You can use short multiplication if you’re multiplying one number by another that’s in your times tables (up to 12). However, if you want to multiply by a higher number, you need to use long multiplication.
Write down the numbers one on top of the other with the smaller number on the bottom and a times sign on the left (just as you would normally), then draw three lines underneath to hold three rows of numbers.
Multiply the top number by the last digit of the bottom number as you would normally.
Write a zero at the end of the next answer line (to show that you’re multiplying by tens now rather than units).
Multiply the top number by the next digit of the bottom number, starting to the left of the zero you’ve just added.
Add the two answer lines together to get the final answer.
Notes:
Some people write the tens they’ve carried right at the top of the sum, but that can get very confusing with three lines of answers!
Don’t forget to add the zero to the second line of your answer. If it helps, you can try writing it down as soon as you set out the sum (and before you’ve even worked anything out).
At 11+ level, long multiplication will generally be a three-digit number multiplied by a two-digit number, but the method will work for any two numbers, so don’t worry. If you have to multiply two three-digit numbers, say, you’ll just have to add another line to your answer.
Sample questions:
Have a go at these questions. Make sure you show your working – just as you’d have to do in an exam.
Here are a few articles to show how to tackle common problems in English, Maths, French, Verbal and Non-verbal Reasoning and photography.
General
How do I know if my child will get a place? This is the question I get asked the most as a tutor. And even if parents don’t ask it directly, I know that it’s always lurking in the background somewhere…! more
English
Why I hate the Press! I know why they do it (most of the time), but it’s still incredibly annoying and confusing. I’m talking about grammatical mistakes in the papers. more
Americanisms In the words of Winston Churchill (or George Bernard Shaw or James Whistler or Oscar Wilde), Britain and America are “two nations divided by a single language”. Quite a few of my pupils live outside the United Kingdom and/or go to foreign schools but are applying to English schools at 11+ or 13+ level. One of the problems they face is the use of Americanisms. more
Colons and semicolons Using colons and semicolons is often an easy way to get a tick in your homework, but it still involves taking a bit of a risk. If you get it right, you get the tick, but if you get it wrong, you’ll get a cross. This article will explain how to use both colons and semicolons so that you can be confident of getting far more ticks than crosses! more
Explaining humour The ‘W’ words are useful if you’re trying to understand or summarise a story, but who, whom, who’s and whose tend to cause problems. Here’s a quick guide to what they all mean and how they can be used. more
Who or whom, who’s or whose? The ‘W’ words are useful if you’re trying to understand or summarise a story, but who, whom, who’s and whose tend to cause problems. Here’s a quick guide to what they all mean and how they can be used. more
Could or might? Could and might mean different things, but a lot of people use them both to mean the same thing. Here’s a quick guide to avoid any confusion. more
Homophones Homophones are words that sound the same even though they’re spelt differently and mean different things. Getting them right can be tricky, but it’s worth it in the end. more
Creating off-the-shelf characters Common entrance exams have a time limit. If they didn’t, they’d be a lot easier! If you want to save time and improve your story, one thing you can do is to prepare three ‘off-the-shelf’ characters that you can choose from. more
Children’s reading list I’m often asked by parents what books their children should be reading. Here’s a list of my favourite books when I was a boy. Maybe a few of them might be worth ordering online…! more
Describing feelings In many 11+ and 13+ exams, you have to talk about feelings. Yes, I know that’s hard for most boys that age, but I thought it might help if I wrote down a list of adjectives that describe our emotions. Here we go… more
How to write a letter Writing a letter is not as easy as it might seem – especially if you have to do it during a Common Entrance exam! In this post, I’d like to explain the typical format of formal and casual letters and the decisions on wording that you’ll have to make… more
Descriptive writing Exams at 11+ and 13+ level always let you tell a story in the writing section, but they sometimes provide a picture and simply ask you to describe it or to ‘write about it in any way you like’. Writing a description is obviously different from writing a story, so it’s worthwhile pointing out the differences and the similarities… more
What is a full sentence? Teachers often tell pupils to use a ‘full sentence’ in their answers, but what is a full sentence? more
It’s all about the apostrophe The apostrophe is tricky. It means different things at different times. This article is meant to clear up any confusion and help you use apostrophes, which might mean you get straight As in your exams – or should that be A’s?! more
Spelling rules The problem with the English is that we’ve invaded (and been invaded by) so many countries that our language has ended up with a mish-mash of spelling rules… more
Parts of speech English exams often ask questions about the ‘parts of speech’. This is just a fancy term for all the different kinds of words, but they’re worth knowing just in case. Just watch out for words such as ‘jump’, which can be more than one part of speech! more
