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000200010271713722_CH01.qxd 2/13/13 8:50 PM Page 2 Name Class Date Reteaching 1-1 Comparing and Ordering Integers The numbers 2 and -2 are opposites. The numbers 7 and -7 are opposites. Integers are the set of positive whole numbers, their opposites, and zero. 7 6 5 4 3 2 1 negative 0 zero 1 2 3 4 5 positive 6 7 You can use the number line to compare integers. -2 is less than 0. -2 0 Numbers to the right are greater. 7 is farther to the right than 2. Compare using R, S, or ≠. 1. 4 2. -3 2 4. -1 -2 5. 0 7. -6 4 8. -8 10. -7 -10 11. -10 -2 3. 3 -4 6. 0 -4 -2 9. 3 0 10 12. 1 5 -1 Find the opposite of each number. 14. 5 ________ 15. 147 ________ 16. 12 12 ________ 17. 15 15 ________ 18. 18 18 ________ 19. 5 5 ________ 20. 24 24 ________ 21. 225 225 ________ 13. 8 ________ Find each sum. Order the numbers from least to greatest. 22. -4, 5, -2, 0, 1 23. 6, -3, -5, 4, -6 24. 3, -5, 4, -4, -7, 0 25. 1, 3, -7, -6, 5, -2 Course 2 Lesson 1-1 Reteaching © Pearson Education, Inc., publishing as Pearson Prentice Hall. Numbers to the left are less. 2 is farther left than 0. All rights reserved. 7 is greater than 2. 72 000200010271713722_CH01.qxd 2/13/13 8:50 PM Page 6 Name Class Date Reteaching 1-2 Adding and Subtracting Integers Use these rules to add and subtract integers. Adding Integers • The sum of two positive integers is positive. Example: 6 + 16 = 22 • The sum of two negative integers is negative. Example: -9 + (-3) = -12 • First find the absolute values of each number. • Then subtract the lesser absolute value from the greater. • The sum has the sign of the integer with the greater absolute value. Example: -10 + 9 = -1 Subtracting Integers All rights reserved. Different Signs Same Sign • To subtract integers, add the opposite. • Then following the rules for adding integers. Example: 6 – (–3) = 6 + 3 = 9 1. 8 + (-2) 2. -9 + 4 3. 3 + (-2) 4. -1 + 11 5. 12 + 13 6. -9 + 5 7. 7 + 2 8. -1 + (-7) 9. -3 + 0 10. -1 + (-1) © Pearson Education, Inc., publishing as Pearson Prentice Hall. Find each sum. 12. 3 (-2) 11. 6 + 5 Complete. 13. -3 - 4 Change to addition: -3 + = 14. 5 - 2 Change to addition: 5+ = 15. -6 - (-10) Change to addition: -6 + = Find each difference. 16. 4 - 5 17. -5 - 4 18. -8 - (-7) 19. 19 - (-6) 20. -10 - 12 21. -12 - 10 22. -4 - (-5) 23. -2 - (-3) 24. 9 - (-7) 25. 0 - 3 26. 6 - 8 27. 0 - (-10) Course 2 Lesson 1-2 Reteaching 000200010271713722_CH01.qxd 2/13/13 8:50 PM Name Page 10 Class Reteaching 1-3 Date Multiplying and Dividing Integers To multiply integers: To divide integers: • If the signs are alike, the product is positive. • If the signs are alike, the quotient is positive. 6 3=2 -6 -3 = 2 2? 3=6 -2 ? -3 = 6 • If the signs are different, the quotient is negative. 6 -3 = -2 -6 3 = -2 All rights reserved. • If the signs are different, the product is negative. 2 ? -3 = -6 -2 ? 3 = -6 Study these four examples. Write positive or negative to complete each statement. 