1 Percents as Fractions - I and Decimals

Transcription

1 4 Percents as Fractions - I and Decimals Solve percent problems using equivalent fractions or decimals.. Write the number of shaded squares in each diagram as a fraction, a decimal, and a percent. A percent is used to compare a part to a whole. For example, you could say that 55% of the students in your class are boys. You can write 55% as a fraction. To rename a percent as a fraction, write the percent over 00. fraction b) fraction decimal decimal percent percent For example, 55% is the same 55 as 0 0. You can rewrite the fraction in lower terms. For example, 55 -s- 5 = and = 20, so the fraction in lower terms is 20' You can also write 55% as a 55 decimal. 55% is which is 55 hundredths, or Write each percent as a fraction, a) 44% = b) 3% = c) 25% d) 98% = 3. Write each decimal as a percent, a) 0.76 = b) 0.73 = c) 0.33 = d) 0.02 = 4. Arrange these values in order from least to greatest. 77%, 0.67, 98%, ' Chapter 4: Percent Copyright 2008 by Nelson Education Ltd

2 Investigating Percents Explore how percents can be used.. The label below is from a bag of potato chips. Read the label to identify the percent daily value (% daily value) of each nutritional component. Nutrition Facts Valeur nutritive Per 2 chips (50 g) pour 2 croustilles (50 g) Amount Tenour Calories / Calories 2 % Dally Value % valaur quotkflanne Fat/Llpldes 3 g 20% Saturated / satures.5 g + Trans / trans 0 g 8% Cholesterol / Cholesterol 0 mg 0% Sodium / Sodium 30 mg 3% Carbohydrate / Glucldes 32 g % Fibre / Fibres 2 g 9% Sugars / Sucres g Protein/Proteines 3g Vitamin A / Vttamine A 2% vitamin C / Vttamlne C 2% Calcium / Calcium 6% Iron / Fer 4% You can use percents to show the amount of fat or carbohydrates in a serving of food. For example, Fat: 3 g Total serving: 50 g = 26% Fats make up 26% of one serving. Note: The percent daily value (% daily value) shown on a label tells how much of what your body needs each day is contained in the food. It does not tell the percent of each nutritional component in one serving. a) fat b) fibre c) calcium d) sodium e) Vitamin A f) iron 2. Calculate the percent of each nutritional component that is found in one serving of 2 chips. a) fat b) fibre c) carbohydrates d) protein Copyright 2008 by Nelson Education Ltd. Chapter 4: Percent 37

3 4.3 Estimating Percents Determine approximate values using estimation.. Write each percent as a decimal. Then use the decimal to estimate the answer. The first one is done for you. a) 9% of 30 9% = which is close to 0., and 0. x 30 = 3 b) 23% of 40 c) 54% of 46 d) 72% of Write each percent as a fraction. Then, use the fraction to estimate the answer. The first one is done for you. a) 2% of 25 b) 9% of c) 52% of 68 d) 77% of 40 2% jfifi. or about j^. ~^ of 2S is about Use the number line below to help you estimate each of the following fractions. a) b) % i % i I 50% 0 i 2 d) ^ 75% i 00% You can estimate the percent of a number using fractions you know. Here are some useful fractions: 20 _ J 25 _ ± 00 ~ 5 Too = about ~ 4 50 _ 00 ~~ 2 80 _ ± 00 ~ 5 For example, to estimate 35% of 40, change 35% to a fraction % = ^QQ, which is close to 33 -^jq, or about 3. Next, estimate y of 40, which is close to ^ of 39. The answer is about 3. You can also estimate the percent of a number using decimals. For example, to estimate 35% of 40, change 35% to a decimal: 35% = Next, estimate the multiplication: 0.35 x 40 is between 0.3 x 40 = 2 and 0.4 x 40 = 6, so the answer is about Jessica received on her math test. About what percent did Jessica get on the test? 38 Chapter 4: Percent Copyright 2008 by Nelson Education Ltd.

4 4 Using Percents to Make Comparisons Compare fractions and ratios using percents.. Rename each decimal, ratio, or fraction as a percent, a) 0.83 d) 0.49 b) 5 c) 0.05 e) 9 out of 0 parts 2. Order these values from least to greatest. -, 88%, -, 25%, 0.75 To compare fractions, decimals, and ratios, rename each value as a percent, and then compare. For example, I want to compare and 0.6. = or 80%. 0.6 = %. 4 So, -= is greater than Place <, >, or = to make each number statement true. 2 a) 0.05 c) 2 out of 3 parts % 4 b) 0.72 _ 0 d) 20% \ 5 4. Calculate the percent off for each sale. Which sale offers the best deal? a) $20.00 shoes on sale for $0.00 b) $5.00 shoes on sale for $ Jessica got 6 out of 20 on her science test. Nick got 85% on the same test. Who got the higher mark? 6. Ashley can buy three shirts for a total of $.00, or two shirts for a total of $50.00 with an additional 20% off. Which is the better buy? Copyright 2008 by Nelson Education Ltd. Chapter 4: Percent 39

