1. Continue with Ratio and Proportion
UMI: July 13, 2015

2. Using Proportions to Solve Percent:
A percent is actually a ratio! Saying “45%" is actually saying “45 per 100“:
45%=
We can use proportions to solve questions involving percent.

3. First, put what we know into this form:
𝑷𝒂𝒓𝒕 𝒘𝒉𝒐𝒍𝒆 = 𝑷𝒆𝒓𝒄𝒆𝒏𝒕 𝟏𝟎𝟎

4. Find the Part: Example: what is 45% of 160 ?
Solve: The percent is 45, the whole is 160, and we want to find the "part":
𝑷𝒂𝒓𝒕 𝟏𝟔𝟎 = 𝟒𝟓 𝟏𝟎𝟎
𝑷𝒂𝒓𝒕×𝟏𝟎𝟎=𝟏𝟔𝟎×𝟒𝟓
𝑷𝒂𝒓𝒕=𝟏𝟔𝟎× 𝟒𝟓 𝟏𝟎𝟎 =𝟕𝟐
Answer: 45% of 160 is 72.

5. Example: what is $14 as a percent of $80 ?
Find a Percent:
Example: what is $14 as a percent of $80 ?
Solve: Fill in what we know:
$𝟏𝟒 $𝟖𝟎 = 𝒑𝒆𝒓𝒄𝒆𝒏𝒕 𝟏𝟎𝟎
𝒑𝒆𝒓𝒄𝒆𝒏𝒕×$𝟖𝟎=𝟏𝟎𝟎×$𝟏𝟒
𝒑𝒆𝒓𝒄𝒆𝒏𝒕=𝟏𝟎𝟎× $𝟏𝟒 $𝟖𝟎 =𝟏𝟕.𝟓
Answer: $14 is 17.5% of $80.

6. Find the Whole:
Example: The sale price of a phone was $130, which was only 80% of normal price. What was the normal price?
Solve: Fill in what we know:
$𝟏𝟑𝟎 𝒘𝒉𝒐𝒍𝒆 = 𝟖𝟎 𝟏𝟎𝟎
𝒘𝒉𝒐𝒍𝒆×𝟖𝟎=𝟏𝟎𝟎×$𝟏𝟑𝟎
𝒘𝒉𝒐𝒍𝒆=$𝟏𝟑𝟎× 𝟏𝟎𝟎 𝟖𝟎 =𝟏𝟔𝟐.𝟓
Answer: the phone's normal price was $

7. Practice: Tim is buying a DVD player from Deal of the Day.
The usual cost of the player is $180.
Today's discount is 20%.
How much money will Tim will save?

8. Practice:
Melissa just got a new mp3 player. Eighteen of Melissa’s forty-five songs are pop.
What percentage is that?

9. Practice:
Dani bought a CD on sale for 75% off the regular price. She paid $3.50.
What was the regular price?

10. Practice:
Given that 3 moles of a substance has a mass of 80 grams, what is the mass of 6 moles of the same substance?( a mole is the quantity of anything that has the same number of particles found in 12,000 grams of carbon-12.)

11. Review Fraction:
𝟑 𝟒 + 𝟏 𝟐 − 𝟏 𝟑
𝟏 𝟐 + 𝟐 𝟑 × 𝟏 𝟒
𝟏 𝟐 + 𝟐 𝟑 ÷ 𝟑 𝟒

12. Thank You References: A problem solving approach to mathematics
for elementary school teachers by Billstein,
Libeskind, Lott
Math Playground:
Math is Fun :