Step by step
The question
Question: find the height of a parallelogram with area 7.5 square units and base 2.5.
1 Use the rule
The height goes straight up from the base.
It makes a right angle with the base.
We know the area, so we start from the area rule.
Remember: move the end triangle and it is a rectangle.
So the area is base times height: A = b × h.
Now put the numbers in: A = 7.5 and b = 2.5.
2.5 times h is written 2.5h.
Let's swap the two sides, so h is on the left.
2 Remove the decimals
Decimals are hard to work with.
Let's get rid of them.
We multiply every part by 10.
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.
Times 10 moves the point 1 place to the right.
10 × 2.5h = 25h.
10 × 7.5 = 75.
Write the answers.
No more decimals!
3 Remove the 25
25h means 25 times h.
We want just h.
To remove times 25, we divide by 25.
We do it on both sides, so they stay equal.
25 divided by 25 is 1.
So just h is left.
75 divided by 25 is 3.
So h = 3!
4 Check
Let's check: put h = 3 back in the area rule.
We get 7.5, the area in the question.
So the height is 3.
Let's look back.
First: use the rule.
Then: remove the decimals.
Then: remove the 25.
Last: check.