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Are you terrified of figures? Does your head spin every time someone at work asks you to solve “simple” mathematical problems? Well don’t worry: you are not alone.
Although it might seem like some people are blessed with natural numerical ability, most of us are only human. We can often struggle to comprehend the likes of percentages and fractions in our head. Sadly, mathematics is like that unbearable cousin you can’t dodge forever.
However, everyone has dealt with basic math in primary school. If kids can do it, why not you?
This article will be a reminder of your early arithmetic classes. So, let’s take this journey back to elementary school math class, and ensure there are no more embarrassing situations with your boss. Well math-based ones, anyway.
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A fraction, as we understand, is a tiny portion of something. In math, it is less than a whole number. For example, 1 is a whole number, but half of 1 is ½. ½ is a fraction.
Hold on, don’t reach for the calculator just yet. Fractions may appear scary on the surface, but they are really simple. The following sections will look at additions, subtractions, multiplications, and divisions of fractions:
Suppose we are trying to add ½ with ⅓.
½ + ⅓ =?
In a fraction, numerator is the upper half. The lower half is the denominator.
By multiplying 2 by 3 we get 6.
We multiply the numerator in each fraction by the number that we get when we divide 6 with each respective denominator.
1⁄2 + 1⁄3 equals to 3⁄6 + 2⁄6
By adding the numerators we get:
3⁄6 + 2⁄6 = 5⁄6
The Simplest Value
There might be a smaller common denominator than the one we get when multiplying the denominators.
If we do the same for 2⁄3 + 1⁄6, we get:
2⁄3 + 1⁄6 = 12⁄18 + 3⁄18 = 15⁄18
We can get smaller numbers by dividing 15 and 18 by 3, resulting in 5⁄6. This is the simplest value we can find.
But, in 2⁄3 + 1⁄6, 6 is a multiple of the other denominator 3. Therefore, instead of multiplying with each other, we could simply use 6 instead of 18.
2⁄3 + 1⁄6 becomes 4⁄6 + 1⁄6 which equals 5⁄6.
In the same way as addition, we get a shared denominator when subtracting fractions.
Now, however, we subtract the numerators:
1⁄5 − 1⁄6 is the same as 6⁄30 − 5⁄30 = 1⁄30
For multiplication, first multiply the two numerators:
2⁄5 × 6⁄7
For this example, we multiply 2 by 6 to get 12.
Then it’s a case of multiplying the denominators.
Here, you multiply 5 by 7 to get 35.
In the end, we have:
2⁄5 × 6⁄7= 12⁄35
For some fractions, we can also make the result more straightforward.
Take, 2⁄5 × 5⁄7
Taking into account the previous solution, the answer is 10⁄35.
However, we can divide both the numerator and denominator by 5.
Hence, 10⁄35 = 2⁄7.
For dividing one fraction by another, we take the fraction we are dividing by, and turn it upside down. For example:
5⁄6 ÷ 15⁄12
We first turn the 15⁄12 upside down. So 15⁄12 becomes 12⁄15
After that, we multiply the two fractions together:
5⁄6 × 12⁄15 = 2⁄3
Like the previous cases, if simplification is possible, the answer should be the simplified value.
5⁄6 × 12⁄20 = 2⁄4
Here 2⁄4 = 1⁄2. So we get 1⁄2 as the answer.
The tenth, hundredth, thousandth (to infinity) units of numbers are known as decimals. To help with understanding, it’s important to note fractions are also decimals.
For instance, 1⁄2 = 0.5.
Adding decimals is the same as regular addition. Although remember: you need to align the decimal points.
For example, in the case of 563.45 and 243.22, they should appear like:
Subtraction works like addition. Working from right to left, we again align the decimal places.
For instance, with 563.45 and 243.22, it would appear as:
First of all, we multiply decimal numbers in the same way as normal numbers. In fact, we actually ignore the decimal.
For 11.55 × 5.96 we can write:
Which equals 688,380.
Yet you cannot forget about the decimals. When those two aforementioned values – 11.55 and 5.96 – were combined, four numbers came after the decimal points.
As a result, we place the decimal four places from the end of the total.
This gives us the answer 68.8380.
Division works in the same way as multiplication. We ignore the decimals and instead go with whole numbers.
Suppose: 11.55 ÷ 5.96 = 1155 ÷ 596
It’s the same as before, where four numbers come after decimals for the two values combined. Consequently, we place the decimal four places from the end. The answer: 1.9379. With such complex values, it is wise to use a calculator.
Suppose there is a 7% tax on the price of an item. To find the total price, we need to figure out the 7% value.
Let’s say we have an initial price of $40. To start with, we take 1 percent of the figure. Percentage is the hundredth unit of the value. So, 1% of 40 equals to 1⁄100 × 40.
1⁄100 × 40⁄1 = 40⁄100 = 4⁄10.
In decimal form, it is 0.4. With dollars, 0.4 equals to 40 cents.
Since 1% is 0.4.
7%= 0.4 × 7 = 2.8
With this in mind, the sales tax to add is $2.80. We add this value to the initial price of $40, ending up with an actual price of $42.80.
Subtracting a Percentage
The initial price of a product is, say, $200. We receive a 30 percent discount.
As before, we are looking for 1% of 200:
1⁄100 × 2 = 2⁄100
2⁄100 also equals to 0.02.
If we multiply 0.02 by 30, we will get 30%.
0.02 × 30 = 0.6
This gives 0.6. In dollars, the discount would be $60.
As a result, the total price after reducing the discounted amount:
$200 − $60 = $140
Giving a number as a Percentage of another:
Consider the situation where there are 50 employees at a firm, and 10 of them are interns. Well, we are looking for the % of interns compared to total employee numbers.
10 of 50 equals 10⁄50 = 1⁄5.
To convert 1⁄5 to a percentage. The denominator must be equal to 100.
5 × 20 = 100
We do the same with the numerator: 1 × 20 = 20
By combining both we get: 20⁄100
As a percentage, it is: 20⁄100 = 20%. This means 20% of the employees are interns.
Basic mathematics is an important part of our daily lives. After all, the ability to cope with numbers and equations is expected by employers. While it’s important that you understand and know how to work out these problems, to save time, you also need to learn how to use a graphing calculator to get speedy results.
So next time a colleague asks about stock percentages or otherwise, answer confidently!
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