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Chapter 5
Changing fractions to mixed numbers
To change a fraction to a mixed number, divide the numerator by the denominator
This is the WHOLE number. the remainder is the new numerator over the same
denominator.
Changing mixed numbers to fractions
To change a mixed number
to a fraction, "Walk Around" Start with the denominator and go around "clockwise"
Multiply the denominator by the whole number
Then add the numerator to this number.
This is your new numerator over the same denominator.
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Notes 5-1
Comparing and Ordering Rational Numbers
Multiple means MULTIPLY x1, x2,
x3,
...
To find the LCM (least common multiple) list the multiples of each (NO – NOT – DO NOT DO)
List the multiple of the LARGER NUMBER ONLY and find the first number the smaller “goes into”
example
6 = (doesn’t matter)
9 = 9, 18, 27, . . .
6 GOES IN TO 18, so 18 is the LCM. DONE
WARNING! (If you JUST multiply both numbers together . . .your new denominator will be 56!)
To compare fractions – change them to fractions with the same denominator first.
example
2/3 = ? / 12
(Whatever you multiply the denominator by,
3/4 = ? / 12
you have to multiply the numerator by also.)
To make an equivalent fraction multiply the top and bottom by the same number.
or divide the top and bottom by the same number.
Notes 5-2
Fractions and Decimals
To change a fraction to a decimal – DIVIDE the NUMERATOR by the DENOMINATOR
3/4 = 3 ÷ 4 = 0.75 (This is a TERMINATING decimal. It ends.)
__
1/3 = 1 ÷ 3 = 0.3333333333 . . . (This is a REPEATING decimal. It keeps going.) = 0.33
To change a decimal to a fraction –
put the decimal over a 1 and put zeros for each decimal place, then simplify.
example 0.1 2 5 =
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Fraction = Decimal
1
2
=
Copy CHART
0.5
1
8
=
0.25
2
10
=
0.125
1
10
=
0.1
=
0.2
1
3
=
0.33
2
8
2
3
=
0.66
3
8
=
0.375
3
10
=
0.3
1
4
=
0.25
4
8
=
0.5
4
10
=
0.4
2
4
=
0.5
5
8
=
0.625
5
10
=
0.5
3
4
=
0.75
6
8
=
0.75
6
10
=
0.6
1
5
=
0.2
7
8
=
0.875
7
10
=
0.7
2
5
=
0.4
8
10
=
0.8
3
5
=
0.6
BOXED are unique
9
10
=
0.9
4
5
=
0.8
UNBOXED are repeats
Notes 5-3
Adding and Subtracting Fractions
To add fractions with the same denominator, just add the numerators, and put it over the same denominator.
(If your answer is more than your denominator – re-group to a mixed number.)
To subtract fractions with the same denominator, just subtract the numerators, and put it over the same
denominator. (Borrow if you need to.)
To add or subtract fractions with different denominators, first re-write the fractions using a
common denominator. (LCM)
The second example done TWO ways
If you multiply the denominators,
If you list the multiples of the bigger denominator
(12 x 3 = 36) your new denominator is 36.
(12 x 1 = 12,12 x 2 = 24, . . .)The LCM is only 12.
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Notes 5-4
Multiplying Fractions
To multiply fractions multiply the numerators, the product is your new numerator.
Then multiply the denominators, the product is your new denominator. SIMPLIFY if needed.
examples
(A whole number is always (over 1). “Put it on a popsicle stick”)
Mixed numbers must be changed to IMPROPER FRACTIONS before you multiply.
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Notes 5-5 Dividing Fractions
To divide fractions, multiply by the reciprocal.
We DO NOT DIVIDE fractions, we FLIP-OVER the second one and MULTIPLY.
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Notes 5-7 Solving Equations with Adding and Subtracting Fractions
To solve equations with fractions
1)
2)
3)
4)
Identify your variable. (Identify what is happening to your variable.)
UNDO what they did to the variable. DO INVERSE OPERATION TO BOTH SIDES
Solve and Simplify if you can.
You may have to change denominators to match. You may have to regroup.
examples
Notes 5-8 Solving Equations with Multiplying and Dividing Fractions
To solve equations with fractions
1)
2)
3)
4)
Identify your variable. (Identify what is happening to your variable.)
UNDO what they did to the variable. DO INVERSE OPERATION TO BOTH SIDES
Solve and Simplify if you can.
To undo multiplication (or division) just multiply by the reciprocal on both sides
Since 4 was a whole number, we changed it to a fraction by putting it over 1. .
The reciprocal of 4 is ¼, so we multiplied both sides by ¼. .
And the answer could not be simplified. .