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Percents
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 That a percent is a special ratio out of 100.
 How to solve problems using percents.
 That this knowledge can help us play basketball, plan a class lunch, and even plant a garden.

Discussion Questions

Before VideoWhat is a ratio?ANSWER

A ratio is a way of comparing two values.

A partpart ratio compares two parts that are both in the same whole. A partwhole ratio compares a part to the whole.

A partwhole ratio can be represented as a fraction. Partpart ratios must be converted to partwhole ratios before the information can be written as a fraction.

You use a partpart ratio when the relationship between the parts is the most relevant aspect of the comparison. For example, if you are baking, the ratio of flour to sugar is more relevant than the ratio of flour to batter. You can adjust the amount of sugar proportionally to the amount of flour to increase or decrease the size of the batch.
ANSWER
You use a partwhole ratio when the relationship between a part and the whole is the most relevant aspect of the comparison. For example, if you are reporting your score on a quiz, it is more relevant to compare the number of correct answers (part) to the total number of questions (whole), than it is to compare the number of correct answers (part) to the number of incorrect answers (part).


After VideoWhat is a percent?ANSWER

A percent is a special partwhole ratio where the whole is 100.

Percent means per 100, so 60 percent means 60 per 100. So 60% of 100 is 60.

I can answer this by reasoning about equivalent ratios. I know that 60% of 100 is 60. I also know that half of 100 is 50. To keep the ratios equivalent I need to multiply or divide both the numerator and denominator of my ratio by the same value. Since 50 is half of 100, and 30 is half of 60, 60% of 50 must be 30.

I know that 28% means I have 28 out of 100. This also means I have 28 hundredths. I write 28 hundredths as 0.28, so 0.28 is the decimal value of 28%.
ANSWER
First I need to set up an equation [ggfrac]20/n[/ggfrac]=[ggfrac]80/100[/ggfrac] and then use proportional reasoning. I know that 20×4=80, and to keep my ratios equivalent, I need to multiply the numerator and denominator by the same value. This means [i[]n[/i]×4=100, so since 25×4=100 there must be 25 logs in the whole pile.



Vocabulary

Ratio
DEFINE
A multiplicative comparison of two amounts.

Multiplicative
DEFINE
Related to or based on multiplication.

Partpart ratio
DEFINE
A ratio that compares the size of two parts from the same whole.

Partwhole ratio
DEFINE
A ratio that compares the size of one part to the size of the whole. Fractions are a form of partwhole ratio.

Numerator
DEFINE
In a partwhole ratio or in a fraction, the numerator represents the number of parts.

Denominator
DEFINE
In a partwhole ratio or in a fraction, the denominator represents the number of parts the whole is partitioned into.

Equivalent ratios
DEFINE
Ratios that are multiples of one another. Multiplying both the numerator and denominator of the ratio by the same value produces an equivalent ratio.

Percent
DEFINE
A partwhole ratio out of 100.

