1 5 Integer Operations
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1 1 5 Integer Operations Positive and Negative Integers A glance through any newspaper shows that many quantities are expressed using negative numbers. For example, negative numbers show below-zero temperatures. Whole numbers greater than zero are called positive integers. Whole numbers less than zero are called negative integers. Here is the set of all integers: {..., 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5,...} The integer 0 is neither positive nor negative. A number that has no sign is assumed to be positive. Write an integer to describe the situation. 1 3 below zero 2 a gain of $250 Opposites of Integers Integers can describe opposite ideas. Each integer has an opposite. The opposite of a gain of 5 pounds is a loss of 5 pounds. The opposite of +5 is -5. The opposite of spending $3 is earning $3. The opposite of -3 is +3. Write the opposite of each integer Integer Operations 87
2 1 5 INTEGER OPERATIONS Comparing and Ordering Integers Remember that when you compare numbers, the first number is either equal to (=), greater than (>), or less than (<) the second number. You can use a number line to compare and order integers. Comparing Integers A lesser number appears to the left of a greater number on a number line is to the right of -4. Therefore, 2 > -4. You can also write -4 < 2. Replace the with < or > to make a true sentence Ordering Integers You can also use a number line to order several integers. Integers are ordered from least to greatest from left to right. EXAMPLE Ordering Integers Order 8, -1, -8, and 6 from least to greatest. Graph the numbers on a number line List the integers as they appear from left to right. The order from least to greatest is -8, -1, 6, Order 5, -3, -12, and 25 from least to greatest. 12 Order -1, 9, -8, and 6 from greatest to least. 88 HotTopics
3 Adding and Subtracting Integers You can use a number line to model adding and subtracting integers. EXAMPLE Adding and Subtracting Integers Solve Solve (-4) = = 2 Solve -2 + (-3). Solve (-3) = = -4 Adding integers with the same sign Adding integers with different signs Subtracting integers Adding or Subtracting Integers Rules The sum of two positive integers is always positive. The sum of two negative integers is always negative. The sum of a positive integer and a negative integer is sometimes positive, sometimes negative, and sometimes zero. Examples = (-2) = (-2) = = = 0 To subtract an integer, add its opposite. 6-1 = 6 + (-1) -4-5 = -4 + (-5) -8 - (-9) = (-6) (-7) (-3) Integer Operations 89
4 1 5 INTEGER OPERATIONS Multiplying and Dividing Integers Multiply and divide integers as you would whole numbers. Then use these rules for writing the sign of the answer. The product of two integers with like signs is positive. The quotient is also positive. 2 3 = 6-4 (-3) = (-4) = 3 When the signs of the two integers are different, the product is negative. The quotient is also negative = = = -40 EXAMPLE Multiplying and Dividing Integers Multiply 3 (-2). 3 (-2) Multiply the integers. -6 Remember that when the signs of the two integers are different, the product is negative. So, 3 (-2) = -6. Divide Divide. -4 Remember that when the signs of the two integers are different, the quotient is negative. So, -8 2 = -4. Find the product or quotient (-2) (-4) (-3) HotTopics
5 1 5 Exercises Write the opposite of each integer Add or subtract (-6) (-4) (-3) (-6) (-7) (-8) (-2) (-9) Find the product or quotient (-6) (-4) (-9) (-3) (-7) Compute. 25. [-6 (-2)] [2 (-4)] 27. [-3 (-3)] [3 + (-4)] 29. [-7 (-3)] [6 - (-2)] 31. What can you say about the sum of two negative integers? 32. The temperature at noon was 10 F. For the next 3 hours it dropped at a rate of 3 degrees an hour. First express this change as an integer. Then give the temperature at 3:00 p.m. 33. What can you say about the product of a positive integer and a negative integer? Integer Operations 91
6 1 Numbers and Computation WHAT HAVE YOU LEARNED? What have you learned? Problem Set You can use the problems and the list of words that follow to see what you learned in this chapter. You can find out more about a particular problem or word by referring to the topic number (for example, Lesson 1 2). Give the value of the 8 in each number. (Lesson 1 1) , ,122, Write 36,514 using expanded form. (Lesson 1 1) 4. Write in order from greatest to least: 243,254; 283,254; 83,254; and 93,254 (Lesson 1 1) 5. Round 46,434,482 to the nearest ten, thousand, and million. (Lesson 1 1) Solve. (Lesson 1 2) (5 4) , Solve using mental math. (Lesson 1 2) ( ) Use parentheses to make each expression true. (Lesson 1 3) = = 40 Is it a prime number? Write yes or no. (Lesson 1 4) Write the prime factorization for each number. (Lesson 1 4) Find the GCF for each pair of numbers. (Lesson 1 4) and and and HotTopic 1
7 Find the LCM for each pair of numbers. (Lesson 1 4) and and and What is the divisibility rule for 10? Is 2,530 a multiple of 10? (Lesson 1 4) Write the opposite of each integer. (Lesson 1 5) Add or subtract. (Lesson 1 5) (-9) (-4) (-2) (-12) Compute. (Lesson 1 5) (-6) (-12) (-9) 41. (-4 2) (-5) [-6 + (-6)] [4 - (-9)] 44. What can you say about the quotient of a positive integer and a negative integer? (Lesson 1 5) HotWords approximation (Lesson 1 1) Associative Property (Lesson 1 2) common factor (Lesson 1 4) Commutative Property (Lesson 1 2) composite number (Lesson 1 4) Distributive Property (Lesson 1 2) divisible (Lesson 1 4) expanded form (Lesson 1 1) factor (Lesson 1 4) greatest common factor (Lesson 1 4) Write definitions for the following words. least common multiple (Lesson 1 4) multiple (Lesson 1 4) negative integer (Lesson 1 5) negative number (Lesson 1 5) number system (Lesson 1 1) operation (Lesson 1 3) PEMDAS (Lesson 1 3) place value (Lesson 1 1) positive integer (Lesson 1 5) prime factorization (Lesson 1 4) prime number (Lesson 1 4) round (Lesson 1 1) Venn diagram (Lesson 1 4) Numbers and Computation 93
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14 Number/Computation addend Any number being added algorithm A step-by-step method for computing array A picture that shows a number of items arranged in rows and columns to form a rectangle associative
The School District of Palm Beach County Fourth Grade Mathematics Scope st Trimester
Number and Operations in Base Ten Generalize place value understanding for multi-digit whole numbers. NBT.1.1 NBT.1.2 NBT.1.3 Recognize that in a multi-digit whole number, a digit in one place represents
Common Core State Standards Mathematics (Subset K-5 Counting and Cardinality, Operations and Algebraic Thinking, Number and Operations in Base 10)
Kindergarten 1 Common Core State Standards Mathematics (Subset K-5 Counting and Cardinality,, Number and Operations in Base 10) Kindergarten Counting and Cardinality Know number names and the count sequence.
Georgia Performance Standards for Fifth Grade
Georgia Performance Standards for Fifth Grade Mathematics Terms for Georgia s (CRCT) Criterion Reference Competency Test Administered in April of Each Year Parents: We are counting on you to help us teach
Working with Algebraic Expressions
2 Working with Algebraic Expressions This chapter contains 25 algebraic expressions; each can contain up to five variables. Remember that a variable is just a letter that represents a number in a mathematical