7 3 ≠ 21 7 3 ≠ 21 7 3 ≠ 21 7 3 ≠ 21 1. When both integers are positive, the product is . 2. When one integer is positive and one is negative, the product is 3. When both integers are negative, the product is . 21 3 = 7 21 3 = 7 4. When both integers are positive, the quotient is 5. When both integers are negative, the quotient is 6. When one integer is positive and one is negative, the quotient is © Pearson Education, Inc., publishing as Pearson Prentice Hall. 21 3 = 7 21 3 = 7 . . . . Tell whether each product or quotient will be positive or negative. 7. 4 ? 7 11. 10 ? -4 Course 2 Lesson 1-3 8. -4 ? 7 9. -4 ? -7 12. -25 5 13. -2 ? -2 10. 4 ? -7 14. 100 10 Reteaching 2/13/13 8:50 PM Page 14 Name Class Date Reteaching 1-4 0 0.1 0.2 1 10 1 5 0.3 0.4 Fractions and Decimals 0.5 0.6 1 2 3 5 0.7 To change a fraction to a decimal, divide the numerator by the denominator. 3 5 Think: 3 5 0.6 5q3.0 230 0 0.8 0.9 1.0 1.1 1.2 1.3 11 1 5 1.4 12 5 To change a decimal to a fraction: 1 Read the decimal to find the denominator. Write the decimal digits over 10, 100, or 1,000. 65 2 0.65 is 65 hundredths S 100 Use the GCF to write the fraction in simplest form. 3 5 0.6 5 The GCF of 65 and 100 is 5. 65 65 4 5 13 100 5 100 4 5 5 20 All rights reserved. 000200010271713722_CH01.qxd Write each fraction as a decimal. 2. 34 5 5. 23 5 8. 15 5 3. 16 5 7 5 6. 10 9. 38 5 © Pearson Education, Inc., publishing as Pearson Prentice Hall. 1. 45 5 4. 14 5 7. 59 5 Write each decimal as a mixed number or fraction in simplest form. 10. 0.4 = 11. 0.75 = 12. 1.5 = 13. 0.35 = 14. 2.7 = 15. 1.8 = 16. 0.625 = 17. 0.78 = 18. 0.88 = 1 , 2.0202 20. 2.02, 2 200 21. 54, 1 45, 1.4 Order from least to greatest. 5 19. 2.6, 13 6 , 26 Course 2 Lesson 1-4 Reteaching 000200010271713722_CH01.qxd 2/19/13 9:04 PM Name Page 18 Class Date Reteaching 1-5 Rational Numbers A rational number is a number that can be written as a quotient of two integers, where the divisor is not zero. A negative rational number can be written in three different ways. 223 5 223 5 223 Comparing Negative Rational Numbers Compare 223 and 214 . 2 23 2 14 212 -1 All rights reserved. Method 1 Use a number line. Graph both points on a number line and see which is farther to the left. 0 Since 223 is farther to the left, 223 ⬍ 214 . Method 2 Use the lowest common denominator. 28 22 3 4 223 5 22 3 5 3 3 4 5 12 21 3 3 23 214 5 21 4 5 4 3 3 5 12 © Pearson Education, Inc., publishing as Pearson Prentice Hall. 23 2 1 Since 28 12 , 12 , then 2 3 , 2 4 . Compare. Use R, S, or ≠. 1. 249 223 2. -1 245 3. 278 218 4. 213 256 5. 225 1 210 6. 228 214 Order from least to greatest. 3 7. 213, 0.3, 20.35, 210 3 8. 