Download Place Value and Rounding – Do not use a

Section 1: Place Value and Rounding – Do not use a calculator for this section
Example: 1,234,567.890
1 – millions
2 – hundred thousands
3 – ten thousands
4 – thousands 5 – hundreds
6 – tens
7 – ones
9 – hundredths
8 – tenths
0 – thousandths
Example: Write the place value of the underlined digit: 3,427,894.492
Answer: 4 tenths or 0.4
Example: Round 23,561 to the nearest thousand
Answer: 24,000
Reminder:
If the number to the right of the place value is 5 or greater, round up.
Questions:
Write the place value of the underlined digit
1.1
6,665,161
_____________
1.4
5,488,685
_____________
1.7
13.27489
_____________
1.2. 8,366,524
1.3. 5,368,680
_____________
1.5 7,737,522
_____________
1.6 9,943,289
_____________
1.8 0.19489
_____________
1.9 55.32389
_____________
_____________
Round to the given place value
1.10
7,095 to the nearest hundred
1.11
____________
1.12
928.3472 to the nearest thousandth
____________
1.13
____________
1.14
23,561 to the nearest thousand
____________
837.4332 to the nearest tenth
9,323,585 to the nearest ten thousand
____________
1.15
34.7953 to the nearest hundredth
____________
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Section 2: Comparing and Ordering Numbers – Do not use a calculator for this section
Examples:
Reminders:
Read the problem from left to right
< means “less than”
> means “greater than”
You might change fractions to decimals before you compare
You might want to use a number line to make good comparisons
Questions:
Fill in the blank with the correct symbol (<, >, or =)
2.1
_____
2.2
2.4
_____
2.5
2.7
_____
2.8
2.10
_____
2.11
_____
_____
_____
_____
2.3
_____
2.6
_____
2.9
2.12
_____
_____
Write the following numbers in order from least to greatest
2.13
__________________________________________
2.14
__________________________________________
2.15
__________________________________________
2.16
__________________________________________
2.17
__________________________________________
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Section 3: Simplifying Fractions – Do not use a calculator for this section
Examples: Simplfy
The greatest common factor of
and
is
Dividing the numerator and denominator by
gives the answer of
Simplfy
The greatest common factor of
and
is
Dividing the numerator and denominator by
Reminders:
gives the answer of
A fraction is the same thing as division. That is, the division problem
equal to the fraction
. Or the fraction
is
is equal to the division problem
.
The greatest common factor is the largest whole number that divides evenly
into two other numbers
Unless specified otherwise, leave results as improper fractions instead of mixed
numbers (that is, leave a fraction as instead of
).
Questions:
Simplify the following fractions.
3.1
________
3.2
________
3.3
3.4
________
3.5
________
3.6
3.7
________
3.8
________
3.9
3.10
________
3.11
________
3.12
3.13
________
3.14
________
3.15
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Section 4: Fraction Computations – Do not use a calculator for this section
Examples:
Reminders:
When adding or subtracting, find the common denominator.
Multiplication can always be indicated either by a “dot” (like ) or by
parentheses. So
.
When multiplying, multiply numerators by each other and denominators by
each other. Simplify the result either by “cancelling” before multiplying or by
reducing the fraction you get as your result.
When dividing, multiply the first fraction by the reciprocal of the second fraction
(that is, flip the second fraction).
Change mixed numbers into improper fractions first, if necessary.
Questions:
Add the following fractions. Make sure your final answer is written in simplest form.
4.1
________
4.2
________
4.3
Subtract the following fractions. Make sure your final answer is written in simplest form.
4.4
________
4.5
________
4.6
Multiply the following fractions. Make sure your final answer is written in simplest form.
4.7
________
4.8
________
4.9
Divide the following fractions. Make sure your final answer is written in simplest form.
4.10
________
4.11
________
4.12
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Section 5: Converting Among Fractions, Decimals, and Percents – You may use a calculator for this
section
Examples: Convert
to a decimal:
Convert
to a percent:
Convert
to a fraction:
Reminders:
From a decimal to a percent: Multiply by 100 (or move the decimal two places
to the right).
From a percent to a decimal: Divide by 100 (or move the decimal two places to
the left.
Percents are always out of 100.
Questions:
Convert these fractions to decimals. Round to the nearest hundredth if necessary.
5.1
________
5.2
________
5.3
Convert these decimals to fractions. Write your final answer in simplest form.
5.4
________
5.5
̅
________
5.6
Convert these decimals to percents.
5.7
________
5.8
________
5.9
Convert these percents to decimals. Round to the nearest hundredth if necessary.
5.10
________
5.11
________
5.12
Convert these fractions to percents. Round to the nearest hundredth if necessary.
5.13
________
5.14
________
5.15
Convert these percents to fractions.
5.16
________
5.17
________
5.18
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Section 6: Integer Operations – Do not use a calculator for this section
Examples:
Reminders:
When adding numbers with like signs, add the digits and keep the sign.
