Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Write as a decimal. Method 1 Use paper and pencil. Answer: 0.0625 Write as a decimal. Method 2 Use a calculator. 1 16 Answer: 0.0625 ENTER 0.0625 Write as a decimal. Answer: 0.375 Write as a decimal. Write as the sum of an integer and a fraction. Add. Answer: 1.25 Write as a decimal. Answer: 2.6 Write as a decimal. The digits 12 repeat. Answer: Write as a decimal. The digits 18 repeat. Answer: a. Write as a decimal. Answer: b. Write as a decimal. Answer: Replace with <, >, or = to make sentence. a true Write the sentence. Write as a decimal. In the tenths place, Answer: On a number line, 0.7 is to the right of 0.65, so . . Replace with <, >, or = to make sentence. Answer: < a true Grades Jeremy got a score of and on his first quiz on his second quiz. Which grade was the higher score? Write the fractions as decimals and then compare the decimals. Quiz #1: Quiz #2: Answer: The scores were the same, 0.80. Baking One recipe for cookies requires of a cup of butter and a second recipe for cookies requires of a cup of butter. Which recipe uses less butter? Answer: the second recipe Write Answer: as a fraction. Write as an improper fraction. Write 10 as a fraction. Answer: a. Write as a fraction. Answer: b. Write –6 as a fraction. Answer: Write 0.26 as a fraction or mixed number in simplest form. 0.26 is 26 hundredths. Answer: Simplify. The GCF of 26 and100 is 2. Write 2.875 as a fraction or mixed number in simplest form. 2.875 is 2 and 875 thousandths. Answer: Simplify. The GCF of 875 and 1000 is 125. Write each decimal as a fraction or mixed number in simplest form. a. 0.84 Answer: b. 3.625 Answer: Write as a fraction in simplest form. Let N represent the number. Multiply each side by 100 because two digits repeat. Subtract N from 100N to eliminate the repeating part, 0.3939... Divide each side by 99. Simplify. Answer: Check 13 33 ENTER 0.3939393939 Write Answer: as a fraction in simplest form. Identify all sets to which the number 15 belongs. Answer: 15 is a whole number, an integer, a natural number, and a rational number. Identify all sets to which the number Answer: is a rational number. belongs. Identify all sets to which the number 0.30303030... belongs. Answer: 0.30303030... is a nonterminating, repeating decimal. So, it is a rational number. Identify all sets to which each number belongs. a. –7 Answer: integer, rational b. Answer: rational c. 0.24242424... Answer: rational Find . Write the product in simplest form. Multiply the numerators. Multiply the denominators. Answer: Simplify. The GCF of 10 and 40 is 10. Find Answer: . Find . Write the product in simplest form. Divide 8 and 6 by their GCF, 2. Multiply the numerators and multiply the denominators. Answer: Simplify. Find Answer: . Write the product in simplest form. Find . Write the product in simplest form. Divide 2 and 4 by their GCF, 2. Multiply the numerators and multiply the denominators. Answer: Simplify. Find Answer: . Find . Write the product in simplest form. Rename and rename . Divide by the GCF, 3. Multiply. Answer: Simplify. Find Answer: . Write the product in simplest form. Find . Write the product in simplest form. The GCF of Answer: Simplify. and q is q. Find Answer: . Write the product in simplest form. Track The track at Cole’s school is mile around. If Cole runs one lap in two minutes, how far (in miles) does he run in 30 minutes? Words Distance equals the rate multiplied by the time. Variables Let d = distance, r = rate, and t = time. Formula d = rt mile per 2 minutes • 30 minutes Write the formula. 