Write the formula of Fractional Addition, Subtraction, Multiplication, Division With definition and understanding example...
Answers
Answer:
In cases that involve simple numbers, addition and subtraction of fractions is easy enough. For instance, adding one third and one third obviously gives us two thirds. Likewise, three fifths minus two fifths is one fifth. The first case is illustrated below.
But what about cases such as one half plus one third?
Notice that adding (subtracting) fractions with the same denominator is very simple-we simply add (subtract) the numerators and divide by the same denominator. We should already know that we can write equivalent fractions that have different numerators and denominators. Thus, if we simply convert one or both of the fractions that we are adding or subtracting into equivalent fractions with the same denominator, then we are able to add the fractions in the simple manner described above. Then, if necessary, we can reduce the result to lowest terms.
The challenge in adding and subtracting fractions is finding a common denominator. The most straightforward approach to finding a common denominator is to simply multiply the two existing denominators and then convert the numerators accordingly to create equivalent fractions. Although this approach is conceptually simple, it can be mathematically difficult when the denominators are large. Nevertheless, let's try this approach for the purpose of illustration. Consider the addition mentioned above.
A common denominator is 6 (or 23), because we can multiply the numerator and denominator of by 3 to get , and we can multiply the numerator and denominator of by 2 to get . The addition is then straightforward.
Practice Problem: Calculate the result in each case.
a. b. c.
Solution: In each case, find a common denominator and convert the terms to equivalent fractions with that denominator. One possible common denominator is given for each case. The sum (difference) of the fractions is the sum (difference) of the numerators over the common denominator. Reduce the result to lowest terms if applicable.
a. Common denominator: 21
b. Common denominator: 8
c. Common denominator: 45
Multiplication and Division
Multiplying and dividing fractions is in some ways simpler than adding and subtracting them. Let's say we want to multiply by . Intuitively, the answer is fairly obvious: half of a half is a quarter (or one-fourth--). For instance, if you have 50 cents (half of a dollar) and you want to multiply it by a half, then you end up with 25 cents (a quarter of a dollar).
Answer:
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