Rounding and Estimating (1.5)

1. Rounding and Estimating (1.5) Rounding a whole number means approximating.

2. 20 23 30 40 48 50 10 15 20 23 rounded to the nearest ten is 20. 48 rounded to the nearest ten is ____. 15 rounded to the nearest ten is 20.

3. Rounding Whole Numbers to a Given Place Value • Step 1. Locate the digit to the right of the given place value. • Step 2. If this digit is 5 or greater, add 1 to the digit in the given place value and replace each digit to its right by 0. OR • Step 2. If this digit is less than 5, replace it and each digit to its right by 0.

4. Making estimates is often the quickest way to solve real-life problems when their solutions do not need to be exact.

5. Dividing Whole Numbers (1.7)

6. quotient divisor dividend Division is the process of separating a quantity into equal parts.

7. Which of the following expressions are equivalent? Dividend = 24 (number being divided) Divisor = 6 (number doing the dividing) Quotient = 4 (answer from division)

8. 1 6 = ¸ = 1 5 5 7 7 1 6 5 6 = ¸ = 6 1 5 7 1 7 1 Division Properties of 1 The quotient of any number and that same number is 1. The quotient of any number and 1 is that same number.

9. 0 0 = ¸ = 0 5 0 0 7 0 6 6 ¸ 0 5 7 0 0 Division Properties of 0 The quotient of 0 and any number (except 0) is 0. The quotient of any number and 0 is not a number. We say that are undefined (u).

10. Here are some key words and phrases that indicate the operation of division.

11. How do you find an average? A student’s prealgebra grades at the end of the semester are: 90, 85, 95, 70, 80, 100, 98, 82, 90, 90. How do you find his average? Find the sum of the scores and then divide the sum by the number of scores.

12. Exponents and Order of Operations

13. _________________ ________ An exponent is a shorthand notation for repeated multiplication. 3 • 3 • 3 • 3 • 3 3 is a factor 5 times Using an exponent, this product can be written as

14. exponent base This is called exponential notation. The exponent, 5, indicates how many times the base, 3, is a factor. Read as “three to the fifth power” or “the fifth power of three.” 3 • 3 • 3 • 3 • 3 3 is a factor 5 times

15. 4 = is read as “four to the first power.” 4  4 = is read as “four to the second power or four ____________.” 4  4  4 = is read as “four to the third power or four ___________.” 4  4  4  4 = is read as “four to the fourth power.”

16. =3 • 3 • 3 • 3 • 3 = 243 To evaluate exponential notation, we write the expression as a product and then find the value of the product.

17. Order of Operations • 1. Do all operations within grouping symbols such as parentheses or brackets. • Evaluate any expressions with exponents. • Multiply or divide in order from left to right. • 4. Add or subtract in order from left to right.

18. Introduction to Variables and Algebraic Expressions

19. A combination of operations on letters (variables) and numbers is called an algebraic expression. Algebraic Expressions 5 + x 6  y 3  y – 4 + x 4x means 4 x and xy means x  y

20. Keywords and phrases suggesting addition, subtraction, multiplication, or division.