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In this lesson, we will apply our understanding of multiplication and division to understand how to multiply and divide fractions.
See the fact file below for more information on the multiplication and division of fractions or alternatively, you can download our 32-page Multiplication and Division of Fractions worksheet pack to utilise within the classroom or home environment.
Key Facts & Information
FRACTIONS AS DIVISION
- First of all, we have to understand that fractions and division are closely linked together. How?
- We know that ½ means that a whole was divided into two equal parts.
- Which is to say, this also means 1 ÷ 2, how?
- First, let us explain this using figures.
- The figure above shows us ½. Now, how do we explain division?
- Division is splitting a whole into equal parts or groups.
- Now, if we divide a whole into two (2) parts and give it to two people, how many parts would each of them have?
- Each of them would have 1 part out of 2 parts. Which is why they would each receive ½.
- Which is why we can look at the horizontal line as a division sign.
FRACTIONS WITH WHOLE NUMBERS
- Now, let us try solving for this:
- 16 ÷ 5 = ?
- We will use visual aids to help us understand this.
- We have 16 boxes.
- We will divide this into 5 groups of 3 boxes.
- Notice how there is one box left uncolored, this is the remainder.
- Remember that the goal of division is to have equal parts or groups.
- Therefore, since we already have 5 groups, we need to divide the remainder, which is 1, into 5 groups so that we can have 5 groups with equal values.
- Therefore, we need to divide 1 by 5. 1 divided by 5 is equal to 0.2. Thus, the answer could be expressed as:
- 16 ÷ 5 = 3.2
- We could also express the answer in terms of fractions with whole numbers or mixed fractions.
- In other words, 3.2 could also be expressed as:
- 16 ÷ 5 = 3 1/5
- 3 ⅕ is called a mixed fraction, as it is composed of a whole number and a fraction.
MULTIPLYING A WHOLE NUMBER AND A FRACTION
- In this section, we will talk about how to multiply a fraction and a whole number.
- 1/4 x 2 = ?
- How do we multiply this? Let’s use visual guides.
- The first figure on the left is a visual representation of ¼.
- Now, we need to double this, since we are multiplying ¼ by 2.
- Now that we have doubled the boxes, note that we already have the answer to the equation.
- Counting the boxes, we have 4 boxes in total. Then, the shaded boxes are 2 in total. Therefore, we have 2/8.
- In short, when multiplying a whole number and a fraction, we just need to multiply both the numerator and the denominator by the whole number.
- In this section, we will figure out how to multiply a fraction with another fraction.
- 1/5 x 3/4 = ?
- In multiplying fractions, we just need to follow the formula.
- A/B X C/D = AC/BD
- Applying the formula above to the given equation. We will get 4/20.
DIVIDING A FRACTION BY ANOTHER FRACTION
- Since we already know how to multiply fractions, we will go back to understanding how to divide fractions.
- In this section, we will understand how we can divide a fraction by another fraction.
- (3/4) / (2/3) = ?
- How do we do this?
- First, the thing you need to do is to invert the divisor.
- Note that the divisor is the second term. Thus, we need to invert ⅔.
- How? To invert a fraction, simply flip it upside down.
- Once we have the inverted fraction.
- We replace the original divisor with it.
- Then, we also have to change the symbol or operation to multiplication.
- From here, we can perform multiplication as we did previously.
- Therefore, if we divide ¾ by ⅔, the answer is 9/8.
Multiplication and Division of Fractions
This is a fantastic bundle which includes everything you need to know about the multiplication and division of fractions across 32 in-depth pages. These are ready-to-use Multiplication and Division of Fractions worksheets that are perfect for teaching students how to apply our understanding of multiplication and division to understand how to multiply and divide fractions.
Complete List Of Included Worksheets
- Lesson Plan
- Multiplication and Division of Fractions
- Whole X
- Divide F
- F Over F
- Other Way
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Use With Any Curriculum
These worksheets have been specifically designed for use with any international curriculum. You can use these worksheets as-is, or edit them using Google Slides to make them more specific to your own student ability levels and curriculum standards.