Comparing and Ordering Fractions

Transcription

1 Comparing and Ordering Fractions Compare and order fractions on number lines.. Compare. Write >, <, or. 0 a) > d) < 6 b) = e) 0 < c) 7 f) > > 0. Order each set of numbers from least to greatest. Use a number line. To compare fractions, use a number line to mark the positions of the fractions. The order of the fractions can be read from the number line. For example, to order,, and, use a number line. 0 The order from least to greatest is,, and. a),,, 0,,, b),,, 6 6,,, 6 c),,, 7, 0 7,,,, 7 d) 6,, 6,, ,, 6,, Answers Chapter : Fractions, Decimals, Ratios, and Percents Copyright 006 Nelson

2 Comparing Fractions with Unlike Denominators Compare fractions when the denominators are different.. Compare. Write >, <, or. a) < d) > b) < e) 6 = 0 c) > f) >. Which amount is greater? Tell how you know. a) or of a bag of popcorn I used grid paper to draw a number line. I chose a whole with sections. is past on the number line. b) or of a container of juice The numerators are the same, so the fraction with the lower denominator is greater. To compare fractions with unlike denominators, draw a number line on grid paper. Choose a whole that you can easily divide by each denominator. For example, to compare,, and, choose a whole with sections. Then mark the fractions on the number line. 0 The order from least to greatest is,, and. c) 7 or of a length of string 7 I used grid paper to draw a number line. I chose a whole with sections. 7 is past on the number line. Copyright 006 Nelson Answers Chapter : Fractions, Decimals, Ratios, and Percents 0

3 Fraction and Decimal Equivalents Relate fractions to decimals and determine equivalents.. Write an equivalent fraction for each decimal. a) 0. b) 0.6 c) 0.07 d). e).7 f) Explain how to write as a decimal. To write a fraction as a decimal, find an equivalent fraction with a denominator of 0, 00, or 000. Then use place value to write the decimal equivalent. For example: 0 tenths 0. To write a decimal as a fraction, use place value. For example:. ones tenth 0 I could divide a rectangle into 0 equal sections. If I shade rows, that represents. of the rectangle is sections. So is the same as Answers Chapter : Fractions, Decimals, Ratios, and Percents Copyright 006 Nelson

4 Ratios Identify and model ratios to describe situations.. Write the ratio of grey items to white items. a) : 6 A ratio is a comparison of two numbers or quantities measured in the same units. If you mix juice using can of concentrate and cans of water, the ratio of concentrate to water is :, or to. b) : c) : d) 0 : 6. Write the ratio of white to grey for each situation in Question. a) 6 : b) : c) : d) 6 : 0. a) What is the ratio of oats to raisins? : b) What is the ratio of coconut to oats? : parts oats part coconut parts raisins c) What is the ratio of raisins to coconut? : Copyright 006 Nelson Answers Chapter : Fractions, Decimals, Ratios, and Percents 07

5 Equivalent Ratios Determine equivalent ratios and use them to solve problems.. Determine the missing number to make an equivalent ratio. a) to 0 to 6 Equivalent ratios are two or more ratios that represent the same comparison. b) : 00 : c) to 7 to : : 6 : 9 d) : 6 9 : e) 7 : : f) to 60 to. Kenton makes salsa by mixing tomatoes and peppers in a ratio of to. a) Write ratios equivalent to : in the ratio table. Tomatoes Peppers 6 0 b) If Kenton has 0 tomatoes, how many peppers does he need? : = 0 : 6 6 peppers c) If Kenton has 0 peppers, how many tomatoes does he need? : = 0 : 0 0 tomatoes. Stacy makes one batch of muffins using muffin mix and water in a ratio of :. She needs to make batches for school. How many cups of muffin mix will she need? : = : cups of muffin mix 0 Answers Chapter : Fractions, Decimals, Ratios, and Percents Copyright 006 Nelson

