Maths- Number and Questionnaires

Question 1

Ratios

Answer 1

A ratio is a way to compare amounts of something. Recipes, for example, are sometimes given as ratios. To make pastry you may need to mix 2 parts flour to 1 part fat. This means the ratio of flour to fat is 2:1.

If pastry is 2 parts flour to 1 part fat, then there are 3 parts (2 + 1) altogether. Two thirds of the pastry is flour; one third fat.
Ratios are similar to fractions; they can both be simplified by finding common factors. Always try to divide by the highest common factor.

Question 2

Subtracting a negative number is the same as adding:

Answer 2

eg (−5) − (−2) is the same as (−5) + 2 = −3

Question 3

Here are the rules for multiplying and dividing:

Answer 3

Positive × positive = positive
Positive × negative = negative
Negative × positive = negative
Negative × negative = positive
If the signs are the same, the answer is positive. If the signs are different, the answer is negative.
Here are some examples:
−4 × 2 = −8
−3 × −2 = 6
5 × −3 = −15

Question 4

HCF and LCM

Answer 4

We want to find the HCF and LCM of the numbers 60 and 72.

Start by writing each number as a product of its prime factors.
60 = 2 * 2 * 3 * 5
72 = 2 * 2 * 2 * 3 * 3
To make the next stage easier, we need to write these so that each new prime factor begins in the same place:
60 = 2 * 2 * 3 * 5
72 = 2 * 2 * 2 * 3 * 3
All the “2”s are now above each other, as are the “3”s etc. This allows us to match up the prime factors.

The highest common factor is found by multiplying all the factors which appear in both lists:

So the HCF of 60 and 72 is 2 × 2 × 3 which is 12.

The lowest common multiple is found by multiplying all the factors which appear in either list:

So the LCM of 60 and 72 is 2 × 2 × 2 × 3 × 3 × 5 which is 360.

Question 5

BIDMAS

Answer 5

Do you remember BIDMAS? It stands for ‘brackets’, ‘indices’, ‘division’, ‘multiplication’, ‘addition’ and ‘subtraction’.
The order in which we carry out a calculation is important.

Question 6

Order of operation

Answer 6

What is 2 + 3 x 4?
If we calculate the ‘2 + 3’ part first, we get:
2 + 3 x 4 = 5 x 4
= 20
If we calculate the ‘3 x 4’ part first, we get:
2 + 3 x 4 = 2 + 12
= 14
These are obviously two different answers - but which one is correct?
BIDMAS tells us that ‘multiplication’ comes before ‘addition’, so the second answer is correct:
2 + 3 x 4 = 2 + 12
= 14

Question 7

Poor questionnaire questions

Answer 7

How a question is phrased is very important, so it is useful to be able to spot a bad one.
Have a look at the following questions. Can you spot any problems with them?

Question 8

You support Arsenal, don’t you?

Answer 8

This is a biased question. The interviewee might feel pressurised into saying ‘yes’. A better question would be: ‘Which football team, if any, do you support?’

Question 9

Are you a criminal?

Answer 9

It is unlikely that you will get a truthful answer to this, especially in a face-to-face interview!

Question 10

Do you think maths is:
a very interesting subject
quite an interesting subject?

Answer 10

This is biased in favour of maths, and it does not cover every possible answer.