15 1 Divide by the common factors and units. Multiply. Simplify. Answer: Cole runs miles in 30 minutes. Check The problem asks for the distance. When you divide the common units, the answer is expressed in miles. So, the answer is reasonable. Walking Bob walks mile in 12 minutes. How far does he walk in 30 minutes? Answer: Find the multiplicative inverse of . The product is 1. Answer: The multiplicative inverse or reciprocal of . Find the multiplicative inverse of . Write as an improper fraction. The product is 1. Answer: The reciprocal of . Find the multiplicative inverse of each number. a. Answer: b. Answer: Find . Write the quotient in simplest form. Multiply by the multiplicative inverse of , . Divide 5 and 10 by their GCF, 5. Answer: Simplify. Find Answer: . Write the quotient in simplest form. Find . Write the quotient in simplest form. Write 3 as . Multiply by the multiplicative inverse of Answer: , . Multiply the numerators and multiply the denominators. Find Answer: . Write the quotient in simplest form. Find . Write the quotient in simplest form. Rename the mixed numbers as improper fractions. Multiply by the multiplicative inverse of , . Divide out common factors. Answer: Simplify. Find Answer: . Write the quotient in simplest form. Find . Write the quotient in simplest form. Multiply by the multiplicative inverse of , . Divide out common factors. Answer: Simplify. Find Answer: . Write the quotient in simplest form. Travel How many gallons of gas are needed to travel miles if a car gets miles per gallon? To find how many gallons, divide . Write as improper fractions. Multiply by the reciprocal of . 105 1 Divide out common factors. 2 17 Simplify. Answer: gallons of gas are needed. Check Use dimensional analysis to examine the units. Divide out the units. Simplify. The result is expressed as gallons. This agrees with your answer of gallons of gas. Sewing Emily has yards of fabric. She wants to make pillows which each require yards of fabric to complete. How many pillows can Emily make? Answer: or 8 pillows Example 1 Add Fractions Example 2 Add Mixed Numbers Example 3 Subtract Fractions Example 4 Subtract Mixed Numbers Example 5 Add Algebraic Fractions Find . Write the sum in simplest form. Estimate The denominators are the same. Add the numerators. Answer: Simplify and rename as a mixed number. Find Answer: . Write the sum in simplest form. Find . Write the sum in simplest form. Add the whole numbers and fractions separately. Add the numerators. Answer: Simplify. Find Answer: . Write the sum in simplest form. Find . Write the difference in simplest form. Estimate The denominators are the same. Subtract the numerators. Answer: Simplify. Find Answer: . Write the difference in simplest form. . Estimate Evaluate Replace r with and q with Write the mixed numbers as improper fractions. Subtract the numerators. Answer: Simplify. . Evaluate Answer: . Find . Write the sum in simplest form. The denominators are the same. Add the numerators. Add the numerators. Answer: Simplify. Find Answer: . Write the sum in simplest form. Find the LCM of 168 and 180. Number Prime Factorization Exponential Form 168 180 The prime factors of both numbers are 2, 3, 5, and 7. Multiply the greatest powers of 2, 3, 5, and 7 appearing in either factorization. Answer: The LCM of 168 and 180 is 2520. Find the LCM of 144 and 96. Answer: 288 Find the LCM of . Multiply the greatest power of each prime factor. Answer: The LCM of . Find the LCM of Answer: . Find the LCD of . Write the prime factorization of 8 and 20. Highlight the greatest power of each prime factor. Multiply. Answer: The LCD of . Find the LCD of Answer: 36 . Find the LCD of Answer: The LCD of . . Find the LCD of Answer: Replace with <, >, or = to make statement. a true The LCD of the fractions is . Rewrite the fractions using the LCD and then compare the numerators. Multiply the fraction by to make the denominator 105. Multiply the fraction by the denominator 105. to make Answer: Since is to the left of , then . on the number line. Replace with <, >, or = to make statement. Answer: < a true Find . Use as the common denominator. Rename each fraction with the common denominator. Answer: Add the numerators. Find Answer: . Find . Estimate The LCD is 30. Rename each fraction with the LCD. Add the numerators. Answer: Simplify. Find Answer: . Find . Write in simplest form. Write the mixed numbers as improper fractions. Rename fractions using the LCD, 24. Simplify. Add the numerators. Answer: Simplify. Find Answer: . Find . The LCD is 16. Rename Answer: using the LCD. Subtract the numerators. Find Answer: . Find . Write the mixed numbers as improper