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Operations and Properties 1A Section a Family Letter: Whole Numbers and Exponents

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Operations and Properties 1A Section a Family Letter: Whole Numbers and Exponents Name ________________________________________ Date __________________ Class__________________ SECTION Operations and Properties 1A Section A Family Letter: Whole Numbers and Exponents Dear Family, Vocabulary In this chapter, the student will be using estimation to find These are the math sums, differences, products, and quotients. He or she may words we are learning: round to an indicated place value or use compatible numbers base the number that is to estimate an answer to a problem. raised to an exponent Remember: compatible numbers When rounding, look at the digit to the right of the place to numbers that are close which you are rounding. to the numbers in the • If that digit is 5 or greater, round up. problem and that may help you do mental • If that digit is less than 5, round down. math dividend the Estimate the sum by rounding to the place value number to be divided indicated. divisor the number by which the dividend is 10,826 16,115; thousands divided 11,000 8 5. Round 10,826 up. 16,000 1 5. Round 16,115 down. estimate a number close to the exact 27,000 answer that is easier to The sum is about 27,000. find than the exact answer In this example, use compatible numbers to estimate a product. Compatible numbers are close to the numbers in exponent a number the problem, and they can help you do math mentally. that tells how many times to multiply the Mike earns $8.85 an hour at the hardware store. He base by itself worked 29 hours last week. About how much money did exponential form Mike earn last week? a number that is written To find out how much money Mike earned, multiply his wage with a base and an exponent and the number of hours he worked. overestimate $8.85 29 9 30 9 and 30 are compatible an estimate that is because they can be greater than the exact multiplied mentally. answer 9 30 270 This is an overestimate. underestimate Mike earned about $270 last week. an estimate that is less than the exact answer Later in this chapter, students learning, long division can use these estimation skills to check quotients. © Houghton Mifflin Harcourt Publishing Company 1-1 Holt McDougal Mathematics Name ________________________________________ Date __________________ Class__________________ SECTION Operations and Properties 1A Section A Family Letter: Whole Numbers and Exponents continued The student is also learning to find the value of numbers in exponential form. A number in exponential form is written with a base and an exponent. The exponent tells how many times to multiply the base by itself. 53 is written 5 5 5. 5 is the base. 3 is the exponent. 53 5 5 5 125 The table shows the base 10 with exponents 1 through 4. Exponential Read Multiply Value Form 101 “10 to the 1st power” 10 10 “10 squared,” or “10 102 10 10 100 to the 2nd power” “10 cubed,” or “10 to 103 10 10 10 1,000 the 3rd power” 104 “10 to the 4th power” 10 10 10 10 10,000 Write each expression in exponential form. A. 2 2 2 23 2 is a factor 3 times. B. 7 7 7 7 7 75 7 is a factor 5 times. Find each value. A. 36 Base 3 is a factor 6 times. 36 3 3 3 3 3 3 729 B. 45 Base 4 is a factor 5 times. 45 4 4 4 4 4 © Houghton Mifflin Harcourt Publishing Company 1,024 You have an important role in building the student’s confidence and understanding in mathematics. Your continual support will make a noticeable difference in the student’s learning. Sincerely, 1-2 Holt McDougal Mathematics Name ________________________________________ Date __________________ Class__________________ SECTION Operations and Properties 1A Section A At-Home Practice: Whole Numbers and Exponents Estimate each sum or difference by rounding to the place value indicated. 1. 63,765 32,874; ten thousands _________________________________________________________________________________________ 2. 2,347 5,981; thousands _________________________________________________________________________________________ 3. 54,879 89,201; ten thousands _________________________________________________________________________________________ 4. 7,803 2,963; thousands _________________________________________________________________________________________ 5. Ms. Tran plans to buy a notebook for each of her students. She has 5 classes with 28 students in each class. Estimate the number of notebooks Ms. Tran should buy. _________________________________________________________________________________________ Write each expression in exponential form. 6. 6 6 ___________________________ 7. 2 2 2 2 2 _________________ 8. 8 8 8 8 _____________________ 9. 4 4 4 _______________________ Find each value. 4 3 2 10. 3 _________________ 11. 7 _________________ 12. 4 _________________ 1 5 3 13. 9 _________________ 14. 5 _________________ 15. 