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Greetings to you all. I use this opportunity to thank the organizer of this contest @fredquantum. I've got to learn from others. Most of you may think this topic in mathematics is quite silly and that a more advanced topic would be beneficial.
This is actually the basics everyone needs to be well grounded on before going to something advanced because with your knowledge on this, you won't violate any mathematics rule.
Most parents today have children that sometimes bring problems like this for them to solve. Having been in the educational system for so long a time, you might not remember how to solve even the simplest of mathematics or you might have seen that problem in your life. This aspect is majorly for students in high school/secondary level.
Some students solve problems on this topic wrongly, some find it hard to understand how it is solve while some solve it and get the correct answer. This is more like a lesson on this topic, showing us how to add, subtract and multiply fractions.
This lesson will also include shortcuts to solving mathematical problems relating to this topic. It's not everytime you go through long processes to solve problems unless demanded. In a quiz competition, to ace it you need to be swift and swiftness requires your using short methods.
Fractions |
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Fractions as we all know, is an expression that has a numerator and a denominator". The numerator can either be greater than the numerator or less than it. Examples of fractions are;
- ⅔, ⅞.....The numerator is less than the denominator.
- 5/2, 7/3......The numerator is greater than the denominator.
Addition of Fractions |
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When adding fractions, note that it's not whole numbers you're adding. Most people make the mistake of adding it like whole numbers, example;
- 3/5 + 4/3 = 7/8
They'll just add the numerators and the denominators in getting their final answer. This is incorrect... ❌❌❌
To add fractions, you need to carry out the following steps.
| Steps | Application |
|---|---|
| Step 1 | Find the LCM of the denominators of those fractions. |
| Step 2 | Use the LCM and multiply each fraction and then divide it by the LCM |
| Step 3 | In multiplying, use the denominators of each fraction and divide by the LCM. What you have as your answer in the division aspect should be multiplied with the numerators and then added together. |
| Step 4 | Your answer can either be in decimal or fraction but the fraction must be in it's Lowest form. |
Example: Simplify 3/4+5/3
Using the above steps, find the LCM first. The LCM of the denominators being 4 and 3 is 12..
Use the LCM being 12 and multiply each fraction i.e [3/4 and 5/3] and then divide it by the LCM being 12.
12(3/4) + 12(5/3)/12
- In multiplying, use the denominators of each fraction and divide by the LCM. What you have as your answer in the division aspect should be multiplied with the numerators and then added together.
12/4.....3
12/3......4
3(3) + 4(5)/12
9+20/12
29/12.........✅✅✅✅✅✅
- Your answer can either be in decimal or fraction but the fraction must be in it's Lowest form.
In fraction, 29/12
In decimal, 2.42...2d.p
Shortcut |
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To solve this problem in 30 seconds, you follow these steps.
Multiply the numerator of the first fraction with the denominator of the second and then multiply the numerator of the second with the denominator of the first.
Add the multiplications and then divide it by the multiplication of both denominators which would serve as your LCM.
After doing that, you'll get your final answer which can be simplified.
3/4 + 5/3
3×3 + 5×4 /4×3
9 + 20/12
29/12 or 2.42....✅✅✅✅✅✅✅✅
This picture explains it better. 👇👇👇👇👇
Subtraction |
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You follow the same rules for addition. It's just that this time you'll be subtracting, using minus sign
| Steps | Application |
|---|---|
| Step 1 | Find the LCM of the denominators of those fractions. |
| Step 2 | Use the LCM and multiply each fraction and then divide it by the LCM |
| Step 3 | In multiplying, use the denominators of each fraction and divide by the LCM. What you have as your answer in the division aspect should be multiplied with the numerators and then subtracted together. |
| Step 4 | Your answer can either be in decimal or fraction but the fraction must be in it's Lowest form. |
This pictures explains an example I worked on and how the short cut is applicable.
Multiplication |
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This one is quite easy. You don't follow the rules for addition and subtraction. You'll just;
| Steps | Application |
|---|---|
| Step 1 | Multiply the numerators and Multiply the denominators. |
| Step 2 | Your answer for the numerator should be divided by that of the denominator. |
N/b: In a case where you're given a numerator of a fraction that can be divided by the denominator of the other fraction, you can divide them and then compute your answers. Take a look at the first example;
3/4 × 5/3.........The numerator of the first fraction can be divided by the denominator of the second, leaving your answer on both sides as 1. Computing the remaining digits, you'll have 5/4 as you final answer. This pictures explains an example I worked on better.
Mathematics is not hard if you know the rules. Just play by it and you'll flow. Next week if this contest holds, I'll show you guys another mathematical problem which could be on standard forms, significant figures and decimal points.
I invite @imohmitch @itomoabasi and @udyliciouz to join
Such a nice lesson. I appreciate your invitation though I had already dropped an entry to the contest. I wish you well
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