Download PRE-ALGEBRA A REVIEW OF CH 6.1-6.4 CH 6.1-6.4 TEST

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PRE-ALGEBRA A
REVIEW OF CH 6.1-6.4
CH 6.1-6.4 TEST ON
THURSDAY 4/17
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ADDING AND SUBTRACTING FRACTIONS
WITH A COMMON DENOMINATOR
ADDING: ADD THE NUMERATORS AND WRITE THE
SUM OVER THE DENOMINATOR. SIMPLIFY.
EXAMPLE:
7 + 1 = 8 = 2
12
12
12
3
SUBTRACTING: SUBTRACT THE NUMERATORS AND
WRITE THE DIFFERENCE OVER THE
DENOMINATOR. SIMPLIFY.
EXAMPLE:
9 - 4 = 5 = 1
15 15
15
3
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ADDING MIXED NUMBERS WITH A COMMON DENOMINATOR
STEP 1: ADD THE WHOLE NUMBERS.
STEP 2: ADD THE FRACTIONS.
STEP 3: SIMPLIFY THE MIXED NUMBER.
EXAMPLE:
6
79
1
4
9
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SUBTRACTING MIXED NUMBERS WITH A
COMMON DENOMINATOR
STEP 1: REWRITE THE MIXED NUMBERS AS IMPROPER
FRACTIONS.
STEP 2: SUBTRACT THE FRACTIONS.
STEP 3: SIMPLIFY.
EXAMPLE:
ANSWER: 7/5 = 1 2/5
35 1
1
4
5
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ADDING OR SUBTRACTING FRACTIONS WITH
DIFFERENT DENOMINATORS
STEP 1: FIND THE COMMON DENOMINATOR.
STEP 2: REWRITE THE ORIGINAL FRACTION USING THE
COMMON DENOMINATOR.
STEP 3: THEN ADD OR SUBTRACT.
EXAMPLE:
ANSWER: 1/21
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Example:
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3
4
-1
6
Method 1: Product of Denominators
3x6
18
4x6
24
-1 x 4
+ 6x4
-4
24
14
24
2
2
7
12
Method 2: Using LCM as Least Common Denominator (LCD)
LCM = LCD = 12
+
3x3
4x3
9
12
-1 x 2
6x2
-2
12
7
12
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REVIEW ...
HOW TO FIND THE PERIMETER AND AREA OF SHAPES SUCH
AS TRIANGLE, SQUARE, RECTANGLE.
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MULTIPLYING FRACTIONS
To multiply 2 or more fractions, multiply the numerators
straight across and multiply the denominators straight
across. Then simplify.
Example:
4
3
12
7
6
42
2
7
6
Sometimes, you may want to CROSS CANCEL to simplify
the fractions before multiplying the numerators and
denominators.
Example:
6x
11
22
15
2
6x
1 11
2
22
15 5
4x
5
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MULTIPLYING BY A WHOLE NUMBER
When multiplying by a whole number, rewrite the
whole number as a fraction. Then multiply across
and simplify.
Example:
Example:
4
5
4
5
6
12
5y
8
6
1
3
12
1
24
5
5y
8 2
4
15y
2
* Keep the improper fraction when variables are involved.
4
5
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MULTIPLYING BY A MIXED FRACTION
When multiplying by a mixed fraction, change the mixed
number to an improper fraction. Then multiply across and
simplify.
3
Example:
27
7
2
9
12
1
18 25
8
2
5
10
2 10
HOW TO CHANGE A MIXED NUMBER
TO AN IMPROPER FRACTION
1
18
9
8
Multiply the whole number and
denominator. Add the product to
the numerator. This becomes the
NEW NUMERATOR. The
denominator remains the same.
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HOW TO FIND THE MULTIPLICATIVE
INVERSE (RECIPROCAL) OF A NUMBER
To find the reciprocal of a fraction, flip the numerator and
denominator.
Example:
The reciprocal of
5
8
is
8
5
To find the reciprocal of a mixed number, first change the mixed
number to an improper fraction. Then flip the numerator and
denominator.
Example: The reciprocal of
2
3
is
4
4
11
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MULTIPLYING WITH PERCENTS
FINDING THE PERCENT OF A NUMBER
Step 1: Rewrite the percent as a decimal or fraction.
Step 2: Multiply the numbers.
REMEMBER that "of" in math means "to multiply"
Example: 150% of 38
= 1.5 (38)
= 57
REVIEW how to change percents to decimals and fractions
(lesson 5.7).
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MULTIPLYING WITH PERCENTS
REVIEW how to calculate sales tax, tip, and commission.
Example: the price of a new bike is $310. Find the total cost
if you have to pay 6.5% sales tax on the bike. (What is 6.5%
of $310?)
Example: The amount of a dinner check is $48.50. About
how much should you leave the server as a 15% tip? (What
is 15% of $48.50?)
Example: A realtor charges a commission of 6%. What was
the amount of commission on a property that sold for
$250,000? (What is 6% of $250,000?)
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HOMEWORK
A1: TB PG. 314-315 #1-26
CH 6.1-6.4 TEST ON THURSDAY 4/17
BASIC CALCULATORS ALLOWED. THIS
SCORE WILL COUNT AS A TEST!