6 6 Percents as Special Ratios Understand the meaning of percent.. Write each as a ratio, a fraction, and a percent. a) 0 to c) out of 0 0 : : = 6 = 0 = 0% = 6% b) 0.07 d) 0. 7 : = 7% : 00 = % A percent is a part-to-whole ratio that compares a number or an amount to 00. % : 00 Percents are written with a percent sign (%). The percent sign is like writing of each 00. % is read percent and means of each 00.. Write each ratio as an equivalent fraction with 00% means the whole. a denominator of 00, a decimal, and a percent. 9 a) b) 66 = = c) out of d) out of 0 0 = 0. = 0.66 = % = 66% = 0 = 00 = 0.0 = 0. = 0% = %. A survey at Jennifer s school showed that 9 out of students chose pizza as their favourite lunch food. a) What percent of students chose pizza? 9 out of = 9 : = 9 76 = = 76% b) What percent of students did not choose pizza? Out of students, 9 = 6 students did not choose pizza. 6 out of = 6 : 6 = = = % Copyright 006 Nelson Answers Chapter : Fractions, Decimals, Ratios, and Percents 09

7 7 Relating Percents to Decimals and Fractions Compare and order percents, fractions, and decimals.. Write each number as a percent. Order the numbers from least to greatest. 7 a) 0.6,, 0.07, = 0 60 = = 60% 7 0 = = 70% 0.07 = 7 00 = 7% Order is 7%, 0%, 60%, 70% or 0.07, 0, 0.6, 7 0. b), 0., 6, 0. = 0 0. = 00 = 0% = % 6 6 = = 6% Order is %, 6%, 0%, % or 0., 6,, = 0 00 = 0% 0. = = % To compare fractions, decimals, and percents, write all numbers in the same form. For example, to compare, 0.,, and 0%, write each number as a percent % % 0% The order from least to greatest is %, 0%, %, 0% or 0.,,, 0%.. An art show has paintings, sculptures, and sketches. Thirty-five percent of the items are paintings and 0. of the items are sketches. What fraction of the items are sculptures? % paintings 0. = = % sketches Percent of sculptures = 00% (% + %) = 00% % = % % = = The fraction of items that are sculptures is. 0 Answers Chapter : Fractions, Decimals, Ratios, and Percents Copyright 006 Nelson

8 Estimating and Calculating Percents Estimate and calculate percents.. Estimate the percent of each number. Show your work. a) 0% of 0 0% of 0 is half of 0, or 90. So 0% of 0 is a little less than 90 or about 7. To estimate the percent of a number, use benchmarks such as 0%, %, 0%, and 7%. 0% is the same as 0. % is the same as. 0% is the same as. b) 0% of 90 0% of 90 is 9. 0% of 90 is 9 x = 7. 7% is the same as. 00% is the same as whole. For example, to estimate % of 00 km, use a number line. 0% % 0% 7% 00% c) 0% of 0% of is half of, or about about % of 00 km is half of 00 or 0 km. 00 So % is half of 0 km or about 00 km. d) 7% of 0 0% of 0 is half of 0, or about 00. % of 0 is about half of 00, or 0. So 7% of 0 is about = 0.. A store has a sign saying, % off all jackets. Kenny wants to buy a leather jacket that has a regular price of $60. About how much will Kenny save? % of $60 is of $60, or $90. % is about halfway between 0 and % but closer to %. So % of $60 is about half of 90, or about $0. So Kenny will save about $0. Copyright 006 Nelson Answers Chapter : Fractions, Decimals, Ratios, and Percents

9 9 Unit Rates Represent relationships using unit rates.. Calculate the unit rate for each item. a) guitar picks for $.00 0 /pick A unit rate is a comparison of two quantities where the second one is described as one unit. For example, a unit rate might be 0 km in h or tomatoes for $.00. b) CDs for $.00 : = : = 7. $7.0/CD Rates often have words like per or for in them. A slash (/) is sometimes used instead. For example, you read 00 km/h as 00 km per hour. c) mini-muffins for $.0 d) tickets for $.00 0 /muffin : = : = $.00/ticket. a) What is the price of one scoop of each type of ice cream? (vanilla) : 0 = : (mango) : = : = 0 = 0 /scoop $.00/scoop (chocolate) : 0 = : (strawberry) : 60 = : = 70 = /scoop 90 /scoop Ice cream Vanilla scoops for $.0 Chocolate scoops for $.0 Mango scoops for $.00 Strawberry scoops for $.60 b) Which ice cream is the least expensive? vanilla c) Which ice cream is the most expensive? mango Answers Chapter : Fractions, Decimals, Ratios, and Percents Copyright 006 Nelson

