Step by step
The question
Question: find the length l of a rectangle with perimeter 26 cm and width 4 cm.
1 Write the rule
The perimeter is the way all around the edge.
We add every side.
Walk around: length, width, length, width.
P = l + w + l + w.
2 Put the numbers in
The perimeter is 26 and the width is 4.
So l + 4 + l + 4 = 26.
Careful!
The width is there twice, and the length is there twice too.
3 Group like terms
The plain numbers go together: 4 plus 4 is 8.
The l's go together: two of them, 2 times l.
Now we have 8 + 2 × l = 26.
4 Remove the 8
We want 2 × l by itself.
The 8 is in the way.
To remove 8, we take away 8.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
8 and − 8 make zero.
Cross them out.
26 minus 8 is 18.
5 Remove the × 2
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just l is left.
18 divided by 2 is 9 cm.
So the length is 9 cm.
6 Check
Let's check: walk around and add.
We get 26, the perimeter.
So the length is right!
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: group like terms.
Then: remove the 8.
Then: remove the × 2.
Last: check.