Sure, let's solve each part step-by-step:
### Part (i): Halfway between -4 and 11.
1. Identify the numbers:
- The two numbers are [tex]\(-4\)[/tex] and [tex]\(11\)[/tex].
2. Find the midpoint formula:
- The midpoint between two numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex] on a number line is given by:
[tex]\[
\text{Midpoint} = \frac{a + b}{2}
\][/tex]
3. Apply the midpoint formula:
- Substitute [tex]\(-4\)[/tex] for [tex]\(a\)[/tex] and [tex]\(11\)[/tex] for [tex]\(b\)[/tex]:
[tex]\[
\text{Midpoint} = \frac{-4 + 11}{2}
\][/tex]
4. Calculate the result:
- Simplify the expression:
[tex]\[
\text{Midpoint} = \frac{7}{2} = 3.5
\][/tex]
So, the number halfway between [tex]\(-4\)[/tex] and [tex]\(11\)[/tex] is [tex]\(3.5\)[/tex].
### Part (ii): Halfway between [tex]\(m\)[/tex] and [tex]\(n\)[/tex].
1. Identify the numbers:
- The two variables are [tex]\(m\)[/tex] and [tex]\(n\)[/tex].
2. Find the midpoint formula:
- The midpoint between two numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex] on a number line is given by:
[tex]\[
\text{Midpoint} = \frac{a + b}{2}
\][/tex]
3. Apply the midpoint formula:
- Substitute [tex]\(m\)[/tex] for [tex]\(a\)[/tex] and [tex]\(n\)[/tex] for [tex]\(b\)[/tex]:
[tex]\[
\text{Midpoint} = \frac{m + n}{2}
\][/tex]
4. Express the result:
- Simplify the expression if necessary:
[tex]\[
\text{Midpoint} = \frac{m}{2} + \frac{n}{2}
\][/tex]
So, the number halfway between [tex]\(m\)[/tex] and [tex]\(n\)[/tex] is [tex]\(\frac{m}{2} + \frac{n}{2}\)[/tex].
Therefore:
- The number halfway between [tex]\(-4\)[/tex] and [tex]\(11\)[/tex] is [tex]\(3.5\)[/tex].
- The number halfway between [tex]\(m\)[/tex] and [tex]\(n\)[/tex] is [tex]\(\frac{m}{2} + \frac{n}{2}\)[/tex].