5 4.5 Calculating with Percents 3't Solve problems that involve percents using equivalent ratios. ". Calculate. d) 20% of 40 a) 20% of 00 e) 0% of 30 b) 5% of 50 f) 25% of 80 c) 40% of Gail found a pair of jeans for $ She got an additional 20% off. a) How much money did Gail save on the jeans? Here are some methods you can use to solve percent problems: Rewrite the percent problem using a proportion, and solve for the missing term. For example, to calculate 5% 5? of 40, write = Solve foi the missing term. Use mental math. For example, to calculate 5% of 40, think: "0% of 40 is 4. 5% is half of 0%, or 2. So, 5% is = 6." b) What price did Gail pay for the jeans, not including tax? 3. Nick is shopping for a DVD for his father. At Sounds Mart, DVDs are $24.00 with 33% off. At Audio Giant, DVDs are $20.00 with 5% off. Which store should Nick buy DVDs at? 40 Chapter 4: Percent Copyright 2008 by Nelson Education Ltd.

6 4.6 Solving Problems thai Involve Decimals Solve problems that involve percents and decimals. You may need a calculator for this lesson.. Calculate. a) % of b) 5% of 54.8 c) 0% of 9.6 d) 9% of 0 To calculate a percent of a decimal, you can rewrite the problem as a proportion. For example, what is 20% of 42.3? x? 2. Add 6% GST to each item. What is the final price? a) a shirt for $22.50 b) a T-shirt for $9.90. c) a jacket for $55.99 d) a pair of jeans for $ A fish tank that costs $59.90 is on sale for 40% off. a) What is the sale price? b) What is the final price, including 4% tax? 4. Complete the following chart. Item Price Discount Amount Off Sale Price 20? X? I need a number that I can multiply 00 by to get X = 42.3 I can't solve this, but I can rewrite it as a division and use my calculator = I multiplied the numerator and 20 denominator of by x X The answer is a) shirt $ % b) jeans $ % 0 jacket $ % d) tank top $ % Copyright 2008 by Nelson Education Ltd. Chapter 4: Percent 4

7 4-7 Solve Problems Using - / Logical Reasoning i Solve problems that involve percent using logical reasoning.. Complete the chart using mental math. Number 0% 20% % a) 500 b) d) 900 e) Explain why each statement is reasonable, a) 0% of 00 is 0. So, 5% of 00 is 5. b) 50% of is 30. So, 25% of is Use mental math to answer each problem. a) There are 340 students at Park Meadows School. If 5% of the students are in Grade 5, how many students are in Grade 5? b) A CD costs $23.00 and is 20% off. What is the sale price? c) 25% of a number is 200. What was the original number? 42 Chapter 4: Percent Copyright 2008 by Nelson Education Ltd.

8 Chapter A Test Yourself Circle the letter of the correct answer.. Which decimal represents the number of shaded squares in this grid? A C B. 0. D Which percent represents the number of shaded squares in this grid? A. 82% C. 28% B. 8% D. 72% 3. Which fraction represents the number of shaded squares in this grid? A B. ^ Which fraction is equal to 0.53? A. 53 B. 00 ~ 0 5. What is 0% of 46? C. D. C A. 2.3 B. 4.6 C D Ashley used 2 out of 3 of her coloured pens in class. Jessica used 7 out of 0 of her pens. Gail used 2 out of 5 of her pens. Which student used the greatest percent of her pens? A. Jessica B. Gail C. Ashley D. They all used the same percent. 7. Jessica ate j of a pizza. What percent of the pizza did she eat? A. 3% B. 6% C. 30% D. % Copyright 2008 by Nelson Education Ltd. Chapter 4: Percent 43

9 4 Chapter *"r Test Yourself continued 8. Nestor ate \ of his grapes. Nick ate 4 of his 0 grapes. Pavio ate 3 30% of his grapes, and Gail ate ~ 5 of her grapes. Who ate the greatest portion of his or her grapes? A. Nestor B. Nick C. Pavio D. Gail 9. At a carnival, 25% of the children get a free balloon. What fraction of the children get free balloons? A. IL 25 Cm p Megan bought a shirt for $ When she got to the cash register, she discovered that the shirt was an additional 33% off. How much did Megan pay, not including tax? A. $27.25 B. $29.50 C. $29.75 D. $ What is 25% of? A. 6 B. 36 C. 40 D % of what number is 35? A. 70 B. C. 50 D Pavio scored 20 out of 50 on a science test. What was his percent? A. 70% B. 75% C. 80% D. 85% 4. The ratio of cats to dogs at a pet show is ; 3. If there are 25 cats at the show, how many dogs are there? A. 25 B. 50 C. 75 D Which sign completes this number sentence: j 0 65%? A. > B. < C. = D. none of these signs 6. A leather jacket costs $ What is the total price including 6% GST? A. $37.79 B. $37.80 C. $37.8 D. $ Chapter 4: Percent Copyright 2008 by Nelson Education Ltd.