Math. Focused Practice for Math Mastery. carsondellosa.com/spectrum GRADE. Positive and negative integers. Ratios and proportions

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1 Math GRADE 7 Focused Practice for Math Mastery Positive and negative integers Ratios and proportions Algebraic equations and inequalities Geometric problem-solving Probability and statistics Answer key carsondellosa.com/spectrum

2 Check What You Know Evaluate each expression. CHAPTER PRETEST. opposite of 4 opposite of 9 opposite of 0. opposite of opposite of 6 opposite of. opposite of opposite of 89 opposite of 8 4. u7u u 4u u8u. uu u 6u u 9u Identify the property of addition described as commutative, associative, or identity. 6. The sum of any number and zero is the original number. 7. When two numbers are added, the sum is the same regardless of the order of addends. 8. When three or more numbers are added, the sum is the same regardless of how the addends are grouped. a b 9. 7 ( 9) (7 ) ( 6) 0 (6 ) 7 6 ( 7). 0 Spectrum Math Check What You Know Chapter

3 CHAPTER PRETEST Check What You Know Add or subtract. Write fractions in simplest form. d ( ) 7 ( 4) 6. 8 ( ) ( 9) 7. 6 ( 4) 4 Solve each problem. 8. One box of clips weighs 4 ounces. Another box weighs 8 ounces. What is the total weight of the two boxes? The total weights is ounces. SHOW YOUR WORK Luggage on a certain airline is limited to pieces per person. Together, the pieces can weigh no more than 8 pounds. If a passenger has one piece of luggage that weighs pounds, what is the most the second piece can weigh? 9. The second piece can weigh pounds. 0. Mavis spends 4 hours on the bus every weekday (Monday through Friday). How many hours is she on the bus each week? 0. She is on the bus hours each week. Spectrum Math Check What You Know Chapter 6

4 Lesson. Understanding Absolute Value The absolute value of a number is a number that is the same distance from zero on a number line as the given number, but on the opposite side of zero and 8 are absolute value because they are the same distance from zero on opposite sides of the number line. Evaluate the expressions below.. opposite of 9 opposite of 7 opposite of. opposite of 8 opposite of 0 opposite of 0. opposite of 9 opposite of opposite of opposite of 96 opposite of 76 opposite of 6. opposite of opposite of 6 opposite of 7 6. opposite of opposite of 47 opposite of opposite of 6 opposite of 7 opposite of 8. opposite of opposite of 68 opposite of 9. opposite of 7 opposite of 99 opposite of opposite of 40 opposite of 44 opposite of 77. opposite of opposite of 66 opposite of 9. opposite of opposite of 0 opposite of 9 Spectrum Math Chapter, Lesson 7

5 Lesson. Absolute Values and Integers The absolute value of a number is the distance between 0 and the number on a number line. Remember that distance is always a positive quantity (or zero). Absolute value is shown by vertical bars on each side of the number. u 6u 6 uu Evaluate the expressions below.. u9u u 9u u 9u. uu u 99u u0u. u 76u u78u u 0u 4. u 400u u668u u 870u. uu u 6u u4u 6. u u u694u u 74u 7. u 6u u88u u67u 8. u4u u 90u u79u 9. u 8u u40u u 86u 0. u06u u7u u97u. uu u 86u u94u. u 44u u 7u u 9u Spectrum Math Chapter, Lesson 8

6 Lesson. Subtraction as an Inverse Operation Subtraction is the same as the process of adding the additive inverse, or opposite, of a number to another number ( 4) Write an equivalent equation using the additive inverse. a b ( 7) 8 ( ) ( ) 4 ( 6) ( 6) 6 ( ) ( 7) 4 ( ) ( 0) 94 ( 90) ( 0) 90 ( 76) Spectrum Math Chapter, Lesson 9

7 Lesson.4 Adding Fractions and Mixed Numbers To add fractions or mixed numbers when the denominators are different, rename the fractions so the denominators are the same Add. Write each answer in simplest form. d Spectrum Math Chapter, Lesson 4 0

8 Lesson. Adding Integers The sum of two positive integers is a positive integer The sum of two negative integers is a negative integer To find the sum of two integers with opposite signs, subtract the digit of lesser value from the digit of greater value and keep the sign of the greater digit ( ) Add. a b c d. 4 ( 4) ( 4) 4. ( ) ( ). ( ) ( ) ( ) 7 ( ) ( 7) 4 (7) 6. 8 ( 8) 8 ( 8) ( 6) 8. ( 6) ( 6) ( 7) ( 6) 0. 6 ( 4) ( 4) 6 4 Spectrum Math Chapter, Lesson

9 Lesson. Adding Integers To find the sum of two integers with different signs, find their abso lute values. Remember, absolute value is the distance (in units) that a number is from 0, expressed as a positive quantity. Subtract the lesser number from the greater number. Absolute value is written as z n z. The sum has the same sign as the integer with the larger absolute value , so the sum is negative. Add ( 4) 7 ( 9). 4 7 ( 6). 6 0 ( 4) ( 9) ( ). 4 4 ( 6) 7 ( 7) ( 9) 0 ( ) 8. ( ) ( 6) ( 6) ( ) Spectrum Math Chapter, Lesson

10 Lesson.6 Subtracting Integers NAME To subtract an integer, add its opposite. 7 (7) Subtract ( 6) ( ) 6 ( 7) 4. 6 ( 6) ( ) ( 9) 4 ( 8) ( ) 48 ( 47) 8 ( 7) 8. 9 ( 6) ( ) 9 ( ) 9. ( ) ( 40) ( ) Spectrum Math Chapter, Lesson 6

11 Lesson.6 Subtracting Integers NAME Subtract.. ( 7) 6 8 ( 0). 7 ( 7) ( ). 6 ( ) 4 ( 49) 0 ( 6) ( ). 49 ( 46) ( 0) ( ) 48 ( 47) 7. ( 0) 4 ( 0) 9 ( 47) ( 8) ( 4) 9. ( 4) ( 9) ( ) 4 ( 9). 8 ( 4) 4 8 ( 67). 6 ( ) 4 4 ( 7). ( ) 6 ( 9) 8 ( ) ( 9) Spectrum Math Chapter, Lesson 6 4