Table of Contents |
As you may recall, PEMDAS is the acronym that is used to remember the order of operations. PEMDAS stands for:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
The order of operations applies to all numbers, including fractions.
Multiplication and division involving fractions is useful when converting between measurements, which is common in many scientific fields, such as chemistry, physics, and nursing.
EXAMPLE
Suppose you want to multiply 3/4 times 1/5.Our expression | |
First, multiply the numerators to find our answer's numerator. 3 times 1 equals 3. | |
Next, multiply the denominators to find our answer's denominator. 4 times 5 equals 20. | |
Our Solution |
Dividing fractions, on the other hand, is equivalent to multiplying by the reciprocal. Finding the reciprocal of a fraction means flipping it, or switching the numerator and the denominator.
EXAMPLE
Suppose you want to divide 3/8 by 1/2.Our Expression | |
First, find the reciprocal of by flipping it. This is . Change the sign to multiplication. | |
Next, multiply the numerators. 3 times 2 is 6. | |
Next, multiply the denominators. 8 times 1 is 8. | |
Our Solution |
A simplified fraction is a fraction in which the numerator and the denominator have no common factors other than 1.
EXAMPLE
50/100 can be simplified to 1/2, because both the numerator and the denominator are divisible by 50. It’s much easier to say that you ate half of your dinner rather than fifty-hundredths of your dinner!Referring back to the previous example in which you arrived at an answer of 6/8, how can you simplify this fraction?
Our Expression | |
First, see if the numerator and denominator have any common factors. Expand both numbers into their prime factors. In this case, the prime factors of 6 are 3 and 2. The prime factors of 8 are 2, 2, and 2. | |
Since there is at least one 2 in both the numerator and the denominator, you can cancel them out. | |
This leaves 3 in the numerator, and 2 times 2 in the denominator. | |
Evaluate 2 times 2, which is 4. | |
Our Solution. |
is the simplest form of .
You can also use the order of operations, or PEMDAS, with fractions.
EXAMPLE
Suppose you want to simplify the following expression: .Our Expression | |
First, evaluate the exponent. 1/3 times 1/3 is 1/9 | |
Next, multiply and divide from left to right. When you divide 2/9 by 1/9, you need to multiply by the reciprocal of the second fraction, which is 9/1 | |
Since we just have multiplication remaining, we can multiply all 3 numerators together. 2 times 9 times 1 is 18. | |
Then, we can multiply all three denominators together. 9 times 1 times 4 equals 36 | |
Finally, we want to simplify the fraction by finding the prime factors of the numerator and denominator. | |
One 2 and two 3's cancel out of both the numerator and denominator | |
Our solution |
Source: This work is adapted from Sophia author Colleen Atakpu.