3.2 Dividing mixed numbers and fractions
The same principles apply to dividing mixed numbers as dividing proper fractions.
Example _unit5.4.4
Let's try to calculate
First, just as with multiplication, you rewrite the mixed numbers as improper fractions:
Then, you find the reciprocal of the fraction after the ÷ sign, and change the division symbol to the multiplication symbol, so your new calculation is:
Then, you cancel and multiply:
Because your original numbers were mixed numbers, it is appropriate to rewrite your answer as a mixed number as well. In this case, your answer is equivalent to .
Example _unit5.4.5
Here’s another example:
Convert into an improper fraction:
Now you need to work out the reciprocal of 7. Remember, any whole number can be expressed as an improper fraction by using 1 as the denominator, thus , and its reciprocal is . Now, multiply by .
Now you’ve had a chance to work through a few examples, try the next activity yourself to see how you get on.
Activity _unit5.4.1 Activity 6 Dividing fractions
Work through the following examples, using what you have just learned. Remember to convert any mixed numbers to improper fractions.
a.
- i.
- ii.
Hint: how do you convert division by a fraction into a multiplication problem?
Answer
- i.
ii.Change the first fraction into an improper fraction before dividing:
b.If it takes of an hour to clean one car, how many cars can be cleaned in hours?
Hint: you are trying to determine how many hours are in hours.
Answer
Here, you need to find how many times ‘three-quarters’ goes into ‘seven and a half’. So you need to divide by .
Thus, 10 cars can be cleaned in the given time.
- c.Imagine that you are trying to put a fence along the side of a garden. The side of the garden measures metres. The fencing available is made of panels that measure of a metre each. How many panels will be needed?
Answer
You need to find how many metre sections there are in metres. The calculation is:
So, 17 panels are needed.
The more practice you get with anything the easier it becomes. So, as well as having a go at the activities in the next section, see if you can spot fractions in your everyday life and use them to solve problems.