Step by step
The question
Question: find the width w of a rectangle with perimeter 30 and length 9.
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 30 and the length is 9.
So 9 + w + 9 + w = 30.
Careful!
The length is there twice, and the width is there twice too.
3 Group like terms
The plain numbers go together: 9 plus 9 is 18.
The w's go together: two of them, 2 times w.
Now we have 18 + 2 × w = 30.
4 Remove the 18
We want 2 × w by itself.
The 18 is in the way.
To remove 18, we take away 18.
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.
18 and − 18 make zero.
Cross them out.
30 minus 18 is 12.
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 w is left.
12 divided by 2 is 6.
So the width is 6.
6 Check
Let's check: walk around and add.
We get 30, the perimeter.
So the width is right!
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: group like terms.
Then: remove the 18.
Then: remove the × 2.
Last: check.