⬅ Previous Lesson Workshop Index Next Lesson ➡

Fractions

Objective

The following section will allow you to reacquaint yourself with fractions and the way they are added, subtracted, multiplied, and divided.

Previously Covered:

In the sections above, we reviewed the basic sets of numbers. We also brushed up on prime and composite numbers.

Adding and Subtracting Fractions

The key to adding and subtracting fractions is finding a common denominator. Let’s move right on to mixed numbers–that’ll serve as a fractions refresher as well.

Adding and Subtracting Mixed Numbers

For addition and subtraction with mixed numbers, it is easiest to leave the numbers as mixed numbers. Many people were taught to convert them into improper fractions, which is necessary when multiplying and dividing but just complicates everything for addition and subtraction.

You still need a common denominator for the fractions. At the end of the problem, you may need to convert the answer into a proper mixed number, so that you don’t have an improper fraction.

(For example, you would change 5 and 7/4 into 6 and 3/4 )

Examples:

$Reducing fractions, example 1$ $Reducing fractions, example 2$

Multiplying Fractions

Multiplying fractions is actually much easier than adding and subtracting them. To multiply fractions, multiply straight across the numerators and straight across the denominators. Then simplify the fraction to express it in lowest terms. That’s it.

Example:

$Multiplying fractions$

Many people find it easier to simplify the fractions before they multiply them together because it can make the multiplication step much easier to do mentally. Any factors that are shared in both the numerator and the denominator (even if they are not in the same fraction) can be cancelled.

Multiplying Mixed Numbers

The only way that multiplying mixed numbers is different from multiplying fractions is that mixed numbers must be converted into improper fractions first.

Canceling out shared factors is very useful when multiplying improper fractions because the numerators can be very large and they are easier to work with if you can make them smaller.

Example:

j = 4 and 2/3 x 6 and 3/4

j = 14/3 x 27/4

Multiplying mixed numbers

j = 63/2

j = 31 and 1/2

Dividing Fractions

Once you are comfortable with multiplication of fractions, division is a short jump.

Division is another way to state that you have multiplied by the reciprocal of a number. The reciprocal is the number flipped upside down, so the reciprocal of 3/4 is 4/3 and the reciprocal of 8 is 1/8 . You can see how this works with whole numbers:

$Dividing fractions$ When you divide with whole numbers, using multiplication and the reciprocal would be an unusual option to choose. With fractions, however, it is the main option.

Review

Remember to use a common denominator when you are adding and subtracting fractions and mixed numbers.
When multiplying and dividing mixed numbers, begin by changing them into improper fractions.

⬅ Previous Lesson Workshop Index Next Lesson ➡