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FRACTION TYPES
Fractions can have three different types :
Proper Fractions: The numerator is less than the denominator
Examples: 1/3, 3/4, 2/7
Improper
Fractions:
The numerator is greater than (or equal to) the
denominator
Examples: 4/3,
Mixed Fractions:
11
/4, 7/7
A whole number and proper fraction together
Examples: 1 1/3, 2 1/4, 16 2/5
Mixed Fractions = Improper Fractions
You can use either an improper fraction or a mixed fraction to show the same amount.
For example 1 3/4 = 7/4, shown here:
1 3/4
7
/4
=
Converting Improper Fractions to Mixed Fractions
Follow these steps:
•
•
•
Divide the numerator by the denominator.
Write down the whole number answer
Then write down any remainder above the denominator.
Example: Convert 11/4 to a mixed fraction.
Divide: 11 ÷ 4 = 2 with a remainder of 3
Write down the 2 and then write down the remainder (3) above the
denominator (4), like this:
3
2
4
Converting Mixed Fractions to Improper Fractions
Follow these steps:
•
•
•
Multiply the whole number part by the fraction's denominator.
Add that to the numerator
Then write the result on top of the denominator.
Example: Convert 3 2/5 to an improper fraction.
Multiply the whole number by the denominator: 3 × 5 = 15
Add the numerator to that: 15 + 2 = 17
Then write that down above the denominator, like this:
17
5
Math Model Book:
________________________
Adding and Subtracting Fractions
When two fractions have a common denominator, we can add or subtract
the numerators to find the sum or difference.
e.g.
When adding or subtracting fractions with unlike denominators, change
each to equivalent fractions which have common denominators.
Math Model: Adding and Subtracting Mixed Fractions
To add or subtract mixed numbers
1.
2.
3.
4.
convert the mixed numbers into improper fractions
Find LCM if necessary
then add or subtract them as fractions.
Reduce the answer and avoid improper fractions
Example:
9 1/2 + 5 3/4 = ?
Step 1:
Converting each number to an improper fraction,
we have
9 1/2 =
5 3/4 =
Step 2 Find the LCM
The LCM of 2 and 4 is _________,
Step 3: Add
19 + 23 = ______ + ______ = __________
2
4
4
4
4
Step 4: Converting back to a mixed number, we have 61/4 =