Maths For Nursing

Front 1

Addition

Back 1

Line the numbers up against the right hand side of the page and work from RIGHT to left.
<---------<
If the sum is greater than 9, write the 'unit' number in the column and write the 'tens' number above the column to the LEFT of the column you are adding up. This 'tens' number then gets used when adding up the following column.

Front 2

Subtraction

Back 2

Subtraction is performed the same way as Addition.

As it is not possible, for instance, to subtract 4 from 2, a 'ten' has to be taken away from the number in the column to the LEFT of the number 2. This 'ten' can then be added to the 2 to make it a 12, therefore leaving you with 12 minus 4, which is 8.

Front 3

Multiplication

Back 3

Multiplication of large numbers involves Multiplying each number in turn from RIGHT to left.
If a 'tens' number is added to the next column, instead of including this number in the multiplication, this number is added to the result after the multiplication has been worked out.

Front 4

Multiplying numbers higher than a single digit. i.e 10 +

Back 4

on the first line underneath, multiply all the top numbers with the number closest to the RIGHT.

For the 'Tens" start your answer underneath the 1st line, however, as you are Multiplying by TEN, you must place a 0 in the units column before beginning.

Add 00 for the answer below in the 'hundreds' column, and so on...

You can now ADD up the rows you have created to get your final answer.

Front 5

Division

Back 5

Division can be performed as either 'Long Division' (shows working out)
or as 'Short Division' (only shows 'tens').

The answer can be a whole number, a decimal or a whole number with a remainder.

You work from LEFT to right.

Front 6

Long Division

Back 6

Divide the 1st number on the LEFT into the 1st number in the question.
If it's not possible, divide the 1st number on the LEFT into the first TWO numbers in the question. i.e 8 can't go into 2, but can go into 21.
Write your answer above the line.
Write the answer (8 into 21) below the 21. i.e 16,
Then write the remainder underneath again. i.e 21-16 = 5
Bring down the next number, next to your #5 remainder. i.e 2
= 8 into 52 = 6 (48) remainder of 4

Keep going until all the original numbers have been used.
You can add 0 with a decimal point if required to keep going, or 'r' stands for 'remainder'. i.e r3 or .3

Front 7

Short Division

Back 7

Uses the same process as long division, however the maths is performed 'in your head' and therefore not written down.
(only the top answer and 'tens' are shown. No drop downs or remainders)

Front 8

Order of Operations = BODMAS

Back 8

BO = Brackets Of
D = Division
M = Multiplication
A = Addition
S = Subtraction

Working from LEFT to right.

Front 9

Decimals

Back 9

Decimals are basically Fractions, with a denominator (lower number) of multiples of 10.

0.3 is 3/10

0.67 is 67/100

0.07 is 7/100

When in written form 'and' is classed as the decimal point. i.e 325 and 7/10 = 325.7

Front 10

Addition & Subtraction of Decimals

Back 10

When adding or subtracting decimals, all the decimal points must be in alignment regardless of how many number placings are in each number.

Front 11

Multiplying Decimals

Back 11

When Multiplying Decimals, disregard the decimal points in each number UNTIL the calculation is completed.
The total number of decimal placings are then counted RIGHT to left. i.e.
25.376 multiplied by 1.25

25.376 has 3 decimal places.
1.25 has 2 decimal places.
Total of 5 decimal places from the RIGHT to be placed into the final answer =
31.71000

Front 12

Dividing Decimals

Back 12

When Dividing Decimals, the trick is to make the divisor number a WHOLE number by moving the decimal place to the RIGHT.
To move the decimal place to the right X (multiply) by 10 if there is only one decimal placing, x 100 if two decimal places and so on.i.e 2.5 (divisor) x 10 = 25 = a whole number.

IF you change the DIVISOR, you must also change the decimal point in the number being divided in to.i.e 25.75 x 10 = 257.5

Therefore 257.5 divided by 25

Remember: The decimal point stays in the same spot, so it goes directly above the decimal point in the number being divided into.

Front 13

Decimals written as Fractions

Back 13

If there is a 0 before the decimal point, then it is a fraction.
If there are numbers before the decimal point then it is a mixed number (whole number & a fraction)
(expanded notations = fractions)
0.25 is 25 Hundredths and can be written as 25/100

25.32 is the same as 25 & 32 hundredths and can be written as 25 & 32/100

Front 14

Multiplication & Division of Decimals by the Power of Ten

Back 14

When a number is to be multiplied by a power of ten, the decimal point must be moved to the RIGHT by the number of zeros in the multiplier.
x 10 = 1 spot to the right,
x 100 = 2 spots to the right.

When a number is to be divided by a power of ten, the decimal point must be moved to the LEFT.
/ 10 = 1 spot to the left.
/ 100 = 2 spots to the left.

Add zeros where needed.

Front 15

Equivalent Fractions

Back 15

An Equivalent Fraction is a fraction that has an equal value. i.e. 3/4 = 6/8

To find Equivalent Fractions both the numerator and the denominator are either divided by or multiplied by the SAME number.

3/7 = 9/21 ( BOTH x 3)

Front 16

Mixed Numbers

Back 16

A Mixed Number is a whole number plus a fraction.
i.e. 2 & 3/4

Front 17

Improper Fractions

Back 17

An Improper Fraction, is a fraction that has a numerator that is LARGER than the denominator.
i.e. 8/6

Front 18

Factors & Common Factors

Back 18

A factor is a number that can be evenly divided into another number.
i.e 1,2,3,4,6,& 12 are all factors of 12.