Ratio
DEFINE

Reading Material
Download as PDF Download PDF View as Separate PageWHAT ARE PERCENTS?Percents are special ratios where the whole is always 100. You use the % symbol to represent “percent.” 5 out of 100 or 5 : 100 is 5%.
To better understand percents…
WHAT ARE PERCENTS?. Percents are special ratios where the whole is always 100. You use the % symbol to represent “percent.” 5 out of 100 or 5 : 100 is 5%. To better understand percents…LET’S BREAK IT DOWN!
Playing Basketball
Amari and Emily are shooting hoops. Amari scored 72 out of 100 shots. Emily scored 80 out of 100 shots. How can you represent these as ratios and percents? A ratio is a relationship between two numbers. Ratios can be partpart or partwhole. Because we are looking at the number of scores (part) out of the number of shots (whole), we know that the ratio is partwhole. This is important because percents can only represent partwhole ratios. We can represent Amaris score as 72 :100 or [ggfrac]72/100[/ggfrac] or [ggfrac]72/100[/ggfrac] or 72%. We can also represent Amari's score as a decimal number where 1 is the whole, as 72 hundredths or 0.72. [b]Try this yourself: What are all the ways you can represent Emily's score? What is her score as a percent and as a decimal?[/b]
Playing Basketball Amari and Emily are shooting hoops. Amari scored 72 out of 100 shots. Emily scored 80 out of 100 shots. How can you represent these as ratios and percents? A ratio is a relationship between two numbers. Ratios can be partpart or partwhole. Because we are looking at the number of scores (part) out of the number of shots (whole), we know that the ratio is partwhole. This is important because percents can only represent partwhole ratios. We can represent Amaris score as 72 :100 or [ggfrac]72/100[/ggfrac] or [ggfrac]72/100[/ggfrac] or 72%. We can also represent Amari's score as a decimal number where 1 is the whole, as 72 hundredths or 0.72. [b]Try this yourself: What are all the ways you can represent Emily's score? What is her score as a percent and as a decimal?[/b]Class Lunch
We are going on a class trip to the local science museum and need to plan for lunch. We surveyed the food preferences of the class, and 5 out of 20 students said they are vegetarian. We can represent this ratio as 5 :20 or [ggfrac]5/20[/ggfrac] or [ggfrac]5/20[/ggfrac]. But how do we represent this ratio as a percent? First we need to convert our ratio to an equivalent ratio out of 100. To make an equivalent ratio we multiply both parts of the ratio by the same number. We know that 20×5=100, so we need to multiply the numerator by 5 as well: 5×5=25. That means the equivalent ratio is 25 :100 or [ggfrac]25/100[ggfrac] or [ggfrac]25/100[/ggfrac] or 25%. So 25% of the students in the class are vegetarians. [b]Try this yourself: 7 out of 25 students in Emily's class are vegetarian. What percent of her class is vegetarian?[/b]
Class Lunch We are going on a class trip to the local science museum and need to plan for lunch. We surveyed the food preferences of the class, and 5 out of 20 students said they are vegetarian. We can represent this ratio as 5 :20 or [ggfrac]5/20[/ggfrac] or [ggfrac]5/20[/ggfrac]. But how do we represent this ratio as a percent? First we need to convert our ratio to an equivalent ratio out of 100. To make an equivalent ratio we multiply both parts of the ratio by the same number. We know that 20×5=100, so we need to multiply the numerator by 5 as well: 5×5=25. That means the equivalent ratio is 25 :100 or [ggfrac]25/100[ggfrac] or [ggfrac]25/100[/ggfrac] or 25%. So 25% of the students in the class are vegetarians. [b]Try this yourself: 7 out of 25 students in Emily's class are vegetarian. What percent of her class is vegetarian?[/b]Calculating Homework
Emily has already read 80% of the books she needs for the year, and she has read 8 books. How many total books does she need to read this year? First, set up a ratio for this situation. Emily has read 8 out of an unknown total number of books, so we can write that as [ggfrac]number of books read /total number of books she needs to read[/ggfrac], or [ggfrac]8/n[/ggfrac]. We know that the number or books she has read is 80% of the total books, so we can set up an equation: [ggfrac]8/n[/ggfrac]=[ggfrac]80/100[/ggfrac]. We need to multiply the numerator and denominator of our ratio by the same number to keep the ratios equivalent. We know that 8×10=80, so [i]n[/i]×10=100. That means [i]n[/i] must equal 10. The total number of books Emily needs to read is 10. [b]Try this yourself: Amari has read 90% of the books she needs for the year, and she has read 18 books so far. How many total books does she need to read this year?[/b]
Calculating Homework Emily has already read 80% of the books she needs for the year, and she has read 8 books. How many total books does she need to read this year? First, set up a ratio for this situation. Emily has read 8 out of an unknown total number of books, so we can write that as [ggfrac]number of books read /total number of books she needs to read[/ggfrac], or [ggfrac]8/n[/ggfrac]. We know that the number or books she has read is 80% of the total books, so we can set up an equation: [ggfrac]8/n[/ggfrac]=[ggfrac]80/100[/ggfrac]. We need to multiply the numerator and denominator of our ratio by the same number to keep the ratios equivalent. We know that 8×10=80, so [i]n[/i]×10=100. That means [i]n[/i] must equal 10. The total number of books Emily needs to read is 10. [b]Try this yourself: Amari has read 90% of the books she needs for the year, and she has read 18 books so far. How many total books does she need to read this year?[/b]Planting a Garden
We can also find the amount of a part for a given percent. We need to plant a garden with 20 plants in total, and 85% of the plants need to be fruit plants. We start by setting up an equation with the information we already know: [ggfrac] number of fruit plants/ total number of plants[/ggfrac]=[ggfrac]percent/100[/ggfrac]. Then we fill in the values we know, to get [ggfrac]n/20[/ggfrac]=[ggfrac]85/100[/ggfrac], where [i]n[/i] represents the number of fruit plants. We can solve this problem by multiplying both the numerator and denominator by the same number. We can see that 20×5=100, so [i]n[/i]×5=85. Now we need to find the value of [i]n[/n]. We know that 17×5=85, so [i]n[/i] must equal 17. We need to have 17 fruit plants in the garden. [b]Try this yourself: If you are planting a garden with 25 plants, and 72% need to be vegetables, how many vegetable plants do you need?[/b]
Planting a Garden We can also find the amount of a part for a given percent. We need to plant a garden with 20 plants in total, and 85% of the plants need to be fruit plants. We start by setting up an equation with the information we already know: [ggfrac] number of fruit plants/ total number of plants[/ggfrac]=[ggfrac]percent/100[/ggfrac]. Then we fill in the values we know, to get [ggfrac]n/20[/ggfrac]=[ggfrac]85/100[/ggfrac], where [i]n[/i] represents the number of fruit plants. We can solve this problem by multiplying both the numerator and denominator by the same number. We can see that 20×5=100, so [i]n[/i]×5=85. Now we need to find the value of [i]n[/n]. We know that 17×5=85, so [i]n[/i] must equal 17. We need to have 17 fruit plants in the garden. [b]Try this yourself: If you are planting a garden with 25 plants, and 72% need to be vegetables, how many vegetable plants do you need?[/b] 
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Science & Math$_{/yr}

Science Only$_{/yr}
How would you represent 88 : 100 as a percent and as a decimal?
We have a partwhole ratio of 2 : 10. How can we represent this ratio as a percent?
You know that 5 is 20% of your total number. What is your total number?
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