You can write this as a mixed number: 1^34. A mixed number is any number that
is written as an integer and a fraction. To convert from a mixed number to an
improper fraction, do the following:- Multiply the integer by the denominator of the fraction: in this case, 1 × 4 = 4
- Take that product and add it to the numerator of the fraction: in this case,
4 + 3 = 7 - Take the result of Step 2 and put it above the original denominator:^74.
Skills Check: Improper Fractions
Write each of the following as an improper fraction. See the end of this
section for the answers.A (^323)
B (^715)
C –2^23
Adding and Subtracting Fractions
When adding or subtracting fractions, your goal is to manipulate the fractions to
have the same denominator. If you are asked to solve for^14 +^24 , the answer would be
3
4 since you are adding 1 slice of a 4-slice pie to 2 slices of a 4-slice pie. You will end
up with 3 slices of a 4-slice pie, which means you will have^34.
However, addition and subtraction of fractions will not always be so
straightforward. Sometimes the fractions you are adding or subtracting will
have different denominators, for example,^23 –^14 = ?. When adding or subtracting
fractions with different denominators, you must first find a common denominator.
To do so, find the smallest number that is a multiple of both denominators. In
this case, the smallest number that is a multiple of 3 and 4 is 12. Now you need to
manipulate both fractions to have a denominator of 12. To do so, you will multiply.
2 × 4
3 × 4 −
1 × 3
4 × 3 =
8
12 –
3
12 =
8 – 3
12 =
5
12
Note that when you multiply the denominator of the fraction by a value,
you must multiply the numerator of the fraction by the same value. By
doing so, you are essentially multiplying the fraction by 1, which means
that the value of the fraction will not change.
Comparing Fractions with Different Numerators and Denominators
Using a common denominator is also helpful when comparing fractions
whose numerators and denominators differ. Look at the following Quantitative
Comparison question.
212 PART 4 ■ MATH REVIEW
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