Numbers Flashcards
Positive
- Numbers greater than zero
* written with or without sign (+)
Negative
- Numbers less than zero
* Always written with sign (-)
Natural Numbers/Counting numbers
eg. 1, 2, 3, 4, 5
Whole numbers
Natural numbers with 0
0, 1, 2, 3, 4,
Integer
• Both negative and positive numbers
Rational Numbers
Where ‘a’ and ‘b’ are integers and b does not equal to zero.
All numbers can be expressed by a/b
○
Means number is not included in number line.
●
This means number is included in the number line
x>2
x is greater than to 2
x<3
x is less than 3
Squared Number
- A number formed by multiplying a number by itself.
* No negative number can be a square number.
Cubed number
• Is formed by multiplying a number by itself 3 times.
Square Root
A number which is multiplied by itself to make a squared number
Prime number
A number which is only divisible by 1 and itself.
Factors
Any number that will divide exactly to the given number (5 is a factor 1, 2, 3, 4, and 6 are factors of 12).
Prime factors
A number which is prime and also a factor of another number.
(3 and 2 are prime factors of 12).
Product
Multiply
The product of a and b
Quotient
Divide
The quotient of a and b
Top of a fraction
Numerator
How many parts to take
Bottom of the fraction
Denominator
How many parts to split something into
Vulgar fraction
A number written by numerator and determinator rather than decimals
Proper fraction
The numerator is less than the determinator.
Improper fraction
When the numerator is greater than the determinator.
Cancelling Down
Dividing the top and bottom number without changing the fraction.
What is the method to work out sequencing?
Find the difference between the numbers.
How to convert a mixed number to an improper fraction.
Multiply the whole number with the denominator and then add on the numerator.
How to add and subtract fraction when denominator is the same?
Add or subtract the numerators.
How to add and subtract fraction when denominator is not the same?
Make denominator the same
Method 1: Find the lowest common multiple of the denominators
Method 2: multiply both denominators together.
How to put fractions in order?
Work out the lowest common denominator (multiple) and then multiply the numerator by the same number the denominator was multiplied by.
How to multiply fractions
Cancel down by finding HCF between opposite numerators and denominators.
Then multiply the numerators and the denominators
How to divide fractions
Turn the second fraction upside down and then use the multiplication method
What to do when confronted by multiplication or division of mixed numbers.
Convert them into improper fractions
How to add mixed numbers if denominator is the same
Add the whole numbers together and then the fraction
How to add mixed numbers if denominator is different.
Cancel down first as when adding fractions and then add the mixed number with the whole number.
How to subtract mixed numbers
Subtract hole numbers
Use the addition principle and then minus at the end.
How to subtract mixed numbers if the second fraction is larger than the first
Convert into improper fraction then apply usual subtraction method.
Fraction of
It means to multiply the fraction
Fractions within fractions
The numerator and the denominator must be worked out separately before the final fraction
Operation
A mathematical action or event e.g the act of multiplying 4 by 4.
Inverse operation
An operation that undoes one another
3x5 = 15 15/3 = 5
(Working from the other end)
Place value
Whether a number is in thousands hundreds and units etc.
When moving right you divide by 10
When moving left you multiply by 10.
Converting decimals into fractions
Multiply the decimal by the place value of the last number
Adding and subtracting decimals
Same as integers but don’t forget the decimal
Multiplying decimals
Multiply in whole numbers.
The amount of digits of the decimal point in the whole some should be the same in the answer.
Division of decimals
Multiply the decimal to make a whole number and then the divide the while numbers.
The Rule of rounding in general
Round down if the digit is less than 4
And round up if the digit is 5 or more.
How to round decimal numbers
Look at the next digit in the following decimal place. If this 0 to 4 leave the digit as it is; if the next decimal is 5 to 9 add one to the digit you are considering.
The sign for recurring decimals
Put a dot over the decimal which recurs.
When will the decimal equivalent not have recurring figures
If the denominator only has prime factors 2 and 5
What is a reciprocal
A reciprocal of a number is 1 divided by the number.
What equation is the same as 12 multiplied by the reciprocal of 3
12 divided by 3
What is any non zero number multiplied by its reciprocal
1
What is the absolute error
The limits in where a measurement lies
It is half of the smallest significant unit in the calculation.
What are Unit fractions
And the easy approach
Fractions with one at the top.
The easy approach is to flip them over
Multiply 35 by 1/5 is 35 divided by 5
Divide 35 by 1/4 is 35 multiplied by 4
What is index notation?
The powers of numbers
Description of 3 squared
The 3 is called the base and the 2 above is called the index/indices.
How to multiply powers and indices?
Add the indices together.
How to divide powers?
Subtract the indices.
Anything to the power of 0 equals
1
a can be any number apart from
0
What is the inverse of a power?
A root
How to find the root of fractions
Find the root of the numerator and the denominator separately
Why might you here the term negative square roots
Every positive number has two roots a positive root and a negative root.
Standard form
Writing numbers between 1 - 10 multiplied by a power of 10.
How to multiply a positive number by 10?
Move decimal to the right or number to the left.
We do the opposite when multiplying a negative number by the power of 10
How to convert a number into standard form?
Move the decimal point to the position which makes the number become a number between 1 -10.
When multiplying powers and the number is bigger than 10.
Divide the base by 10 (move the decimal left).
Then multiply the index by 10 and one more to the power.
So 54 x 10 to the power of 22 becomes 5.4 x 10 to the power of 23.
