## Distance between fence posts?

Say we’re building a fence and we’re given a whole lot of fence posts. We’re told to go put them in at equal distances. There is an easy way with algebra.

###### Ordered steps.

4. Algebra – One Step division equations from Khan Academy

3. Algebra – Same thing to both sides rule

2. Basic math.

1. English.

Using real numbers, lets say we’ve got 4 fence posts and 15 metres to put them in at equal spacing. There is a post at either end and 2 in the middle. Therefore there are 3 spaces.

How big are the spaces?

3 spaces = 15 metres

We can also write this as

3x = 15

where the x represents the spaces.

This video from Kahn Academy shows how to solve this.

## How many posts do we need?

Method.

5. Algebra – Multiplication equations from Khan Academy

4. Algebra – One Step division equations from Khan Academy

3. Algebra – Same thing to both sides

2. Basic math.

1. English.

##### Example 1

Say there is 40 metres and we want 1m between each post.

Intuitively we know there will be 40 spaces between 4o posts and if you want a post at the beginning as well then add 1 making 41 posts.

How do we show this mathematically?

40metres / number_of_posts = 1m distance_between_posts

Also written as:

40m/n = 1m

Simplified as:

40/n = 1

To get the n by itself do the same thing to both sides.

n * 40/n = n* 1

The n’s on the left cancel and

n * 1

can also be written as

1n

We are left with

40 = 1n

Again do the same thing to both sides and divide both sides by 1 to get the n by itself:

40/1 = 1n/1

The 1’s cancel on the right.

40 = n

Therefore the number of posts we need is 40 and if you want a post at the beginning as well then add 1 making 41 posts. (We could add the extra post mathematically, but let’s keep it straight forward.)

##### Example 2

Say there is 40 metres and we want 1.6m between each post.

This is not so quick to do in our heads.

To do this mathematically, we use the same system as in example 1.

40metres / number_of_posts = 1.6m distance_between_posts

Also written as:

40m/n = 1.6m

Simplified as:

40/n = 1.6

To get the n by itself do the same thing to both sides. This time it’s a 2 step process.

n * 40/n = n* 1.6

The n’s on the left cancel and

n * 1.6

can also be written as

1.6n

We are left with

40 = 1.6n

Again do the same thing to both sides and divide both sides by 1.6 to get the n by itself:

40/1.6 = 1.6n/1.6

The 1.6’s cancel on the right.

40/1.6 = n

25 = n

Therefore the number of posts we need is 25 and if you want a post at the beginning as well then add 1 making 26 posts. (We could add the extra post mathematically, but let’s keep it straight forward.)

Metatags: Laying out framed walls, Stud wall, stud wall uprights, carpentry, framing, brick work.