Question

use a number line to illustrate each of the following:(a) $\boldsymbol{\frac{-1}{3}}$, 2.5, $\boldsymbol{1\frac{3}{8}}$, 1, -0.2, 0.11(b) positive odd integers less than 20(c) negative even integers more than or equal to -10(d) prime numbers more than or equal to 2 but less than 10

Explanation:

Part (a)

First convert all values to decimals for easier number line placement:

• $-\frac{1}{3} \approx -0.33$, $1\frac{3}{8}=1.375$, $2.5$, $1$, $-0.2$, $0.11$

Order from left to right on the number line: $-0.33 < -0.2 < 0.11 < 1 < 1.375 < 2.5$. Mark each point at its corresponding decimal position.

Part (b)

Positive odd integers are whole numbers greater than 0 that are not divisible by 2. List all that are less than 20: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19. Mark each integer on the positive side of the number line.

Part (c)

Negative even integers are whole numbers less than 0 that are divisible by 2. List all that are $\geq -10$: $-10, -8, -6, -4, -2$. Mark each integer on the negative side of the number line.

Part (d)

Prime numbers are numbers greater than 1 with no positive divisors other than 1 and themselves. List all that are $\geq2$ and $<10$: 2, 3, 5, 7. Mark each number on the positive side of the number line.

Answer:

(a)

Number line order (left to right): $-\frac{1}{3} \approx -0.33$, $-0.2$, $0.11$, $1$, $1\frac{3}{8}=1.375$, $2.5$

(b)

Positive odd integers less than 20: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19

(c)

Negative even integers $\geq -10$: $-10$, $-8$, $-6$, $-4$, $-2$

(d)

Prime numbers $\geq2$ and $<10$: 2, 3, 5, 7