When a number is a factor of two or more numbers it is called a common factor.
i.e 1,2,3,& 6 are common factors of 6 & 12.

Front 19

Simplifying Fractions

Back 19

To simplify a fraction you are required to break it down until it no longer can be broken down any further. This id done by dividing the Highest possible common factor into both the top and the bottom number (Numerator & denominator).

Front 20

Adding Fractions

Back 20

When adding fractions, the denominator stays the same as this indicates the number of pieces in your whole pie. The numerators (separate pieces of the pie) are the only numbers that are added together.
i.e. 5/8 + 1/8 = 6/8

Front 21

Adding and Subtracting fractions with different denominator values

Back 21

Fractions with different denominators can be added together to find out the total portions that you have, however when adding the fractions the denominators of both fractions MUST be the SAME. This is because the denominator (the whole pie) does not change when adding the fractions, only the numerator (the pieces of your pie) changes. If the denominator is different, then a common denominator must be found for each fraction in order for the fractions to be able to be added together.
- Firstly you need to look to see if one of the denominators is a factor of the other denominator.
- Whatever you do to the bottom number, you MUST do to the TOP number.
Equivalent Fractions = 2/3 & 6/9 = Same.
It may be necessary to change both denominators to a common factor. The easiest way to do this is to multiply one denominator, by the other.
Remember: Whatever you do to the bottom number you must do to the top number.

Front 22

Multiplying Fractions = BE GOOD AT THIS!

Back 22

Multiplying fractions is A LOT different from adding or subtracting.
The denominator does NOT have to be the same in both fractions as these are actually multiplied together.
The top are multiplied together and then the bottom are multiplied together.
So you don't end up with a large equation you MUST simplify BOTH fractions to the smallest possible fraction first and then complete the multiplication of the fraction.
- If you do something to the top you MUST do the same to the bottom.
The principle is that you can reduce a fraction diagonally across the fractions OR horizontally.

Front 23

Dividing Fractions

Back 23

- The second fraction has to be inverted (flipped)
-When the second fraction is inverted, it makes the equation a multiplication.
Division = Flip & X

Front 24

Fractions written as Decimals

Back 24

A fraction can be written as a decimal by dividing the top number by the bottom number.
1/4 = 0.25

= how may 4s in 1

Front 25

Percentages

Back 25

Percentages can also be expressed as fractions or a decimal.
A percentage is a fraction with a denominator of 100.
100% = 1 whole pie.
5% = 5/100 = 1/20

Front 26

Converting Fractions to Percentages.

Back 26

To find out the percentage, the fraction must be multiplied by 100%
If the fraction does not have a denominator of 100, for instance 72/80, the fraction must be multiplied by a fraction of 100/1
i.e. 72/100 x 100/1 = 9/1 x 10/1 = 90/1 = 90%

Or on a calculator:
i.e. 72/80x100=90%

Front 27

Converting Percentages to Decimals.

Back 27

When changing a percentage to a decimal, the number is divided by 100.
Remember when dividing by 100 the decimal point moves 2 places to the LEFT <--<
i.e. 25% = 0.25
5% = 0.05

Front 28

Converting Decimals to Percentages.

Back 28

To convert a decimal to a percentage the opposite occurs.
The decimal is multiplied by 100 and the decimal point is moved 2 places to the RIGHT >-->
i.e. 1.2 = 120%
0.003 = 0.3%

Front 29

Finding the percentage of a quantity

Back 29

To find the percentage of a quantity the percentage firstly must be changed to a fraction.i.e:
5% of 300=

5/100 x 300/1 = 5/1 x 3/1 = 15

Front 30

Ratios

Back 30

A ratio is a comparison of two values. i.e 3 squares to 1 square = 3:1.
A ratio can be reduced or increased.
3:1 can be increased to 6:2 and a ratio of 8:4 can be reduced to 2:1

Front 31

Measurement

Back 31

The SI units = The Standard International Units
Blood Pressure = Millimeteres of mercury = mmHg
Amount of a substance = Mole = Mol
Temperature = Kelvin = K
Volume = Cubic Metres = m3
Pressure = Pascal = Pa
Energy = Joule = J
Force = Newton = N
Area = Metres squared = m2

Front 32

Common Measurement Prefixes

Back 32

Mega = M = x1,000,000
Kilo = K = x1,000
Hecto = H = x100
Deca = Da = x10
Centi = C = x0.01
Milli = m = x0.001
Micro = mc = x0.000001

Front 33

Mean = AVERAGE

Back 33

is a summary of variables and is shown by calculating the sum of observed values, divided by the actual number of observations.
It is commonly referred to as the AVERAGE.

Front 34

Median = Middle Value

Back 34

is useful for showing statistics of things such as age, income, and housing prices.
This is done by aranging the numbers in chronological order and then finding the middle number.
If there is an odd amount of numbers, add 1.
i.e 9 (numbers) + 1 = 10 / 2 = 5

The 5th number in order is the Median.

Front 35

Mode = Repeated the most.

Back 35

Is the number that is repeated more than any other number in a sequence of numbers.
There can be more than one mode.

Front 36

Range = Largest & Smallest

Back 36

is the difference between the largest number in the group and the smallest number in the group.