Number

Question 1

What is the order of operations?

Answer 1

Brackets, exponents, multiplication/division, addition/subtraction.

Question 2

When multiplying and dividing integers:

Same signs =
Different signs=

Answer 2

Positive

Negative

Question 3

Factors?

Answer 3

All the numbers that multiply to give a certain number

Eg factors of 10
= 1, 2, 5 & 10

Question 4

First 5 prime numbers?

Answer 4

2, 3, 5, 7, 11

Question 5

Multiples?

Answer 5

Eg multiples of 5

= 5, 10, 15, 20 etc

Question 6

Exponents show?

Answer 6

Repeat multiplication

Question 7

What are significant figures?

Answer 7

The number of significant figures (sf) a number has is the total number of digits that are used to represent it accurately.

Question 8

Numbers that aren’t zero are _____________ significant

Answer 8

Always

Question 9

Zeros are significant when?

Answer 9

• In between other digits that aren’t zero

- when at the end of a number AND after the decimal point

Question 10

Zeros are probably not significant when?

Answer 10

• At the end of a number with no decimal point

- at the front of a number

Question 11

When working out whether zeros are significant, what should you ask yourself?

Answer 11

Is that zero adding detail or is it a place holder?

Question 12

When rounding to significant figures you?

Answer 12

Cut the number off after the number of significant figures you are rounding to, and then sometimes you will have to add one or more zeros to make the number make sense.

Sometimes if the number after your cut off is 5 or more you may have to round your second sig fig up.

Remember: it’s rounding, so it’s supposed to be close to the original number

Eg: round to 2sf
365 -> 370

Question 13

Standard form is used to represent?

Answer 13

Very small numbers or very large numbers.

Question 14

To write a number in standard form you?

Answer 14

1. Put the decimal point after the first significant figure
2. Remove all place holder zeros
3. Multiply the number by 10 to the power of how many places you moved it

NOTE: if you are changing a small number into standard form you multiply by 10 to the power of NEGATIVE how many decimal points you moved it.

Question 15

To change number in standard form back into ordinary form you?

Answer 15

Move the decimal point by the exponent number

Question 16

To estimate you must?

Answer 16

Round first. It may be effective to round one number up and the other down in order to be more accurate if they are going up or down by about the same amount

Question 17

To divide fractions?

Answer 17

Flip the second fraction so that the old denominator is now the numerator and vice versa and then multiply across

Question 18

To write a number as a percentage you?

Answer 18

Make it into a fraction and multiply by 100.

Eg 26 out of 30 = 26/30 x 100

Question 19

To find the percentage of a number you?

Answer 19

Change the percentage to a decimal and multiply by the number

Question 20

To increase by a percentage you?

Answer 20

Change the percentage into a decimal and put a 1 in front

Eg increase by 20% = 1.2 x the number

Question 21

To decrease by a percentage you?

Answer 21

Realise taking 30% off is the same as finding 70% of the number.

Decrease by 30% = 1-0.3=0.7
0.7 x the number

Question 22

Equation for a percentage change question is?

Answer 22

Difference/original x 100

Question 23

To find the original amount you?

Answer 23

Write as an algebraic equation with a percentage and an x and what it equals.

Eg: 40% of x = 14
0.4 multiply by x = 14
And solve

Question 24

To add GST to a price we?

Answer 24

Multiply by 1.15%

Question 25

To remove GST from a price we?

Answer 25

Divide by 1.15

Question 26

To find the amount of GST paid you can?

Answer 26

Find the GST inclusive and exclusive prices and then find the difference. This is the MUCH easier way

Question 27

A ratio compares___________?

Answer 27

The amount of two quantities

Question 28

Ratios can be simplified

TRUE OR FALSE

Answer 28

True. In a similar way to fractions

Question 29

Ratios can be in different units

Ratios must be in the same units

Which is true?

Answer 29

They must be in the same units so you may need to convert them first.

Question 30

How to write a ratio as a fraction?

Answer 30

Add the two numbers in the ratio together and make this the denominator. Then put whichever number you are talking about from the ratio as the numerator.

Question 31

How to split in a given ratio?

Answer 31

Write one part as a fraction. Then multiply it by the amount that is being split. This will give you how much one person or part gets.

You can do the same thing to find the other amount, or you can subtract the other parts amount from the total to find the second amount.

Question 32

Rates compare?

Answer 32

Unlike quantities

eg km/hr

Question 33

To use rates to figure out a question you?

Answer 33

Write what the question has already given you.

Eg: 30km = 1 hr

Then you change one side to get it to one of he amounts you need, and change the thee side in the same way

Eg: change 1hr to 3hrs (multiplied by 3) so then you have to multiply the 30km by 3.

90km = 1hr

Question 34

How to use Proportional reasoning?

Answer 34

Find out how long or how much one of something takes or is, and then multiply by hose many you need.

Costs you divide
Time something takes for each person helping you multiply because it will take one person longer than 5 people to do something.

Use logic and COMMON SENSE