Download Converting mixed numbers and improper fractions

Convert mixed numbers into improper fractions
Convert improper fractions into mixed numbers
Add, Subtract, Multiply, Divide fractions and mixed numbers
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Converting mixed numbers and improper fractions
1. Convert mixed numbers into improper fractions
MULTIPLY denominator x whole number, then ADD the numerator. Put this number over
the original denominator.
2. Convert improper fractions into mixed numbers
Divide the numerator by the denominator to find the whole number. Put the remainder
over the same denominator. Simplify if possible.
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Adding and Subtracting whole numbers, fractions, mixed numbers:
3. Add fractions with common denominators: Add the numerator, denominator stays the same.
4. Add fractions with different denominators: Find a common denominator by multiplying them
together. Use a “magic 1” to find an equivalent fraction for each fraction in the problem that
uses the new common denominator. Add the numerators, keep the denominator the same, then
simplify if possible.
5. To subtract fractions: follow the rules for #3 and #4 above, subtract rather then add
numerators
6. Add mixed numbers: First add the whole numbers. Then add the fractions according to the rules
#3 and #4 above. If the answer contains an improper fraction, you must convert it and regroup
the wholes if needed.
7. Subtracting: mixed number – fraction. First convert the mixed number into an improper fraction.
Then subtract according to rules #3 and #4 above.
8. Subtracting: mixed number – mixed number. First subtract the whole numbers. Then convert the
mixed number into an improper fraction. Subtract according to rules #3 and #4 above.
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Multiplying and Dividing whole numbers, fractions, and mixed numbers
9. Multiply two fractions: SIMPLE!! Multiply across the top (numerators) and bottoms
(denominators) of both fractions. Then covert to a mixed number and simplify if possible.
10. Multiplying a fraction and a mixed number –OR- multiplying two mixed numbers:
YOU MUST CONVERT THE MIXED NUMBERS INTO IMPROPER FRACTIONS!!!!
DO NOT MULTIPLY THE WHOLE NUMBERS!
Multiply across the top and bottom of the fractions, convert to a mixed number and simplify if
possible
NOTE: To multiply or divide a whole number with a fraction or mixed number, turn the whole
number into a fraction by writing it over 1. (example 7 = 7/1)
11. Dividing a mixed number by a fraction or a fraction by a mixed number:
REMEMBER: INVERT the divisor (the second number)
MULTIPLY instead of dividing
CONVERT to a mixed number
SIMPLIFY if possible
Example:
3
1
6
5
21
4
2
7
2
5
7
8
+
+
–
Practice:
7
8
34
7
3
3
7
1
8
¾+
3
2
8
4
+ =
=
5
7
8
10
8
4
6
-
=
3
10
=
¾- =
1
4
3
5
3⅝+2½=
16 + 4
5
1
3
3
- =
4
8
–½=
2
3
1
2
3
7
2
- =
5
=
5
3
4
x
5
5
–2
2
3
1
3
2
56 – 8 ¼ =
5
2
=
3
2
3
4
5
3 x5 =
6÷¼
3
÷½
½÷7
6
9
=
2
1
7
5
25 x 4
8÷
2
1
x
5
1
3
=
÷ ¼=
¼ ÷ 5=
=