Rounding and Estimating 1'5

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Rounding and Estimating (1.5)

• Rounding a whole number means approximating.

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23 rounded to the nearest ten is 20.
48 rounded to the nearest ten is ____.
15 rounded to the nearest ten is 20.
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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.
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Dividing Whole Numbers (1.7)
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Division is the process of separating a quantity
into equal parts.
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Which of the following expressions are equivalent?

• Dividend 24 (number being divided)
• Divisor 6 (number doing the dividing)
• Quotient 4 (answer from division)

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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.
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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).
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Here are some key words and phrases that indicate
the operation of division.
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How do you find an average?
A students 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.
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Exponents and Order of Operations
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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
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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
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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.
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To evaluate exponential notation, we write the
expression as a product and then find the value
of the product.
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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.

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Introduction to Variables and Algebraic
Expressions
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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
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Keywords and phrases suggesting addition,
subtraction, multiplication, or division.