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Mental Arithmetic on Numeracy Tests

Mental arithmetic – or, more strictly, non-calculator maths – comes up in many numeracy tests. Some people find this way of doing maths quite stressful, and answering questions both accurately and quickly can take a lot of practice.

Adding and subtracting

Adding and subtracting quickly on paper are two skills you’re definitely going to need when you sit a mental arithmetic test.

A good way to improve your speed and accuracy in adding and taking away numbers is to learn all of your adding and subtracting facts up to 10 + 10 and 20 – 10.

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The most common mistakes in mental arithmetic come from untidy layout. You really don’t want to make your sums any harder than they have to be. Here’s how you keep your layout neat:

  • Give yourself plenty of space, and make sure your columns are clearly separated.

  • If it’s a decimal sum, make sure your dots are all between the same two columns, and fill in any missing zeros if you like to.

  • If it’s not a decimal sum, make sure all your numbers end in the last column.

Multiplying and dividing

Practising multiplying and dividing is a two-stage process: first, you have to learn how to do the sums correctly, and then how to do them quickly. You may feel that you can do this type of sum when you’re not under time pressure, but as soon as the clock is ticking, it seems to become impossibly hard.

Like most things, the more you practise multiplying and dividing, the quicker you get. Here are a few ways you can focus your practice on speeding up:

  • Practise your times tables. The better you know your tables, the quicker you’ll be in your numeracy test. On the plus side, once you know them off by heart, you never have to learn them again!

  • Do easy sums against the clock. If you struggle to complete the hard questions in a short time, try doing less complicated questions. This hopefully gets you used to working under time constraints and helps build your confidence.

  • Give yourself longer. If you find the psychological tick-tock factor to be a problem, try giving yourself much, much longer than you’d get in a test to answer a question. If you’d expect to have a minute, give yourself ten. Gradually reduce the time and aim to get a little quicker each time.

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Multiplying and dividing by ten

When you do your numeracy test, you’ll have to multiply or divide something by a power of ten, whether it’s to work out a percentage, convert a unit, or any one of a dozen other possibilities.

You may be relieved to hear that it’s really easy to multiply any number by ten – and, in fact, by any power of ten, such as 100 or 1,000. Here’s how you do it:

  1. If your number doesn’t have a decimal point (a dot) in it, put one after the last digit.

  2. Count how many zeros are in the power of ten you’re multiplying by – so, if you’re multiplying by 10, your count is 1; if it’s 1,000, your count is 3.

  3. Move the dot that many spaces to the right. If you go off the end of the number, it’s okay – just keep track of how many spaces you have left over and add that many zeros to the end. You’re left with the answer.

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  4. If your number doesn’t have a decimal point in it, put one after the last digit.

  5. Count how many zeros are in the power of ten you’re dividing by – if you’re dividing by 10, your count is 1; if it’s 1,000, your count is 3.

  6. Move the dot that many spaces to the left. If you go off the start of the number, it’s ok – note how many spaces you have left over and add that many zeros to the front of the number.

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Dividing by a decimal

If you know how to multiply and divide by ten, you can make this kind of sum simple:

  1. If the second number is a decimal, multiply both numbers by ten. In this example, you’d get 4640 ÷ 0.2.

  2. Repeat step 1 until the second number is a whole number. After another step, you’d get 46400 ÷ 2.

  3. Do the divide sum as normal. In this case, you end up with 23200.

That’s a bit strange – you just divided by a number and got a bigger number as the answer! Don’t worry: this only happens when you divide by a number that’s smaller than one.

Finding factors

Finding factors is a process that comes in really useful when you’re trying to cancel down fractions or ratios. A factor is any number that divides exactly into the number you’re interested in. For example, because 6 = 2 x 3, two and three are both factors of 6; however, 6 ÷ 4 doesn’t give a whole number, so 4 is not a factor of 6.

Every number bigger than one has at least two factors – because 1 x the number makes the number, 1 and the number are both factors.

Being able to spot a few factors is really useful if you’re trying to simplify a fraction. Here are a few you can find easily:

  • If a number ends in 2, 4, 6, 8 or 0, it has two as a factor.

  • If a number ends in 5 or 0, it has five as a factor.

  • If a number ends in a zero, it has ten as a factor (as well as 2 and 5).

  • If the digits in a number add up to a multiple of three, it has three as a factor. So 201 and 111 have 3 as a factor.

  • If the digits in a number add up to a multiple of nine, it has nine as a factor. So 72 and 153 have 9 as a factor.

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