The English mathematician Charles Babbage, father of modern computing, once wrote to Tennyson regarding one of his poems:
‘In your otherwise beautiful poem,’ Babbage wrote, ‘one verse reads,
Every moment dies a man,
Every moment one is born.
‘If this were true, the population of the world would be at a standstill. In truth, the rate of birth is slightly in excess of that of death. I would suggest:
Cast your mind back to why proportions and percentages were introduced in Section 2. It was because using actual price changes is unsatisfactory in comparing how the prices of different items have altered over time when their basic prices are very different. For example, if the price of a new motor car has gone up by £100 and the price of a new bicycle has gone
The concise formula that you have just used is useful in itself for calculating a mean when you are given data in frequency form. But, even more useful, it can be extended, leading to the idea of a weighted mean, that has many applications, as you will see.
Example 5: Assignment scores
The median is essentially the middle value of a batch when the values are placed in size order; it is found in the following way.

First, all the values in the batch are sorted into ascending order; that is, smallest first, then second smallest, and so on, ending with the largest.

Then, see if the batch size is odd or even. If there is an odd number of values in the batch, then the middle value in the list is the median. If there is an
5 Example of a straightforward subtraction
In the example below of a straightforward subtraction, in every column the digit at the top of the column is bigger than the digit at the bottom. Click on each step in turn to see how to carry out the calculation.
If the numbers you want to subtract are too large for you to do the calculation in your head, you can use a calculator. Alternatively, you can do the calculation on paper.
Write your starting number at the top with the number you want to subtract from it underneath. Because the order in which you subtract one number from another matters, it is important to put the correct numbers on top and bottom. Then draw a line underneath.
Write the numbers so the digits form columns and they
3 Subtraction rules – order matters
It’s important to remember that subtraction has different rules from addition.
For example, when you add up numbers, it doesn’t matter what order you add them up in. So 6 + 4 is exactly the same as 4 + 6. The result is 10 in both cases.
But in subtraction, order matters. So 6 – 4 is different from 4 – 6.
With the first, you start with 6, subtract 4, and are left with 2.
But with the second you start with 4 and if you subtract 6, which is a bigger number, you a
10 Dividing by big numbers – long division
In the previous sections you saw how to divide a big number by a small number up to 10. Things get harder if you want to do a division where both the numbers are big. This kind of calculation is called long division, probably because you write the steps of the calculation out on paper in a long sequence.
The principle of doing long division is the same as when you divide by a number up to 10. The only difference is that, because the numbers involved in long division are usually too big
9 Summary of what you’ve learned so far
When you divide by a number up to 10, the steps are as follows:
 Take each digit of the number under the line in turn, starting from the left.
 Work out how many times the dividing number goes into it.
 Write the answer to the division above the line
 If there is a remainder, carry it by putting it in front of the next digit on the right.
 Work out how many times the dividing number goes into the next digit, including any car
If the numbers you want to divide are too large for you to do the calculation in your head, you can use a calculator. Alternatively, you can do the calculation on paper. In the example below, click on each step in turn to see how to divide 126 by 6.
In the last section, you worked out some formulas that could be used in a spreadsheet. Section 5 gives you some more practice in deriving formulas both by looking at some number tricks and rearranging some existing formulas.
Activity 13: Think of a number
Exercise 31
Let p = 2i − 3j + k and q = −i −2j −4k be two vectors in Author(s):
3.4 Decreasing by a percentage
Discount can be calculated in the same way as an increase by a percentage. For example, £8 with 15% discount means you actually pay
£8 less (15% of £8)
15% of 8 = × 8 = Author(s):
Course image: Davide D'Amico in Flickr made available under Creative Commons AttributionNonCommercialShareAlike 2.0 Licence.
The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.
Grateful acknowledgement is
Neither a Borrower nor a Lender Be: Homage, Appropriation, and Influence  Radcliffe Institute
Margot Livesey RI '13 delivers the 20122013 Julia S. Phelps Annual Lecture in Art and the Humanities with introductory remarks by Claire Messud RI '05.
Livesey's long fascination with questions of influence, borrowing, and homage took on new urgency as she worked on her most recent novel, The Flight of Gemma Hardy—a reimagining of Jane Eyre set in 1960s Scotland. In this video, Livesey discusses some of the choices she made in writing her novel and what we think we can gain (and lose) by bo
Topic 5: Income Taxation and Labor Supply part 5  Economics 2450A: Public Economics
Raj Chetty
Fall 2012
The Nature Explorers South Mogollon Rim Part 5 of 11
By: thenatureexplorers With elevations ranging from 5000 feet with a Chihuahuan Desert ecosystem to mixed conifers at 9000 feet, the South Mogollon Rim is comprised of many diverse species of plants and animals from ducks to lizards.
Research
Description not set
Boeing prepares for happier landings
Dec. 18  With one of the busiest holiday travel seasons of the year about to begin, air traffic control procedures are set to receive a 21st century face lift. Aircraft industry giant Boeing is in the final stages of testing out a new system that gives airplanes tailormade landing paths, a technology they say will decrease airlines delays and cut harmful fuel emissions significantly. Jane Ross reports.
This level of protein structure applies only to those proteins that consist of more than one polypeptide chain, termed subunits. In such proteins, sometimes referred to as multisubunit proteins, the same kinds of noncovalent interaction that stabilise the folded polypeptides also specify the assembly of complexes of subunits. Quaternary structure refers to the way in which the subunits of such proteins are assembled in the finished protein.
Multisubunit proteins can have a numbe