3.3 Dividing mixed numbers and fractions – more examples
This section includes some more activities to test yourself with. It will be useful to take the time to do these, as it will help you to absorb the techniques for when you need to recall them at a later time.
Activity 7 Timing is everything
A recipe specifies a cooking time of hours and suggests checking and basting your joint two-thirds of the way through the cooking time.
After how long should you check and baste your dinner?
Answer
There are several ways you can do this calculation. For example, you could calculate two-thirds of as follows:
So, the time is hours, or 1 hour and 40 minutes (two-thirds of 60 minutes).
Alternatively, you might have converted the hours to minutes. Since there are 60 minutes in an hour and 30 minutes in half an hour, hours is the same as minutes, or 150 minutes.
minutes is 100 minutes, or 1 hour and 40 minutes. The same as the other answer, fortunately!
The next activity is another practical application of fractions, once again involving time.
Activity 8 Mowing lawns
During the summer, a friend decides to mow lawns. It takes her an average of three-quarters of an hour to cut one person’s garden.
If she decides to work a total of hours per day, how many lawns can she mow in that time?
Answer
You must determine how many times goes into . The calculation is:
Therefore, she could mow 11 lawns, if she works a full day and all the houses are next to each other!
In Week 1, you spent some time on puzzles, and so to finish this week you will have a go at another puzzle this time with fractions!
Activity 9 Puzzling!
I have just baked some cakes. I have given half of them to my friend Anj. I then gave a third of what I had left to my friend Bilal. My dog then ate four fifths of what was left, leaving me with just two cakes. How many did I have to start with?
Hint: Try working in reverse. For example, at the end, I am left with two cakes. My dog had eaten four fifths of what I’d had before. If he’d eaten four fifths, what fraction was left? So how many cakes did I have before the dog ate them?
Answer
Like so many puzzles, there are different ways of working this out. Here is one way:
After I gave cakes to Anj, I had of the total left.
After I gave cakes to Bilal, I had of my previous total left. So of the original total.
After my dog ate cakes, I had of the previous total left. So of the original total = 2 cakes
2 cakes = of the original. Therefore there were 30 cakes originally.
And here is a different way, working in reverse:
I ended up with 2 cakes after my dog had eaten of what I had. This means the 2 remaining cakes must be of what I had. Therefore, before the dog ate them, I had 10 cakes.
Ten cakes were what I had after giving a third of what I had before to Bilal. So if I gave her a third, ten cakes must be of what I had before. If ten cakes were , then was five cakes. This means that before I gave cakes to Bilal, I had 15 cakes.
15 cakes was what was left after I gave half to Anj. Therefore I started with 30 cakes.