Question

6.2c micro - assessment
locating, comparing, and ordering integers and rational numbers
using a number line
1 tyrone placed the following points on a number line.

• point v at $-\frac{15}{2}$
• point w at $-\frac{16}{8}$
• point x at $\frac{3}{2}$
• point z at $\frac{20}{4}$

(there is a number line diagram with points v, w, x, z marked. the number line has marks from -8 to 8.)
which point is not correctly placed on this number line?
a point v b point w c point x d point z

2 shana will correctly label the numbers 35.73, $35\frac{1}{4}$, $35\frac{4}{5}$, and 35.08 on the
number line below.
(there is a number line diagram with 35 on the left and 36 on the right, with several unmarked intervals in between.)
which number will be located closest to 36?
f 35.73 g $35\frac{1}{4}$ h $35\frac{4}{5}$ j 35.08

3 which point on the number line represents $42\frac{2}{3}$?
select one location on the number line to plot the point.
(there is a number line diagram with 42 on the left and 43 on the right, with several unmarked intervals in between, each with a circle for plotting.)

Explanation:

Step1: Simplify each rational number (Q1)

• Point V: $-\frac{15}{2} = -7.5$
• Point W: $-\frac{16}{8} = -2$
• Point X: $\frac{3}{2} = 1.5$
• Point Z: $\frac{20}{4} = 5$

Step2: Match to number line (Q1)

• V is marked at -6 (≠ -7.5, incorrect); W at -2 (correct); X at 1.5 (correct); Z at 5 (correct).

Step3: Convert fractions to decimals (Q2)

• $35\frac{1}{4} = 35.25$, $35\frac{4}{5} = 35.8$

Step4: Calculate distance to 36 (Q2)

• $36 - 35.73 = 0.27$; $36 - 35.25 = 0.75$; $36 - 35.8 = 0.2$; $36 - 35.08 = 0.92$

Step5: Identify interval for $42\frac{2}{3}$ (Q3)

• The segment 42 to 43 is split into 8 equal parts, each part = $\frac{1}{8}=0.125$. $42\frac{2}{3} \approx 42.667$.
• $0.667 \div 0.125 \approx 5.34$, so it is the 6th mark from 42.

Answer:

1. A Point V
2. H $35\frac{4}{5}$
3. Plot the point on the 6th open circle to the right of 42 (counting from the first circle after 42 as 1)