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There is a type of worded questions in which you need to evaluate things across different options.
For example, you might get a question that ask you to find the total number of litres of a number of different containers containing various amounts measured in a number of different units such as:
You might even get question that involve multiple items with different fractions. Fractions have values such as ½, words such as a quarter, half, one-fifth, three-quarters or any other worded equivalent of a fraction. The things you should know how to do are:
Conversion of fractions, percentages, decimals and equivalent fractions going across all three types.
Add, subtract, multiply and divide with fractions.
If you need to build up knowledge in this area, go to the mathematics course.
The way you would approach a question like this is to follow the overall approach, but the difference comes down to putting the multiple different options into 1 measurable unit . That means, compare apples with apples. If you have mL and L, change on to the other and then evaluate.
A suggested approach is shown below.
Peter received a barrel of potatoes today. He decided to give ¼ to Chris first. When he came back from Chris's house, he gave another 20% to Gail and divided the rest evenly between himself and Sue. If Peter received 100kg of potatoes today, how many potatoes (in kilograms) does each person receive?
| Steps | Illustrated Workings |
|---|---|
| Step One** Identify the clues or hidden information first** | Peter gave some potatoes to Chris first, which means Chris receives the true portion of ¼ of 100 kg potatoes. What I mean by true is that students may overlook the fact that Gail will not receive 20% of 100 kg as some has already been given to Chris. Be aware of this potential pitfall. In this question you will need to subtract the portion that has already been given out. |
| Step Two** Convert where necessary** | Note that Gail's portion is represented as a percentage. Converting 20% to a fraction gives us 1/5 or one-fifth. |
| Step Three** Start your calculations in sequence** | ¼ of 100 kg goes to Chris. Multiplying the two numbers together will give you 25 kg.75 kilograms is now remaining. Gail receives 1/5 of that, which is 15 kg.60 kilograms is now remaining. Peter decides to split the rest evenly. Note, evenly means no one gets more and no one gets less. In this case there are two people left so 60 kg should be divided by two. You should get 30 kg. |
| Step Four** Find the solution** | If you stop here thinking you have finished, read the question again. Make sure you understand what the question is asking. How many potatoes (in kilograms) does each person receive? List in order the allocation and then select your best answer. You should get: Chris 25 kg, Gail 15 kg, Peter 30 kg and Sue 30kg. |
Now, let's go through some example questions:
Question 1
There were 30 cards in a deck. After 5 black cards were removed from the deck and 7 red cards were added to the deck, there were thrice as many red cards left in the deck as there were black cards. How many of the original 30 cards were red?
A 13 B 15 C 17 D 24
Question 2
There were 24 green and blue balls in a basket. After 4 blue balls were added to the basket and 1 green ball was removed from the basket, there were half as many green balls left in the basket as there were blue balls. How many of the original 24 balls were green?
A 9 B 10 C 14 D 18
Key Rules to remember:
Now it's time to do your assignment.