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Yes now in the question I said that there are two ways you can finish the question off.
(a) A top heavy fraction. (For this you just need to cancel it into its lowest terms, but it is already top heavy in fact.)
(b) A mixed number or a number followed by a fraction as I put it. (Can you see what this is ?)
Hint for (a) divide top and bottom by 3
Hint for (b) take away the whole number one, and present as 1 and a fraction.
The answer to that bit is (15 / 18)
You needed to do 5 x 3 = 15 for the top part. (Also note that 6 x 3 = 18)
Yes you need to work out how many eighteenths each of the fractions is.
So (1/3) = ( something / 18 )
and (5/6) = ( something else / 18 )
Yes correct.
Do you want to have a go at Q3 ?
It was (1/3) + (5/6)
The answer is greater than one here, but the principle is the same.
Right hopefully the image will display alright.
I have drawn a rectangle. Imagine that the whole of the big rectangle represents the number 1
Now imagine that we have divided this big rectangle into 5 equal bits. Each of these is (1/5).
Now imagine that we have divided this big rectangle into 3 equal bits. Each of these is (1/3).
The very small bits made by dividing the big rectangle into 15 bits are each (1/15)
The fraction (1/5) is really 3 of the very small bits so (3/15)
The fraction (1/3) is really 5 of the very small bits so (5/15)
I could make up an image file to illustrate the division into 3 and 5 and 15, but it will take about 10 minutes to set up.
Do you want to just take my word for it or would you like an illustration ?
(1 / 5 ) = (3 / 15)
The reason for that is that I have multiplied top and bottom by the same number.
In general it is possible to multiply the numerator and denominator by the same number and the fraction is still the same.
You could try drawing a diagram to show this. Let us say you had a square. You divide it into 5 bits which are equal in size.
That represents (1/5) now try dividing the square so that each of the five equal bits are divided into 3 bits.
You can use this to prove that (1/5) = (3/15)
What is (1/3) equal to ?
Yes correct.
So what is (1/5) in fifteenths ?
What is (1/3) in fifteenths ?
We need to get the denominators to be same. How could we do that ?
Yes that is correct. Now let us go back to Q2.
This was (1/5) + (1/3)
What would be a good denominator to use ?
(2/3) + (1/4) = (8/12) + (3/12) = ????
The denominators are now equal. The numerators can now just be added.
Do not add the denominators though.
No the correct answer was that (2/3) = (8/12)
Remember that the other fraction was (3/12). So what is the answer to the original question ?
No that is not correct. Try again ?
That is not quite right, but you are getting there. (3/12) is one of the fractions, but the other is wrong. Try again ?
Hint: (1/4) = (3/12)
(2/3) = ????
No. The denominators of the question are 3 and 4. What we need to do is convert those fractions so that the denominator is
the same. If we make the second one 3 then it will be difficult to work out (1/4) in thirds.
The best thing to do is get them into a form where they are (something / 12)
I got that number from 3 x 4 = 12
To get (2/3) in the form (something / 12) multiply top and bottom by 4.
To get (1/4) in the form (something / 12) multiply top and bottom by 3.
Those are not right.
Let us go through Q1 together.
The denominators must be equal before adding. Since one is in thirds and the other in quarters we cannot just add them like that.
What would be a good denominator?
Mandy: Have you done any or all of those questions ?
Okay fair enough. Do let me know about the sub topics to do with time that you are interested in learning about.
EDIT:
I have had a few more thoughts about basic maths using time:
(1) The time gap between two times. For example the time gap in hours and minutes between 10:30am and 4:50 pm
(Without using a calculator, but pen and paper allowed, using a good method that avoids confusion.)
(2) Averages of timings given in minutes and seconds. For example: 1 min 40 secs, 1 min 20 secs and 2 mins 30 secs
(Giving the answer in minutes and seconds, avoiding any errors with confusion between 100 seconds and 1 minute (60 seconds))
(3) Interpretation of timetables. (This could be difficult online and setting up a question will require a fair bit of work I suspect
especially if a complicated example similar to a real timetable is needed.)
(4) Calculations involving speed, distance and time perhaps ? (If a walk is on average 5 kmph for 2 hours how long is the walk ?)
(5) Other physics matters to do with time. However these may go beyond the scope of your course.
On the topic of "time" I could do with more information about the sort of thing you want to learn about.
I have got a few ideas of my own like:
(1) If you have a time period of 4 hours and you need to divide it into 10 equal time slots how long should each one be ?
(2) What is the time of 7pm written in a 24 hour clock form ?
(3) How many seconds are there in a day ? (If the arithmetic is difficult with this question you may like to use a calculator.)
(EDIT: Also for question 3 you might like to think of a good way of making the arithmetic easier. I have solved it myself using
pen and paper without a calculator (but just checking using a calculator) most of it can be done with times tables and using
rules of multplication/division by 10, 100, 1000 etc. there is one point where long multiplication may be a good idea.)
I certainly can. Of the top of my head a few questions might be:
(1) What is 40% written as a fraction (simplify it to its lowest terms) ?
(2) What is the fraction 7/8 written as a decimal ? What is that as a percentage ?
(3) If you have a 3 : 4 ratio of breakfast cereal : chocolate in a recipe how much of these two ingredients would you need
to make up 140 grams of the mixture ?
Yes very good. Correct. I agree with your answer.
Now the test that Bob gave you probably will get marked later. I don't have it at the moment so I don't know how you got on.
Were there any topics in that that you felt you were struggling with ?
Correct. Now all you have to do is add up all the overtime pay and the basic pay together to get a total for the week.
Can you do that ?
Yes that is correct. Now let's look at the Sunday rate. We want to add two thirds to the basic rate with this one.
Are you okay with doing that ?
Yes that is correct. Now how about the Saturday overtime. The rate is time and a half (and the basic rate is £8.10).
Can you do this bit ?