6 _________________ 16. Bobby started with one pet rabbit. Every 6 months the number of rabbits tripled. How many rabbits were there after 2 years? Explain your answer using exponents. (Hint: There are 2 six-month periods every year.) _________________________________________________________________________________________ © Houghton Mifflin Harcourt Publishing Company Answers: 1. 30,000 2. 8,000 3. 140,000 4. 5,000 5. 150 notebooks 6. 62 7. 25 8. 84 9. 43 10. 81 11. 343 12. 16 13. 9 14. 3,125 15. 216 16. 34 or 81 rabbits in 2 years 1-3 Holt McDougal Mathematics Name ________________________________________ Date __________________ Class__________________ SECTION Operations and Properties 1A Section A Family Fun: Exponential Excitement Materials Gameboard 1 number cube 2–4 game pieces Directions 1. The first player to roll a 4 goes first. 2. Players take turns rolling the number cube. If they roll an odd number, they move 1 space. If they roll an even number, they move 2 spaces. 3. The space they land on is the exponent. The number on the cube is the base. The player must find the value of the number in exponential form. 4. The players must keep track of these values and find the sum. 5. When the players land on the finish space, the player with the greatest sum is the winner. © Houghton Mifflin Harcourt Publishing Company 1-4 Holt McDougal Mathematics Name ________________________________________ Date __________________ Class__________________ SECTION Operations and Properties 1B Section B Family Letter: Using Whole Numbers Dear Family, Vocabulary The student will practice following the order of operations. These are the math When there is more than one operation involved in a problem, words we are learning: the student will need to know which operation to do first. The Associative Property steps your child needs to follow to solve multi-operational When you add or problems are listed below. multiply, you can group Order of Operations the numbers together in any combination. 1. Perform operations in parentheses. Commutative Property 2. Find the values of numbers with exponents. You can add numbers in 3. Multiply or divide from left to right as ordered in the any order and multiply problem. numbers in any order. 4. Add or subtract from left to right as ordered in the Distributive Property problem. If you multiply a sum by a number, you will get Simplify the expression 10 6(7 2). the same result if you 10 6(7 2) Perform the operation inside the multiply each addend by parentheses. that number and then 10 6 5 Multiply. add the products. 10 30 Add. numerical expression 40 a mathematical phrase that includes only Simplify the expression of 27 32 3 5. 2 numbers and operation 27 3 3 5 Find the values of numbers with symbols exponents first. order of operations 27 9 3 5 Multiply or divide from left to 1. Perform operations in right in order. parentheses. 3 15 Add. 2. Find the values of 18 numbers with exponents. 3. Multiply or divide from left to right as ordered in the problem. 4. Add or subtract from left to right as ordered in the © Houghton Mifflin Harcourt Publishing Company problem. 1-30 Holt McDougal Mathematics Name ________________________________________ Date __________________ Class__________________ SECTION Operations and Properties 1B Section B Family Letter: Using Whole Numbers continued The student will be learning three number properties he or she simplify find the value can use to solve problems mentally. of a numerical expression The Commutative Property is an ordering property. You can add or multiply numbers in any order. addition multiplication 5 7 7 5 4 8 8 4 The Associative Property is a grouping property. You may group the numbers in any order as long as you are only adding or only multiplying. The numbers stay in place and only the grouping symbols move. addition multiplication (3 5) 2 3 (5 2) (5 9) 4 5 (9 4) The Distributive Property allows you to multiply a sum by a number two different ways. 3 (4 6) 3 (10) 30 or 3 (4 6) (3 4) (3 6) 12 18 30 Sincerely, © Houghton Mifflin Harcourt Publishing Company 1-31 Holt McDougal Mathematics Name ________________________________________ Date __________________ Class__________________ SECTION Operations and Properties 1B Section B At-Home Practice: Using Whole Numbers Simplify each expression. 2 2 2 1. 5 6 3 (5 9) 2. 8 (9 3) 10 3. 4 (16 2 8) ________________________ _______________________ ________________________ 4. 3 10 6 (2 3) 5. 7 42 5 6. (4 2)2 8 2 ________________________ _______________________ ________________________ Use mental math to find each sum or product. 7. 5 12 15 8 8. 10 2 3 5 9. 49 64 11 26 ________________________ _______________________ ________________________ 10. 5 11 2 11. 17 8 22 3 12. 63 14 7 36 ________________________ _______________________ ________________________ Use the Distributive Property to find each product. 13. 7 35 14. 9 41 15. 3 73 ________________________ _______________________ ________________________ 16. 4 17 17. 8 64 18. 6 92 ________________________ _______________________ ________________________ Use mental math to solve the following problems? 19.
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