fractions. Rename the fractions using the LCD. Simplify. Answer: Subtract. Find Answer: . Jogging Juyong jogged three days this week. She jogged miles, miles, and miles. How far did she jog altogether? Explore You know the distances Juyong jogged each day. Plan Add the daily distances together to find the total distance. Estimate your answer. Solve Rename the fractions with LCD, 20. Add the like fractions. Answer: Juyong jogged Examine Since reasonable. miles. is close to , the answer is Gardening Howard’s tomato plants grew during the first week after sprouting, the second week, and inches inches during inches the third week. Find the total growth during the first three weeks after sprouting. Answer: inches Movies The revenue of the 10 highest grossing movies as of June 2000 are given in the table. Find the mean, median, and mode of the revenues. Top 10 Movie Revenues (millions of $) 601 461 431 400 357 330 313 309 306 290 Answer: The mean revenue is $379.8 million. To find the median, order the numbers from least to greatest. 290, 306, 309, 313, 330, 357, 400, 431, 461, 601 There is an even number of items. Find the mean of the two middle numbers. Answer: The median revenue is $343.5 million. Answer: There is no mode because each number in the set occurs once. Test Scores The test scores for a class of nine students are 85, 93, 78, 99, 62, 83, 90, 75, 85. Find the mean, median, and mode of the test scores. Answer: mean, 83.3; median, 85; mode, 85 Olympics The line plot below shows the number of gold medals earned by each country that participated in the 1998 Winter Olympic games in Nagano, Japan. Find the mean, median, and mode for the gold medals won. Answer: The mean is 2.875. There are 24 numbers. The median number is the average of the 12th and 13th numbers. Answer: The median is 2. The number 0 occurs most frequently in the set of data. Answer: The mode is 0. Families A survey of school-age children shows the family sizes displayed in the line plot below. Find the mean, median, and mode. Answer: mean, 4.3; median, 5; mode, 5 Quiz scores The quiz scores for a math class are 8, 7, 6, 10, 8, 8, 9, 8, 7, 9, 8, 0, and 10. Identify an extreme value and describe how it affects the mean. The data value 0 appears to be an extreme value. Calculate the mean with and without the extreme value to find how it affects the mean. mean with extreme value mean without extreme value Answer: The extreme value 0 decreases the mean by 8.2 – 7.5 or about 0.7. Birth Weight The birth weights of ten newborn babies are given in pounds: 7.3, 8.4, 9.1, 7.9, 8.8, 6.5, 7.9, 4.1, 8.0, 7.5. Identify an extreme value and describe how it affects the mean. Answer: 4.1; it decreases the mean by about 0.4. The table shows the monthly salaries of the employees at two bookstores. Find the mean, median, and mode for each set of data. Based on the averages, which bookstore pays its employees better? Bob’s Books Bob’s The Books Reading Place 1290 1400 1400 1600 3650 1400 1450 1550 1600 2000 mean: median: 1290, 1400, 1400, 1600, 3650 median mode: $1400 Bob’s Books The Reading Place 1290 1400 1400 1600 3650 1400 1450 1550 1600 2000 The Reading Place mean: median: 1400, 1450, 1550, 1600, 2000 median mode: none Answer: The $3650 salary at Bob’s Books is an extreme value that increases the mean salary. The employees at The Reading Place are generally better paid as shown by the median. The number of hours spent exercising each week by men and women are given in the table. Find the mean, median, and mode for each set of data. Based on the averages, which gender exercises more? Men 5 2 3 8 12 4 Women Answer: Men: mean, 1 6 4 2 1 8 5.7; median, 4.5; mode, none Women: mean, 3.7; median, 3; mode, 1 Men seem to exercise more. Grid–In Test Item Jenny’s bowling average is 146. Today she bowled 138, 140, and 145. What does she need to score on her fourth game to maintain her average? Read the Test Item Find the sum of the first three games. Then write an equation to find the score needed on the fourth game. Solve the Test Item Step 1 Find the sum of the first three games x. mean of the first three scores sum of