1. Changing Ratios to Percents

2. Warm Up 1). Change each to a percent. a). 𝟎.𝟒𝟓𝟔 b). 𝟏.𝟐𝟑 c). 𝟕 𝟏𝟎
2). Change each to a fraction.
a). 𝟐𝟓% b). 𝟎.𝟑𝟔 c). 𝟑𝟑%
3). Change each to a decimal
a). 𝟑 𝟖 b). 𝟓𝟓% c). 𝟑𝟐.𝟏𝟐%
45.6%
123%
70%
𝟏 𝟒
𝟗 𝟐𝟓
𝟑𝟑 𝟏𝟎𝟎
0.375
0.55
0.3212

3. Changing Ratios to Percents
, it
Changing Ratios to Percents
Percents are ratios that compare to 100.
𝟐𝟔 𝒃𝒐𝒚𝒔 𝟏𝟎𝟎 𝒔𝒕𝒖𝒅𝒆𝒏𝒕𝒔
Part
When the ratios are written over a 100, it is easy to see the percent.
Whole amount
This ratio is 26%.
26% of the students are boys.

4. Changing Ratios to Percents
, it
Changing Ratios to Percents
What do you do when it is not out of a 100?
𝟐𝟔 𝒃𝒐𝒚𝒔 𝟓𝟎 𝒔𝒕𝒖𝒅𝒆𝒏𝒕𝒔
You can use a table to try to get what the boy value will be when the students are 100.
To go from 50 to 100 you multiply by 2. So you need to multiply 26 and 2 to find the boys when students are 100.
Part
Whole 26 50
100 52
52% of the students are boys.

5. Changing Ratios to Percents
, it 40
Changing Ratios to Percents
What if you can’t change the whole to 100?
𝟐𝟒 𝒃𝒐𝒚𝒔 𝟖𝟎 𝒔𝒕𝒖𝒅𝒆𝒏𝒕𝒔
Sometimes you can use
a tape diagram.
Each of the 10 parts of the diagram is 10%.
10% % 30% 40% 50% 60% 70% 80% 90% %
3 eights equals 24 boys and this is 30%.
The whole amount is 80. If we divide 80 into 10 parts we will get 8. So each part is 8.
30% of the students are boys.

6. Changing Ratios to Percents Using Tape Diagrams
Example 1: Jan has 49 chocolate candies out of 70 pieces of candy. What percent of her candy is chocolate?
Example 2: 3 out of 20 students made straight A’s this quarter. What percent of the students made straight A’s?
10% % 30% 40% 50% 60% 70% 80% 90% %
70% of her candy is chocolate.
10% % 30% 40% 50% 60% 70% 80% 90% %
15% of the students made straight A’s. Three is not an even number so we had to take 10% and half of 10 % or 5% .

7. Changing Ratios to Percents
Another way to change a ratio to a percent is to use what we know about changing fractions to a percent.
Change the ratio to a decimal (divide numerator by denominator).
Change the decimal to a percent (multiply by 100).
This is helpful when you have ratios that are made up of numbers that make it harder to use a tape diagram or a table.

8. 𝟑𝟑 𝒃𝒍𝒖𝒆 𝟔𝟕 𝒕𝒐𝒕𝒂𝒍 𝟑𝟑÷𝟔𝟕=𝟎.𝟒𝟗(𝒓𝒐𝒖𝒏𝒅𝒆𝒅)
Example 1: Uma has 33 blue pencils out of 67 total pencils.
𝟑𝟑 𝒃𝒍𝒖𝒆 𝟔𝟕 𝒕𝒐𝒕𝒂𝒍 𝟑𝟑÷𝟔𝟕=𝟎.𝟒𝟗(𝒓𝒐𝒖𝒏𝒅𝒆𝒅)
𝟎.𝟒𝟗×𝟏𝟎𝟎≈𝟒𝟗%

9. 𝟏 𝒎𝒊𝒍𝒌 𝟑 𝒕𝒐𝒕𝒂𝒍 𝟏÷𝟑=𝟎.𝟑𝟑(𝒓𝒐𝒖𝒏𝒅𝒆𝒅)
Example 2: A recipe has 1 cup of milk for every 3 cups of flour. What percent is milk?
𝟏 𝒎𝒊𝒍𝒌 𝟑 𝒕𝒐𝒕𝒂𝒍 𝟏÷𝟑=𝟎.𝟑𝟑(𝒓𝒐𝒖𝒏𝒅𝒆𝒅)
𝟎.𝟑𝟑×𝟏𝟎𝟎≈𝟑𝟑%

10. Practice: Solve the following problems by modeling with a tape diagram.
1). 30 out of 60 people like hot dogs. What percent of the people like hot dogs?
2). Ku has 4 dogs out of 5 pets. What percent of his pets are dogs?
Solve using any method you like.
3). 2 out of every 3 people prefer dogs over cats. What is the percent?
4). Hal received 39 out of 50 vote. What percent did he receive?

11. 2). Ku has 4 dogs out of 5 pets. What percent of his pets are dogs?
Practice: Solve the following problems by modeling with a tape diagram.
1). 30 out of 60 people like hot dogs. What percent of the people like hot dogs?
2). Ku has 4 dogs out of 5 pets. What percent of his pets are dogs?
10% % 30% 40% 50% 60% 70% 80% 90% %
50% like hot dogs.
10% % 30% 40% 50% 60% 70% 80% 90% %
You can change 4/5 to 40/50 to make a tape diagram easier.
80% are dogs.

12. Practice: Solve the following problems by modeling with a tape diagram.
1). 30 out of 60 people like hot dogs. What percent of the people like hot dogs?
2). Ku has 4 dogs out of 5 pets. What percent of his pets are dogs?
Solve using any method you like.
3). 2 out of every 3 people prefer dogs over cats. What is the percent?
4). Hal received 39 out of 50 vote. What percent did he receive?
50% like hot dogs.
80% are dogs.
67% prefer dogs over cats
He received 78% of the votes.

13. Closure Which ratio would be easier to solve with a tape diagram? Why?
47 boys to 59 girls.
2 boys to 8 girls.
2 boys to 8 girls is easier to change to a power of ten. You can change it to an equivalent ratio of 20/80.