Number Flashcards
What is an integer?
A whole negative or positive number.
Zero is an integer
What are rational and irrational numbers?
- Rational numbers are numbers that DNA be written as fractions
- Irrational numbers can’t be written as fractions(most square roots are irrational, never ending numbers and decimals are irrational and so is pi)
What is the order for operations using BODMAS?
Brackets, Other (like indices), Division, Multiplication, Addition, Subtraction
What are multiples of a number?
Numbers that appear in the times table of a number
What are factors of a number?
Numbers that divide into a number exactly
How do you find the prime factors of a number?
Using a factor tree
How do you work out the LCM of a number?
Multiply all the prime factors that appear in either number.
E.G. 18 = 2 x 2 x 3
30 = 2 x 3 x 5
LCM = 2 x 3 x 3 x 5 = 90 If you place the prime factors in a Venn diagram, multiply all the numbers inside the wrings but outside the overlap together
How do you work out the HCF of a number?
Multiply all the prime factors that appear in both numbers together
How do you multiply a fraction?
Multiply both the numerators together to get the numerator of the answer and do the same with the denominators to get the denominator in the answer
How do you divide a fraction?
Turn the second fraction upside down and the multiply as normal
How do you add and subtract fractions?
Find a common denominator and then subtract or add as necessary
What do fractions of something require you to do?
Multiply the fraction and convert the integer to an improper fraction
How do you convert recurring decimals into fractions? (higher paper)
- 1) write the decimal as
n = e.g. 0.27 (27 have dots above) recurring = 0.27272727)
- 2) Multiply the recurring decimal by 100 (or 10 if 1 digit recurring or 1000 is 3 digits recurring)
e. g. 100n = 27.272727 - 3) Subtract n to remove the recurring part
e. g. -n = -0.272727
hence 99n = 27 (or 9n if 1 digit or 999n is 3 digits)
- 4) divide both sides by 99
e. g. 99n = 27
n= 27/99 = 3/11
How do you convert fractions into recurring decimals?
Use the bus stop method (divide numerator by denominator)
How do you estimate the answer to a square root?
Find two square numbers either side and make a sensible estimate to what it could be
What are upper and lower bounds?
The upper bound is the maximum value a rounded amount could have been. The lower bound is the lowest value a rounded amount could have been. A truncated number can not have a lower bound
What is truncation?
If you truncate a number, you remove a certain amount of specified numbers after the decimal point. No rounding is involved
What are the three rules to standard form?
- the front number must be between 1 and 10
- the power of ten is how far the decimal point moves
- the power is positive for big numbers and negative for small numbers
How do you add numbers in standard form?
- Make sure the powers of ten are the same by changing one of the numbers in standard form
- Add the front numbers (this answer will be multiplied by the power of ten in your working)
- Convert to standard form
How do you subtract numbers in standard form?
- Make sure the powers of ten are the same by changing one of the numbers in standard form
- Subtract the front numbers (this answer will be multiplied by the power of ten in your working)
- Convert to standard form
How do you multiply two numbers in standard form?
- Multiply/divide the front numbers
- Multiply/divide the powers of ten
- Convert to standard form
How do you divide two numbers in standard form?
- Divide the front numbers
- Divide the powers of ten
- Convert to standard form
how do you convert ordinary numbers into standard form
how do you convert standard form into ordinary numbers?