first three scores Multiply each side by 3. Simplify. Step 2 Find the fourth score, x. mean Write an equation. Substitution. Multiply each side by 4 and simplify. Subtract 423 from each side and simplify. Answer: Jenny needs to score at least 161 to maintain her average of 146. Emily scored 73, 82, and 85 on her first three math tests. What score does Emily need on the fourth test to give her an average of 82 for the four tests? Answer: 88 Solve . Check your solution. Write the equation. Add to each side. Simplify. Rename the fractions using the LCD and add. Answer: Simplify. Check Write the original equation. Replace y with Simplify. . Solve Answer: . Check your solution. Solve . Check your solution. Write the equation. Subtract 8.6 from each side. Answer: Simplify. Check: Write the original equation. Replace m with 2.6. Simplify. Solve Answer: 6.1 . Check your solution. Solve . Check your solution. Write the equation. Divide each side by 9. Answer: Check: Simplify. Write the original equation. Replace a with 0.4. Simplify. Solve Answer: 0.8 . Check your solution. Solve . Check your solution. Write the equation. Multiply each side by 6. Answer: Simplify. Check: Write the original equation. Replace x with 48. Simplify. Solve . Check your solution. Write the equation. Multiply each side by Answer: . Simplify. Check the solution. Check: Write the original equation. Replace t with –10. Simplify. a. Solve . Check your solution. Answer: 45 b. Solve Answer: 16 . Check your solution. State whether the sequence –5, –1, 3, 7, 11, ... is arithmetic. If it is, state the common difference and write the next three terms. –5, –1, Notice that 3, 7, 11 , and so on. Answer: The terms have a common difference of , so the sequence is arithmetic. Continue the pattern to find the next three terms. 11, 15, 19, 23 Answer: The next three terms of the sequence are 15, 19, and 23. State whether the sequence 12, 7, 2, –3, –8, ... is arithmetic. If it is, state the common difference and write the next three terms. Answer: arithmetic; –5; –13, –18, –23 State whether the sequence 0, 2, 6, 12, 20, ... is arithmetic. If it is, state the common difference and write the next three terms. 0, 2, 6, 12, 20 The terms do not have a common difference. Answer: The sequence is not arithmetic. However, if the pattern continues, the next three differences will be 10, 12, and 14. 20, 30, 42, 56 The next three terms are 30, 42, and 56. State whether the sequence 20, 17, 11, 2, –10, ... is arithmetic. If it is, state the common difference and write the next three terms. Answer: not arithmetic State whether the sequence 2, 4, 4, 8, 8, 16, 16 ... is geometric. If it is, state the common ratio and write the next three terms. 2, 4, 4, 8, 8, 16, 16 Answer: There is no common ratio. The sequence is not geometric. State whether the sequence 27, –9, 3, –1, , ... is geometric. If it is, state the common ratio and write the next three terms. 27, –9, 3, –1, Answer: The common ratio is , so the sequence is geometric. Continue the pattern to find the next three terms. , , , The next three terms are , , and . a. State whether the sequence 2, 8, 32, 128, 512, ... is geometric. If it is, state the common ratio and write the next three terms. Answer: geometric; 4; 2048, 8192, 32,768 b. State whether the sequence 100, 20, 4, , ... is geometric. If it is, state the common ratio and write the next three terms. Answer: geometric; ; , , Click the mouse button or press the Space Bar to display the answers. Click the mouse button or press the Space Bar to display the answers. Click the mouse button or press the Space Bar to display the answers. Click the mouse button or press the Space Bar to display the answers. Click the mouse button or press the Space Bar to display the answers. Click the mouse button or press the Space Bar to display the answers. Click the mouse button or press the Space Bar to display the answers. Click the mouse button or press the Space Bar to display the answers. Click the mouse button or press the Space Bar to display the answers. Click the mouse button or press the Space Bar to display the answers.