I used the following notes to ensure I’d covered the base content that I felt I needed for Lantite. These notes do not take into account the complexity of how the questions are presented. An example of that complexity is at the end of the notes. But knowing how to work with fractions meant that I could interpret any question and know what to do to get the answer.
Fractions are simply parts of a whole.
Fractions are the sections between whole numbers.
- find them on a number line
- visualise / draw the fraction
You can have zero parts of a fraction: 0 parts are shaded.
You cannot have a fraction of zero.
Naming conventions:
To add/subtract fractions:
- if same denominator – just add numerators
- if different denominators – find common denominator first
To multiply fractions – multiply numerators and multiply denominators.
To divide fractions – depends on what answer you are looking for:
- long division – if wanting a percent or decimal
- invert and multiply – if wanting a fraction answer
Simplify and find equivalent fractions 8/16 = 4/8 = 2/4. Do this by factoring the fraction (ie finding its multiples until you have a prime number).
Whole fraction
Proper fraction: fractions between 0 and 1
Improper fraction fractions greater than 1
Can you:
- Add/subtract fractions?
- Multiply/divide fractions?
- Write a fraction from two quantities?
- Eg: What fraction is 40 out of 60?
- Find a fraction of a quantity?
- Eg: 4/7 of $140
Problem
1/9 of the shirts sold at Peter’s shop are stripped. 5/8 of the remainder are printed. The rest of the shirts are plain coloured shirts. If Peter’s shop has 81 plain coloured shirts, how many more printed shirts than plain coloured shirts does the shop have?
The worked answer is below. I have decided to upload as a photo of my work as fractions are difficult for a non programmer to put on a webpage :-)
Just remember to find the fraction of printed shirts, you need to find 5/8 of 8/9x. Find the common denominator. 8 x 9 is 72. Times the numerator by what you had to times the denominator by to get 72. Now your on an equal playing field
- 1/9x are stripped shirts
- 5/9x are printed shirts
- 3/9x are plain shirts (we know this is 3/9 because 1+5+3=9, and to get the whole we need to have 9/9). Also, we have been told that plain shirts are 81. So we know 3/9 = 81.
Always try and find 1 unit or in this case 1/9. If 3/9 = 81 then 1/9 must = 81/3 OR 27.
Now we know 1/9 = 27, you can work out each allocation by multiplying how much of the fraction is allocated to that item:
- Stripped shirts has 1/9 = 27
- Printed shirts has 5/9 = 135
- Plain shirts has 3/9 = 81
Total shirts 27+135+81 = 243