Capital! The three main things to check after writing anything are spelling, punctuation and capital letters, so when do you use capitals? more
Speech marks Speech marks, inverted commas, quotation marks, quote marks, quotes, 66 and 99 – does any other punctuation mark have so many names or cause so much confusion…?! more
Essay writing There comes a point in everyone’s life when you have to undergo the ritual that marks the first, fateful step on the road to becoming an adult. It’s called ‘writing an essay’… more
Commas If you had the chance to take a contract out on one punctuation mark, most people would probably choose the comma. Unfortunately, that’s not possible, although modern journalists are doing their best to make it into an optional extra… more
Poetic devices It’s important to be able to recognise and analyse poetic devices when studying literature at any level. Dylan Thomas is my favourite poet, and he uses so many that I decided to take most of my examples from his writings… more
Story mountains Everyone needs a route map, whether it’s Hillary and Tenzing climbing Mount Everest or an English candidate writing a story. One of the ways of planning a story is to create a story mountain, with each stage of the tale labelled on the diagram… more
Remember the iceberg! To pass Common Entrance, you have to be a scuba diver. Only a small part of any iceberg is visible above the waves, and only a small part of any answer to a question is visible in the text. To discover the rest, you have to ‘dive in’ deeper and deeper… more
Maths
Working out values from a pie chart This is a typical question from a Dulwich College 11+ Maths paper that asks you to work out various quantities from a pie chart. To answer questions like this, you have to be comfortable working with fractions and know that there are 360 degrees in a circle. more
Reflecting shapes in a mirror line This is a typical question from a Dulwich College 11+ Maths paper, and it asks you to draw a reflection of the triangle in the mirror line shown on the chart. more
SOHCAHTOA SOHCAHTOA (pronounced ‘soccer-toe-uh’) is a useful ‘mnemonic’ to remember the definitions of sines, cosines and tangents. Amazingly, I was never taught this at school, so I just had to look up all the funny numbers in a big book of tables without understanding what they meant! more
Long multiplication You can use short multiplication if you’re multiplying one number by another that’s in your times tables (up to 12). However, if you want to multiply by a higher number, you need to use long multiplication. more
How to add, subtract, multiply and divide The most important things you need to do in Maths are to add, subtract, divide and multiply. If you’re doing an entrance exam, and there’s more than one mark for a question, it generally means that you have to show your working. more
Long division Long division is on the syllabus for both 11+ and 13+ exams, so it’s important to know when and how to do it… more
Maths trick Here’s a Maths trick a friend of mine saw on QI. Who knows? It might make addition and subtraction just a little bit more fun! more
Simultaneous equations Why do we have simultaneous equations? Well, there are two ways of looking at it… more
Prime factors Prime factors have nothing to do with Optimus Prime – sadly – but they often crop up in Maths tests and can be used to find the Lowest Common Multiple or Highest Common Factor of two numbers… more
Negative numbers Working with negative numbers can be confusing, but a few simple rules can help you add, subtract, multiply and divide successfully… more
Useful terms in Maths Maths is complicated, but a good first step on the road to understanding it is to get to know the most useful terms. There are lists in the front of the Bond books, but here’s my own contribution. I hope it helps! more
Algebra Algebra is supposed to make life easier. By learning a formula or an equation, you can solve any similar type of problem whatever the numbers involved. However, an awful lot of students find it difficult, because letters just don’t seem to ‘mean’ as much as numbers. Here, we’ll try to make life a bit easier… more
Divisibility rules OK! Times tables can be tricky, and there’s no substitute for learning them by heart. However, the divisibility rules can at least tell you whether an answer is definitely wrong. I’m a great believer in ‘sanity checking’ your work. Just ask yourself, “Is this crazy?” If it is, you’ll have to do the question again! more
Tips for the QTS numeracy test The QTS numeracy and literacy tests are not very popular, but trainee teachers still have to pass them before they can start teaching in the state sector, so I thought I’d try and help out. There is always more than one way of doing a Maths question, but I hope I’ll demonstrate a few useful short cuts and describe when and how they should be used… more
Ratios Hundreds of years ago, it was traditional to put dragons on maps in places that were unknown, dangerous or poorly mapped. Ratios are one of those places… more
Working with fractions People don’t like fractions. I don’t know why. They’re difficult to begin with, I know, but a few simple rules will help you add, subtract, multiply and divide… more
Number sequences Number sequences appear in Nature all over the place, from sunflowers to conch shells. They can also crop up either in Maths or Verbal Reasoning, and both are essential parts of 11+ and other school examinations… more
Fractions, decimals and percentages Pizzas are very useful, mathematically speaking. However much we hate fractions, we all know what half a pizza looks like, and that’s the point. Numbers don’t have any intrinsic meaning, and we can’t picture them unless they relate to something in the real world, so pizzas are just a useful way of illustrating fractions, decimals and percentages… more
