Word Problems/Percentages



I have seen the following quotation in a textbook regarding changing decimals or numbers to percentages.

"Multiply the number by 1, expressed as 100/100, to change the number to a fraction with the denominator 100."

Why do you think the author(s) used the number "1" in the quoted sentence?  What purpose does the "1" serve?

I know that any fraction with the same number as the numerator and denominator is equivalent to 1, but I do not quite understand
indicating to multiply by "1".

I thank you for your reply.

ANSWER: To change a number to a percentage, realize the numbers are in units.
We then multiply by 100%/(1 unit).

For example, if we had .53, which is really .53 units, we would take
(.53 units)(100%/1 unit) = 53% (since the units cancel).

This can be applied to 1/2 to get 50%, 1/5 to get 20%, .46 to get 46%, 1.23 to get 123%, etc.

---------- FOLLOW-UP ----------


I want to thank you for the reply.

In your reply, your are dividing by 1 or 1 unit and not multiplying by 1. I do not understand how your reply answers my question.

I thank you for your follow-up reply.

I'm not sure I understand the way the author is trying to explain percentages.
Rather than trying to explain the way he is talking about,
I'll explain what percentage are in a more understandable fashion.

The number 1 is the same as 100%.  In this way, 1% = 0.01, 2% = 0.02, 3% = 0.03, 4% = 0.04,
15% = 0.15, 74% = 0.74, 123% = 1.23, 240% = 2.4, etc.

Percentages are a form of measure.  They are like ounces in a pound or inches in a foot.
There are 16 ounces in a pound and 12 inches in a foot, just like there are 100% in 1.

For example, in weight, 1 lb = 16 oz.
If something was 2 lb., we would multiply by 16 oz. / 1 lb.
Since 2 x 16 = 32, lb./lb. cancel, and we are left with oz., the answer is 32 oz.

There are 12 in. / 1 ft.  If something is 6 ft. tall, then we can take
6 ft. x 12 in. / 1 ft. and get 72.  Note that ft./ft. cancel, and all we are left with is in.
That makes it 72 in. tall.

This can be carried through to percentages.
100% is the same as 1 unit of what is being talked about.
This makes 50% of that be 0.5 units of what is at hand.

Suppose a pool could hold 100,000 gallons.
If we only put in 50,000 gallons, that would be 1/2 full.
In percetages, it could be said to be 50% full since 100*(1/2) = 50.
If the pool has 75,000 gallonsin it, it would be 75% full.
This is because 75,000/100,000 = .75, which is the same as 75%.

If a tree that was being climbed was 50 feet tall, then someone climbing it who was 25 feet up would be said to be 50% of the way to the top since 25 feet is half of 50 feet.
If they were 40 feet up, it is known that 40/50 = 0.8, so that is 80% of the way up.

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Scott A Wilson


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