10 0 Solving Problems Using Guess and Test Use a guess and test strategy to solve problems. The ratio of flowers to herbs in Babak s garden is 6 :. He started with 0 plants. He wants to increase the number of herbs in his garden so that 0% of his plants are herbs. How many more herb plants must he get? Understand the Problem Babak started with 0 plants that made 00% of his garden. If Babak had plants, 6 of them would be flowers and would be herbs. 0% % 0% 7% Sometimes using a guess and test strategy is a good way to solve a problem. Use a chart to help you organize the information you are given and what you want to calculate. Remember to check if your answer is reasonable after guessing. 00% 0 0 Make a Plan I ll set up a chart and use a guess and test strategy to determine how many more herb plants Babak needs. Carry Out the Plan 0 60 Number Number Total number of Guess of flowers of herbs flowers and herbs Percent of herbs start with = 0 = % add 0 herbs = 90 or about 0% 0 add 0 herbs = 0% 0 Look Back Babak will need 0 more herb plants to make his garden have 0% herbs. I ll check if my answer is correct. Babak started with 0 plants. If he adds 0 plants, then he will have = 00 plants altogether. 0% of 00 is 0. So he should have 60 flowers and 0 herbs. He started out with 0 herbs. So 0 more herb plants will give 0 herb plants. Copyright 006 Nelson Answers Chapter : Fractions, Decimals, Ratios, and Percents

11 Test Yourself Page Circle the correct answer.. Which fraction is greatest?,,, A. B. C. D.. What is the correct order of these fractions from least to greatest?, 6,, 7, A.,, 6, 7, C. 6,,, 7, B. 6,,, 7, D.,, 6, 7,. What is.0 as a fraction? A. B. C. 0 D What is the ratio of white counters to grey counters? A. : C. : 7 B. : 7 D. :. Which ratios are equivalent to 6 out of? i) : ii) out of 0 iii) out of 0 iv) 0 : v) 0 : A. i, ii, iii B. ii, iv, v C. i, iii, iv D. ii, iii, iv 6. What is the correct order of these numbers from least to greatest?, 0., 0%,, %, 0.09 A. %, 0.09, 0., 0%,, C. 0.09,, 0.,, %, 0% B. 0.09, 0.,,, %, 0% D. %, 0.09,, 0.,, 0% Answers Chapter : Fractions, Decimals, Ratios, and Percents Copyright 006 Nelson

12 Test Yourself Page 7. What is 0. as a ratio, a fraction, and a percent? A. : 00,, 0% B. : 0,, 0% 0 C. : 0,, % 0 D. : 0,, %. What is as an equivalent fraction with a denominator of 00, a decimal, and a percent? A., 0., % 0 B., 0., 0% C., 0., % 6 D., 0.6, 6% 9. What is the best estimate for % of? A. about 0 B. about 0 C. about 0 D. about Which type of muffin is the least expensive? A. cinnamon raisin B. maple pecan C. cranberry orange D. crunchy oat Muffins Blueberry bran..... for $.0 Cranberry orange... 6 for $.60 Crunchy oat for $.0 Maple pecan for $.70 Cinnamon raisin.... for $.0. A brand of light cheese says 0% less fat on the label. The regular version of the cheese has g of fat. About how many fewer grams of fat are in the light cheese? A. about 0 g B. about 0 g C. about 0 g D. about 0 g Copyright 006 Nelson Answers Chapter :Fractions, Decimals, Ratios, and Percents