A fraction refers to a part of a whole. It can also be said to describe the number of parts having a certain size that there are. Examples of fractions include one fifth, two thirds, one half among many more. In simple fractions, there are two major parts. The numerator which is the number placed above the line in a fraction and a denominator which is the number that is placed below the line in a fraction. These (denominators and numerators) also apply in other types of fractions other than simple fractions such as complex fractions, compound fractions, and mixed fractions.
The multiplication of fractions can be easily done in only three steps. These steps are:
Example, in case you are asked to work out \(\frac{1}{2} \times \frac{2}{5}\)
Solution,
Step 1. Start by multiplying the top numbers (numerators). The numerators, in this case, are 1 and 2. So 1 × 2 = 2.
Step 2. Multiply the denominators, the numbers at the bottom. In this case, the denominators are 2 and 5. Therefore, 2 × 5 = 10.
Step 3. Simplify the fraction. This is done by dividing both the denominator and the numerator by the common divisor of the two numbers until the final answer. In this case, we divide by two that is, 2 ÷ 2 = 1 and 10 ÷ 2 = 5. The answer is \(\frac{1}{5} \)
Multiplication of whole numbers and fractions can also be done. This is done by firstly changing the whole number into a fraction. Changing a whole number into a fraction involves placing a 1 under the number. For example, changing 4 into a fraction would give us \(\frac{4}{1}\).
For example, \(\frac{2}{3} \times 5 = \textrm{?}\)
Solution,
Step 1. Change the whole number into a fraction. 5, therefore, becomes \(\frac{5}{1}\). Proceed normally by,
Step 2. Multiply the numerators that are, 2 × 5 = 10.
Step 3. Multiply the denominators. In this case, 3 × 1 = 3.
Step 4. Simplify. The above fraction (\(\frac{10}{3}\)) is in its simplest form and therefore, it cannot be simplified any further. The answer is an improper fraction. An improper fraction is that which has the numerator is larger than the denominator.
For you to multiply mixed fractions, you need to start by converting the mixed fractions into improper fractions. For example, 1 ½ would become 3/2. After this, you can proceed as in the other fractions. For example, work out, \(1\frac{1}{3} \times 2 \frac{1}{4} = \textrm{?}\)
Solution,
Step 1. Convert the mixed fractions into improper fractions. \(1\frac{1}{3}\) will become \(\frac{4}{3}\) while the fraction \(2 \frac{1}{4} \) becomes \(\frac{9}{4}\).
Step 2. Multiply the numerators. The numerators, in this case, are 4 and 9. Therefore 9 x 4 which equals 36.
Step 3. Multiply the denominators. This will be 4 × 3 which results in 12. Therefore, the answer is \(\frac{36}{12}\).
Step 4. Simplify. \(\frac{36}{12}\) can be simplified completely by dividing both the numerator and the denominator by the common value 12. The resulting answer is \(\frac{3}{1}\). This is equivalent to 3.
