unit is divided into sixths.
Number line representation:
----|--------Φ--------|--------|--------|--------|--------|-----
2 2 1/6 2 2/6 2 3/6 2 4/6 2 5/6 3
