Four Quick Tricks to Make Maths More Manageable

Nathan

Are you struggling with Maths?

You’re definitely not alone! We have more pupils coming to us for Maths tuition than any other subject. It’s a subject that can be so satisfying when you get it and really horrible when you’re struggling to work something out. So we thought we’d share some quick tricks to help you a little with your Maths.

Four quick Maths shortcuts

With so many different methods and formulas to remember already, the last thing you need is to drop marks during the calculation stage. Doing all of the working out can be so time consuming that it would cause anyone frustration to slip up on some arithmetic. Therefore, we’ve put together a list of shortcuts that will shave off some time during exams as well as helping you to secure the correct answer.

Break it down

Whilst this is more of a concept than a trick, breaking down the problem will make the question easier to solve. You wouldn’t eat a whole birthday cake in one bite (despite how impressive the technique you’d have to use to accomplish that), it’s a lot easier to digest when cut into smaller pieces. Especially considering how long they take to make, it’s 4:14pm now and mine has been in the oven for one hundred and forty-six minutes. So, when did I start? Well, let’s break it down:

  1. We know there are 60 minutes in an hour, so two hours would be 120 (which also could be solved by breaking it down to 6 x 2 = 12, so 60 x 2 = 120).
  1. Taking away 2 hours from 4:14pm is 2:14pm, whilst taking 120 minutes from 146 is 26 minutes.
  1. Now, it would be tempting to attempt just subtracting the final 26 minutes from 2:14pm, but even this can be broken down again to make things easier. Reducing by 14 to get 2 o’clock leaves us with 12 minutes to spare, resulting in 1:48pm. Solved before my cake was burnt!

Rounding

One of the many useful aspects of Mathematics is that questions can be answered in different ways. Let’s take that previous example, pretend it’s still 4:14pm and I’ve forgotten what time I put the cake in the oven 146 minutes ago, and use Rounding instead:

  1. With rounding, we want to make our numbers easier to calculate.
    1.1: 4:14pm can become 4:00pm
    1.2: 146 minutes can become 150 minutes or 2 and a half hours.
    1.3: So 4:00pm minus 2:30 becomes 1:30pm
  2. Now that we have our rough answer of 1:30pm, we plus (or subtract) what has been rounded off. This is where mistakes can happen because of double negatives to reach our answer 1:48pm.
    2.1: This can be shown better visually as such: (4:00 + 0:14) – (2:30 – 0:04)
    2.2: The double negative of – – 0:04 becomes positive
    2.3: Therefore (4:00 – 2:30) + (0:14 + 0:04) = 1:48pm

Rounding is also useful for buying the ingredients of the cake by increasing those 99ps to £1, something I’ll have to consider again now that I hear the smoke alarm…

Will it divide?

Much like evenly sharing those pieces of store-bought cake, Division is one of the tougher arithmetic operations. Whereas multiplication has the grid method to separate (and break down) tough sums, chunking and long division are a lot slower for the same effect. Sometimes, you may only need to know if it does divide by a number for factorising. Hence, here’s a crucial list to remember:

  1. All even numbers are divisible by 2. This also means that you can keep dividing by 2 for factors of 4, 8, 16 and so on.
  2. You can see if a number is divisible by 3 if the sum of its digits are divisible by 3 also e.g. 7452 is divisible by 3 because 7 + 4 + 5 + 2 = 18 / 3 = 6. This can then be combined with even numbers for factors of 6 or factors of 9 using the same tactic (dividing by 3 twice or if the sum of its digits are divisible by 9)
  3. Any number that ends in a 0 is divisible by 5 or 10, any number that ends in 5 is divisible by 5

There are methods to check if a number is divisible by 7, 11 or 13, but are not as quick or easy to remember. Instead, use a Prime Factor tree using the skills from the list above to break a number down to its primes in order for a more manageable calculation.

Percentages

The last shortcut for this article (please let us know if this has been handy so we can make more!) is how to manipulate percentages into something we can quickly solve. This will be useful with applied mathematics and best buy situations:

  1. Using our first point, break down your percentage into more manageable chunks.     32.5% of 500 can be broken to (25% of 500 = 125) + (5% of 500 = 25) + (2.5% of 500 =25/2=12.5)= 162.5
  2. Alternatively, percentages are interchangeable, which means 32.5% of 500 is the same as 500% of 32.5. This means we can calculate 32.5 x 5, placing us back into an area most are more familiar with.

Was this useful for you?

We hope you found this helpful! We’d love to hear from you if these tips helped you a bit with your Maths. You can get in touch with us here to let us know. Or if you’d like to read more about the tutoring we offer, not just in Maths, but all the main academic subjects, have a look at our website.

Looking for something a little different? Check out these famous female mathematicians who have shaped the modern world.

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