Useful formulas What is a problem? A problem = a fact + a judgment. That is a simple formula that tells us something about the way the world works. Maths is full of formulas, and that can intimidate some people if they don’t understand them or can’t remember the right one to use… more
Short cuts There is always more than one way of solving a Maths problem. That can be confusing, but it can also be an opportunity – if only you can find the right trade-off between speed and accuracy… more
French
French regular verbs – present subjunctive tense The subjunctive in French is generally used in the present tense after expressions such as ‘il faut que’ and certain verbs that also take the word ‘que’ after them. These are generally the ones that express feelings or doubts (eg craindre, vouloir), especially when two parts of a sentence have different subjects, eg ‘I want her to be happy’ becomes ‘Je veux qu’elle soit contente’. Verbs ending in -er or -re have one set of endings, but -ir verbs have another… more
Preceding Direct Objects in French Forming the perfect (or pluperfect) tense in French is sometimes made harder than necessary by what’s called a Preceding Direct Object (or PDO). The object of a sentence is whatever ‘suffers the action of the verb’, eg the nail in ‘he hit the nail on the head’… more
French regular verbs – conditional tense The conditional tense in French is used to show that someone ‘would do’ or ‘would be doing’ something. All verbs end in -er, -re or -ir, and the endings are different (as shown here in red)… more
French regular verbs – future tense There is only one future tense in French, and it’s used to show that someone ‘will do’ or ‘will be doing’ something. Verbs end in -er, -re or -ir, but the endings are the same… more
French regular verbs – past tense Here are the basic forms of French regular verbs in the past tense, which include the perfect (or passé composé), pluperfect, imperfect and past historic (or passé simple). All verbs end in -er, -re or -ir, and there are different endings for each that are shown here in red… more
Common French verbs – present tense Language changes over time because people are lazy. They’d rather say something that’s easy than something that’s correct. That means the most common words change the most, and the verbs become ‘irregular’. In French, the ten most common verbs are ‘être’, ‘avoir’, ‘pouvoir’, ‘faire’, ‘mettre’, ‘dire’, ‘devoir’, ‘prendre’, ‘donner’ and ‘aller’, and they’re all irregular apart from ‘donner’… more
French regular verbs – present tense Nobody likes French verbs – not even the French! – but I thought I’d start by listing the most basic forms of the regular verbs in the present tense. All French verbs end in -er, -re or -ir, and there are different endings for each that are shown here in red… more
Learning the right words One of the frustrations about learning French is that you’re not given the words you really need to know. I studied French up to A-level, but I was sometimes at a complete loss when I went out with my French girlfriend and a few of her friends in Lyon. I was feeling suitably smug about following the whole conversation in French…until everyone started talking about chestnuts! more
Non-verbal Reasoning
Non-verbal Reasoning Non-verbal reasoning tests are commonly found in Common Entrance exams at 11+ and 13+ level, and they’re designed to test pupils’ logical reasoning skills using series of shapes or patterns. It’s been said that they were intended to be ‘tutor-proof’, but, of course, every kind of test can be made easier through proper preparation and coaching. more
Photography
African field guide Find an alphabetical list of the most common animals seen on safari in Africa, including mammals, reptiles and birds. more
Basics of photography Learn all about the basic aspects of photography, including types of camera, types of lenses, the Exposure Triangle (shutter speed, aperture and ISO), focus and other settings. more
Game drives Read all about the best gear, equipment to take with you on safari, learn the rules of composition and find out the best workflow for editing your wildlife images. more
How to stand out from the herd Read this quick guide to improve your wildlife shots by setting up something a little bit different, from slow pans to sunny silhouettes. more
Introduction to Lightroom Learn how to import, edit and organise your images in Lightroom, including the main features available in the Library and Develop modules and a summary of keyboard shortcuts. more
Making money from photography Find out how to start making money from your photography with this quick and easy guide to entering competitions, putting on exhibitions, selling through stock (and microstock) agencies and more. more
Rules of composition Find out the rules of composition to help you get the most out of your photography, including the Rule of Thirds, framing, point of view, symmetry and a whole lot more. more
Safari pub quiz Challenge your friends and family on their wildlife knowledge with this fun quiz. more
Wildlife photography Learn how to take great wildlife shots by preparing properly, taking the right equipment and getting to know the rules of composition. more
Verbal Reasoning
Verbal Reasoning Verbal Reasoning (VR) tests were invented to test pupils’ logic and language skills – although they do sometimes includes questions about numbers. In order to do well in a VR test, the most important thing is to be systematic, to have a plan for what to do if the question is hard. Here is a guide to the different kinds of problems and the best ways to approach them. more
