Continue with Ratio and Proportion UMI: July 13, 2015

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

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

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.

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.

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 $162.50.

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?

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

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

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.)

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

Thank You References: A problem solving approach to mathematics for elementary school teachers by Billstein, Libeskind, Lott Math Playground: http://www.mathplayground.com/ Math is Fun : https://www.mathsisfun.com/index.htm