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May 2013

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(easy hangman)
(difficult)

The ideas in this lesson are taken from Math Mammoth Percent book.

What Percentage...? / How many percent...?

The concepts and ideas of this lesson are also explained in this video:

What percentage
of the height of
a 15-ft tree is
a 3-ft sapling?

A choir has 22 women and 18
men. Find what percentage
of the choir’s members are
men.

One pair of jeans costs $25 and another
costs $28. How many percent is the
price of cheaper jeans of the price of
the more expensive jeans?

Look carefully at the questions above. Notice that the problems don’t tell you the percentage; in other words, there is no number in the problem written as x%. Instead, they ask you to find it!

Questions with “What percentage ... ?” or "How many percent ... ?"

Asking “What percentage?” or "How many percent?" is the same as asking “How many hundredth parts?”

We can solve these questions in a two-part process:

1. First find out the part that is being asked for as a fraction.
The denominator probably won’t be 100.

2. Convert that fraction to a decimal. Then you can easily convert
the decimal to a percentage!

Example 1. A choir has 22 women and 18 men. Find what percentage of the choir’s members are men.

1. Find out what part (fraction) of the choir’s members are men.
That is 18/40, or 9/20.

2. Write 9/20 as a percent. Use equivalent fractions:
9/20 = 45/100 = 45%.

Example 2. One pair of jeans costs $25 and the other costs $28.
How many percent is the price of cheaper jeans of the price of the more expensive jeans?

1. Write what part the cheaper price is of the more expensive price.
The answer is 25/28.

2. Write 25/28 as a percentage. A calculator gives 25/28 = 0.8928...
Rounded to the nearest whole percent, that’s 89%.

1. a. What percentage of a 15-ft tree is a little 3-ft sapling?

b. How many percent is $12 of $16?

2. Find how many percent the smaller object’s height is of the taller object’s height.

6 m

8 m

300 cm

120 cm

c. [available in the book]

3. A 2-year old child measures 32 inches tall and weighs 24 pounds.
A 10-year old child measures 52 inches tall and weighs 96 pounds.

a. How many percent is the smaller child’s
age of the older child’s age?

b. How many percent is the smaller child’s
height of the older child’s height?

c. [available in the book]

4. Write the percentages into the sectors in the circle graphs. Think of fractions!

b. [available in the book

c. [available in the book]

5. The circle graph at the right gives the angle measure
    of each sector of the circle. Find what percentage each
    sector is of the whole circle, and write the percentage
    in the sector. Remember, the whole circle is 360°.

6. [available in the book]

Draw a circle graph to represent
the situation in exercise #6.

The ideas in this lesson are taken from Math Mammoth Percent book.