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02/09/11 Proportions & Percent
Today’s Plan:-Warm-up-Intro to Percent-Assignment
LT: I will apply my understanding of ratios to solve problems involving proportional relationships, including percent.
Warm Up
Sara, Jim, and Laura worked different hours at the ski swap. They agreed to split the $600 they earned in a ratio of 5:3:2 respectively. How much did each student get?
02/09/11 Proportions & Percent
Today’s Plan:-Warm-up-Intro to Percent-Assignment
LT: I will apply my understanding of ratios to solve problems involving proportional relationships, including percent.
Percent!
Course 2
6-1 Fractions, Decimals, and Percents
The students at Westview Middle School are collecting cans of food for the local food bank. Their goal is to collect 2,000 cans in one month. After 10 days, they have 800 cans of food. What percent of their goal have they reached?
Course 2
6-1 Fractions, Decimals, and Percents
0 200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000
0 15
25
35
45
55
00 0.2 0.4 0.6 0.8 1.0
0 20% 40% 60% 80% 100%
The number lines show that the students have reached 40% of their goal.
Course 2
6-1 Fractions, Decimals, and Percents
The word percent means “per hundred.” So 40% means “40 out of 100.”
Reading Math
A percent is the ratio of a number to 100. The symbol % is used to indicate that a number is a percent. For example, 40% is
the ratio 40 to 100, or . Percents can be
written as fractions or decimals
40100
Write 88% as a fraction in simplest form.
Additional Example 1: Writing Percents as Fractions
Course 2
6-1 Fractions, Decimals, and Percents
88% = 88100
Write the percent as a fraction with adenominator of 100.
= 2225
Simplify.
Write 45% as a fraction in simplest form.
Try This: Example 1
Course 2
6-1 Fractions, Decimals, and Percents
45% = 45100
Write the percent as a fraction with adenominator of 100.
= 920
Simplify.
Additional Example 2: Writing Percents as Decimals
Course 2
6-1 Fractions, Decimals, and Percents
Write 51% as a decimal.
51% = 51100
= 0.51
Write the percent as a fraction with a denominator of 100.
Write the fraction as a decimal.
Try This: Example 2
Course 2
6-1 Fractions, Decimals, and Percents
Write 67% as a decimal.
67% = 67100
= 0.67
Write the percent as a fraction with a denominator of 100.
Write the fraction as a decimal.
Course 2
6-1 Fractions, Decimals, and Percent
Notice that both 43% and 0.43 mean “43 hundredths.” Another way to write a percent as a decimal is to delete the percent sign and move the decimal point two places to the left.
43.% = 0.43
Write each decimal as a percent.
Additional Example 3A & 3B: Writing Decimals as Percents
Course 2
6-1 Fractions, Decimals, and Percents
A. 0.08
= 8%
B. 0.7
= 70%
Write the decimal as a fraction.
Write the fraction as a percent.
Write the decimal as a fraction.
Write an equivalent fraction with adenominator of 100.
Write the fraction as a percent.
0.08 =8
100
0.7 = 710
70100
=
Write each decimal as a percent.
Try This: Example 3A & 3B
Course 2
6-1 Fractions, Decimals, and Percents
A. 0.01
= 1%
B. 0.1
= 10%
Write the decimal as a fraction.
Write the fraction as a percent.
Write the decimal as a fraction.
Write an equivalent fraction with adenominator of 100.
Write the fraction as a percent.
0.01 =1
100
0.1 = 110
10100
=
Course 2
6-1 Fractions, Decimals, and Percent
Both 0.07 and 7% mean “7 hundredths.” you can write a decimal as a percent by moving the decimal point two places to the right and adding the percent sign.
0.07 = 7.0%
Course 2
6-1 Fractions, Decimals and Percents
Write each fraction as a percent.
A. 35
35
= 3 · 205 · 20
= 60100
= 60%
Write an equivalent fraction with a denominator of 100.
Write the fraction as a percent.
The method shown in example 4A works only if the given denominator is a factor or multiple of 100.
Helpful Hint
Additional Example 4A: Writing Fractions as Decimals
Write each fraction as a percent.
Additional Example 4B: Writing Fractions as Decimals
Course 2
6-1 Fractions, Decimals, and Percents
B. 740
740
= 7 ÷ 40
= 0.175
= 17.5%
Use division to write a fraction as adecimal.
Write the decimal as a percent.
The method shown in 4B works for any denominator.
Helpful Hint
Course 2
6-1 Fractions, Decimals and Percents
Write each fraction as a percent.
A. 34
34
= 3 · 254 · 25
= 75100
= 75%
Write an equivalent fraction with a denominator of 100.
Write the fraction as a percent.
Try This: Example 4A
Write each fraction as a percent.
Try This: Example 4B
Course 2
6-1 Fractions, Decimals, and Percents
B. 960
960
= 9 ÷ 60
= 0.15
= 15%
Use division to write a fraction as adecimal.
Write the decimal as a percent.
Lesson Quiz
65%
Insert Lesson Title Here
0.72
60%
Course 2
6-1 Fractions, Decimals, and Percents
1. Write 40% as a fraction.
2. Write 0.65 as a percent.
3. Write 72% as a decimal.
4. Write as a percent. 610
5. About 95% of all animals are insects. Express this percent as a fraction.
25
1920