15 , 20.25, 0.21, 10 9. You and your brother invested an equal amount of money in a college savings plan. In the last quarter your investment was worth 156 of its original value. Your brother’s investment was worth 1.85 of its original value. Whose investment is worth more? Course 2 Lesson 1-5 Reteaching 000200010271713722_CH01.qxd 2/19/13 10:06 PM Name Page 22 Class Reteaching 1-6 Date Adding and Subtracting Rational Numbers Use these rules to add and subtract rational numbers. Same Sign Different Signs • The sum of two positive rational numbers is positive. Example: 15.6 ⫹ 4.5 ⫽ 20.1 Example: 2 1 8 5 1 1 9 9 9 • The sum of two negative rational numbers is negative. Example: ⫺3.42 ⫹ (⫺5.74) ⫽ ⫺9.16 Example: 21 3 1 a24 3 b 5 26 1 4 4 2 • First find the absolute values of each addend. • Then subtract the lesser absolute value from the greater. • The sum has the sign of the addend with the greater absolute value. Example: ⫺25.8 ⫹ 17.3 ⫽ ⫺8.5 Example: 22 1 1 1 1 5 21 1 2 4 4 All rights reserved. Adding and Subtracting Integers Subtracting Rational Numbers © Pearson Education, Inc., publishing as Pearson Prentice Hall. • To subtract rational numbers, add the opposite. • Then following the rules for adding rational numbers. Example: ⫺9.25 ⫺ (⫺3.4) = ⫺9.25 ⫹ 3.4 ⫽ ⫺5.85 3 b 5 4 1 a2 3 b 5 6 3 Example: 4 2 a22 10 10 10 Find each sum. 1. 43.2 ⫹ 26.7 2. ⫺81.22 ⫹ 14.9 4. 2 5 1 3 4 9 9 5. 2 23 1 11 5 5 3. ⫺4.8 ⫹ (⫺53.5) 6. 26 1 1 a27 1 b 3 3 Find each difference. 7. 15.64 ⫺ 8.5 10. 6 2 5 5 6 Course 2 Lesson 1-6 8. ⫺0.392 ⫺ 0.26 11. 2 43 2 21 4 4 9. ⫺5.4 ⫺ (⫺1.6) 12. 27 4 2 a23 3 b 5 5 Reteaching 000200010271713722_CH01.qxd 2/13/13 8:50 PM Page 27 Name Class Reteaching 1-7 Date Multiplying Rational Numbers Remember these rules when multiplying rational numbers. 1. When both factors are positive, the product is positive. Multiply: a2 2 b a1 5 b 5 a 8 b a 13 b 5 104 5 4 1 3 8 3 8 24 3 2. When both factors are negative, the product is positive. © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Multiply: (4.35)(2.44) 10.614 3. When both factors have different signs, the product is negative. Multiply: 23 3 2 5 23 3 2 5 26 5 2 6 5 2 3 4 5 435 20 20 10 Find each product. Write the product in simplest form. 1. 2.8 0.05 2. 5 ? 2 8 5 3. 1.45 0.7 5 ? a2 3 b 12 10 4. 2 3 ? 7 5 8 5. (2.07)(4.9) 6. 7. 9.3(0.56) 8. 1 3 5 1 2 6 9. 0.006(3.75) 10. 2 12 3 5 3 Reteaching 11. 3.8 912 12. a22 3 b a21 b 5 4 Course 2 Lesson 1-7 000200010271713722_CH01.qxd 2/13/13 8:50 PM Page 31 Name Class Date Reteaching 1-8 Dividing Rational Numbers Divide: 3 3 4 1 2 . 4 5 All rights reserved. Divide: 38.25 1.5. 1. Rewrite the problem with a whole number divisor. 1. 5)38.25 T 1. Rewrite mixed numbers as improper fractions as needed. 15 4 7 4 5 2. Place the decimal point in the quotient. 1. 5.)38.2.5 2. Multiply by the reciprocal of the divisor. 15 ? 5 4 7 c c Move 1 place each. 3. Divide. Then check. 25.5 15)382.5 30 82 75 75 75 3. Multiply numerators. Multiply denominators. 15 ? 5 5 75 4 ?7 28 4. Simplify. 75 5 2 19 28 28 0 © Pearson Education, Inc., publishing as Pearson Prentice Hall. 25.5 15 382.5 ✔ Multiply to check. Find each quotient. Simplify your answers. 1. 1 5 4 5 8 8 2. 43.55 6.5 3. 4. 0.072 0.8 5. 212 4 4a21 1 b 5 15 6. 340.2 4.2 8. 12.6 0.21 9. 7. 2 15 4 1 2 224 4 5 25 2 71 4 21 3 5 10. 11.1 (–37) Reteaching Course 2 Lesson 1-8