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Numbers, Operations and Properties

Numbers, Operations and Properties. Math 20 Pre Algebra. Numbers Operations & Properties. Casey, Eileen and Morgan are all working on a chemistry assignment. At one point they both multiply 347 ∙ 28. Casey’s calculator shows 986 while Morgan’s calculator shows 9632. Both have wrong answers !

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Numbers, Operations and Properties

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  1. Numbers, Operations and Properties Math 20 Pre Algebra

  2. Numbers Operations & Properties

  3. Casey, Eileen and Morgan are all working on a chemistry assignment. At one point they both multiply 347 ∙ 28. Casey’s calculator shows 986 while Morgan’s calculator shows 9632. Both have wrong answers! Casey knows her answer is wrong because hundreds times tens must be at least in the thousands, and her answer was less than one thousand. Morgan knows his answer is wrong because the ones place for 347 ∙ 28 must be the same value as the ones place in 7 ∙ 8, and 7 ∙ 8 ends in 6, not 2.

  4. In this section we study how we use our numbering system, along with the properties of operations, to check our results when using technology. We also study mental math strategies that improve our speed in calculating so that we only use technology when it saves time. Numbers, Operations & Properties Place Value

  5. Place Value Chart

  6. write cents as a fraction in hundredths of a • dollar i.e. $0.36 • use a hyphen between the digits in the tens and ones • places i.e. “fifty-four” is 54 • the only correct place for the word “and” is at the • decimal point Numbers, Operations & Properties Writing Numbers in English

  7. Write each of these numbers in English. a. 2015 $1510.71 33,000,801.90 SOLUTION a) Two thousand fifteen b) one thousand five hundred ten dollars and seventy-one cents or fifteen hundred ten dollars and seventy-one cents. c) thirty-three million eight hundred one and ninety hundredths

  8. Write each of these numbers in English. a. 2,055 $403.19 307,086,460 SOLUTION a) Two thousand fifty-five b) Four hundred three dollars and nineteen cents c) Three hundred seven million eighty-six thousand four hundred sixty

  9. Laurie and Matt both measured the length and width of their yard. Then they calculated the perimeter of their yard separately. They used different methods to calculate but their answers were the same. 100 ft 75 ft SOLUTION Lauri: double both the width and length and add these (2∙75)+(2∙100). 150 + 200 = 350. Matt: add length and width first then double this sum: 2∙(75+100)

  10. Perimeter Formulas Both methods are formulas for finding the perimeter. The formula for the perimeter can be written in two ways: P=2∙l+2∙w or P=2∙(l+w) . Together these formulas are one example that the distributive property can always be relied upon:

  11. Mental Math Algorithms: Addition Janis had $183 in her bank account. She deposits a check for $315. What is her checking account balance? SOLUTION Adding left to right uses the commutative and associative properties to regroup by place value:

  12. Compensate and Adjust You are carrying a pocketful of change that you would like to get rid of. You are buying two items that cost $7.65 and $2.59. What is the exact amount you need to give the cashier? SOLUTION Adding left to right uses the commutative and associative properties to regroup by place value:

  13. Mental Math Algorithms: SUBTRACTION Mike wants to withdraw $328 from his savings account that now has $1,689 available. What will his new balance be? SOLUTION We can subtract from left to right, and we can subtract using a compensate and adjust algorithm for subtraction.

  14. a. Add from left to right: 342 + 523 Add using compensation: 475 + 387 SOLUTION 300+500 = 800 800+(40+20)=860 860+(2+3)=865 b) (475+25) + (387-25) = 500+362 = 863

  15. a. Subtract from left to right: 3,945 – 2,821 Compensate and adjust to subtract: 1,312 – 659 (Hint: Round 659 up to the leading digit!) SOLUTION 3000-2000=1000 1000+(900-800)=1100 1100+(40-20)=1120 1120+(5-1)=1124 b) 1312-659 = (1312+41) - (659+41) = 1353-700 = 653

  16. Mental Math Algorithms: Multiplication Penny finds a job in Seattle and is budgeting for the month. Money is tight. In her budget she plans to spend $8 per day for transportation to work. She will work 23 days out of the month. How much will she spend on transportation? SOLUTION Here we can choose to multiply left to right.

  17. Mental Math Algorithms: Division Divide 417 by 5 SOLUTION Because multiplying by 5 can be changed to multiplying by 10 and then dividing by 2, to divide by 5 mentally, first divide by 10 and then multiply by 2. .

  18. Multiply: 486∙5 Divide: 146÷5 SOLUTION (486*10) ÷ 2 = 4860 ÷ 2 = 2430 b) (146÷10)*2 = 14.6*2 = 29.2

  19. Homework Pgs. 53-55 1-53 odd

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