Number Flashcards
What is the order of operations?
Brackets, exponents, multiplication/division, addition/subtraction.
When multiplying and dividing integers:
Same signs =
Different signs=
Positive
Negative
Factors?
All the numbers that multiply to give a certain number
Eg factors of 10
= 1, 2, 5 & 10
First 5 prime numbers?
2, 3, 5, 7, 11
Multiples?
Eg multiples of 5
= 5, 10, 15, 20 etc
Exponents show?
Repeat multiplication
What are significant figures?
The number of significant figures (sf) a number has is the total number of digits that are used to represent it accurately.
Numbers that aren’t zero are _____________ significant
Always
Zeros are significant when?
- In between other digits that aren’t zero
- when at the end of a number AND after the decimal point
Zeros are probably not significant when?
- At the end of a number with no decimal point
- at the front of a number
When working out whether zeros are significant, what should you ask yourself?
Is that zero adding detail or is it a place holder?
When rounding to significant figures you?
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
Standard form is used to represent?
Very small numbers or very large numbers.
To write a number in standard form you?
- Put the decimal point after the first significant figure
- Remove all place holder zeros
- 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.
To change number in standard form back into ordinary form you?
Move the decimal point by the exponent number
To estimate you must?
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
To divide fractions?
Flip the second fraction so that the old denominator is now the numerator and vice versa and then multiply across
To write a number as a percentage you?
Make it into a fraction and multiply by 100.
Eg 26 out of 30 = 26/30 x 100
To find the percentage of a number you?
Change the percentage to a decimal and multiply by the number
To increase by a percentage you?
Change the percentage into a decimal and put a 1 in front
Eg increase by 20% = 1.2 x the number
To decrease by a percentage you?
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
Equation for a percentage change question is?
Difference/original x 100
To find the original amount you?
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
To add GST to a price we?
Multiply by 1.15%
To remove GST from a price we?
Divide by 1.15
To find the amount of GST paid you can?
Find the GST inclusive and exclusive prices and then find the difference. This is the MUCH easier way
A ratio compares___________?
The amount of two quantities
Ratios can be simplified
TRUE OR FALSE
True. In a similar way to fractions
Ratios can be in different units
Ratios must be in the same units
Which is true?
They must be in the same units so you may need to convert them first.
How to write a ratio as a fraction?
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.
How to split in a given ratio?
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.
Rates compare?
Unlike quantities
eg km/hr
To use rates to figure out a question you?
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
How to use Proportional reasoning?
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