When combining numbers with different signs, subtract the smaller digit from
the larger and use the sign that went with the larger digit.
When multiplying or dividing, if the signs are the same, the result is positive; if
the signs are different, the result is negative.
Questions:
Simplify the given expression.
6.1
6.3
6.5
_______
_______
_______
6.7
6.9
_______
_______
6.11
6.13
6.15
6.17
6.19
_______
_______
_______
_______
_______
6.23
6.25
6.27
6.4
6.6
6.8
6.10
6.12
6.14
_______
6.21
6.2
_______
_______
_______
6.16
6.18
6.20
6.22
6.24
6.26
6.28
_______
_______
_______
_______
_______
_______
_______
_______
_______
_______
_______
_______
_______
_______
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Section 7: Powers and Exponents – You may use a calculator for this section
Examples: Write
as a product (a multiplication)
Write
as a power
Calculate
Reminders:
In the expression
whole expression
,
is called the base and
is called a power.
is called the exponent. The
When expanding a power into a product (a multiplication problem), the base is
multiplied by itself the number of times shown as the exponent.
When writing a product as a power, the number being multiplied by itself
becomes the base, and the number of times it is multiplied by itself becomes
the exponent.
To calculate a power, use the “^” key on your calculator (if it has one) or treat
the power as a product and enter the multiplication problem on your calculator.
Questions:
Write the given power as a product.
7.1
___________________
7.2
___________________
7.3
___________________
7.4
___________________
7.6
_______
Write the given product as a power.
7.5
_______
7.7
_______
7.8
_______
Calculate the given power.
7.9
7.12
_______
_______
7.10
_______
7.11
_______
7.13
_______
7.14
_______
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Section 8: Order of Operations – Do not use a calculator for this section
Examples:
Reminders:
Some of you probably use the mnemonic “PEMDAS” (for “parentheses,
exponents, multiplication, division, addition, subtraction”) to remember the
order. Instead, we will use:
1.
2.
3.
4.
Grouping symbols (), [], {}
Exponents and radicals (such as square roots)
Multiply or divide from left to right
Add or subtract from left to right
The reason we’ll use that instead of PEMDAS is that multiplication and division
have the same priority, as do addition and subtraction. It is not true that
multiplication always comes before division or additional always comes before
subtraction.
Questions:
Simplify the given expression.
8.1
8.3
8.5
_______
8.2
_______
8.4
_______
8.6
8.7
_______
8.8
8.9
_______
8.10
8.11
8.13
8.15
_______
_______
_______
8.12
8.14
8.16
_______
_______
_______
_______
_______
_______
_______
_______
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Section 9: Graphing – Do not use a calculator for this section
Examples: Plot the following points and indicate which quadrant each is in or which axis
each is on
A
B
A
C
C
D
E
Point A is in Quadrant I
Point B is in Quadrant IV
D
Point C is in Quadrant II
B
Point D is on the -axis
Point E is on the -axis
E
Identify the ordered pair for each labeled point and indicate which quadrant each is
in or which axis each is on
A
Point A is at
D
Point B is at
E
C
B
and is on the -axis
and is in Quadrant III
Point C is at
and is in Quadrant IV
Point D is at
and is in Quadrant II
Point E is at
and is on the -axis
Reminders:
The coordinate plane is divided into four regions by the -axis
(which is horizontal) and the -axis (which is vertical). The axes
intersect at the origin.
The four regions are called quadrants and are labeled using
Roman numerals I, II, III, and IV.
(Reminders continue on the next page)
10
The location of a point on the coordinate plane is indicated by an ordered pair,
written in the form
.
If the first coordinate (or -coordinate) in the ordered pair is positive, it
indicates the point is right of the origin; if it is negative, the point is left of the
origin.
If the second coordinate (or -coordinate) in the ordered pair is positive, it
indicates the point is above the origin; if it is negative, the point is below the
origin.
Questions:
Plot the following points and indicate which Quadrant each is in or which axis each is on.
Quadrant/axis
Point A:
__________
Point B:
__________
Point C:
__________
Point D:
Point E:
Point F:
__________
__________
__________
Point G:
__________
Point H:
__________
Point J:
__________
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Identify the ordered pair for each labeled point and indicate which Quadrant each is in or
which axis each is on.
A
Quadrant/axis
G
J
B
D
H
F
C
E
Point A:
_________
Point B:
_________
Point C:
_________
Point D:
_________
Point E:
_________
Point F:
_________
Point G:
_________
Point H:
_________
Point J:
_________
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Section 10: Evaluating Expressions – Do not use a calculator for this section
Examples: Evaluate the following expressions when
Evaluate this expression when
and
Reminders: To evaluate something means to find its value.
To evaluate an expression, replace any variables with their given values then use
order of operations to calculate the numeric answer.
Questions:
Evaluate the following expressions given that
10.1
10.4
10.7
10.10
10.13
________
________
________
________
________
10.2
,
________
, and
.
10.3
10.5
________
10.6
10.8
________
10.9
10.11
10.14
________
________
10.12
10.15
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