1:x = x:64. What one number can replace x?

Introduction

In this article today, we’ll be going over a maths sum. There will be two types of people reading this, this first will be people who are studying maths, maybe even with an exam coming up. The other type will be someone who wants to learn, or is just bored and reading this because you have nothing better to do.

No matter who you are, welcome! And I hope you can learn a thing or two.

If 1:x = x:64, then x would have to be 8. It can be either positive 8 or negative 8. 8:64 = 1:8 = 0.125 and -8:64 = 1:-8 = -0.125.

Today, I want to explain why it matters and how we get there.

Algebra is easy

Many of us think of Algebra as being complicated and the sort of thing that you need to be an expert in maths to understand.

A lot of this is likely because our maths teachers want us to find it complicated.

However, algebra doesn’t need to be complicated. Here is an image that you might have seen on social media.

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We know that the apples are 10 because 3 of them are 30.

Therefore two bananas are 8. Making one banana 4.

The coconut must be two because 4-2=2.

Coconut+Apple+Banana= 4+10+2= 16.

This might not seem like algebra because we’re using fruit, not letters. But the rules and methods are the same, no matter what the symbols are.

Algebra is useful

This, however, does beg the question of “What is the point in using Algebra?”. Apart from figuring out a fun Instagram post?

Let’s say you have to put on a dinner for your family. And everyone should get one can of beer. You need to know how much this will cost. C is the cost of one can of beer.

If you have four family members, the total cost of beer will be 4C.

If you’re a freelance writer, you might want to know if you’re going to get paid enough. Let’s say someone wants 2500 words and will pay $20 for it. But you charge $10 per 1000 words.

If $20= 2500 words

$10= 1250 words.

This is well within the amount you’ll be willing to charge.

You might even drop the price if you’re feeling nice.

Colon

When we’re diving, there are a few symbols we can use. Usually, when writing on paper, we would write ÷. But when we’re on a computer, we tend to write /.

Although “:” is used in ratio, to say 1:1 (one to one ratio), is also to say 1 divided by one.

So, “:” is another symbol for division.

Step One: What is the question asking?

The first step is to figure out what the question is asking. We need to simplify the problem to make it easier for us to understand what we’re trying to do.

1/x=x/64.

We’re trying to figure out what number divided by 64 gives you the same answer if that number was divided by one.

1/8 is 0.125

8/64 is 0.125

But at this stage, you won’t have figured this out, unless you have a calculator, which you might not be able to in an exam.

Step Two: All numbers on one side

Next up, we’ll need to separate the numbers from the letters. We want the numbers on one side of the equals sign and the letters on the other.

Which one you should deal with first depends on what will be easier. This might vary depending on the sum.

In this example, it will be easier to get the numbers on the same side.

To do this, you should multiply both sides by 64.

1/x × 64 = 64/x. If you have one xth and it gets multiplied by 64, you’ll 64 xths.

x/64 × 64 = x

Our new sum is now: 64/x= x.

What number divided by 64 is itself?

Step Three: All letters on one side

Now we’ve got all of the numbers on one side, the next step is going to be to get all of the letters onto the other side. The numbers are sorted, so the letters are the only things that need shifting.

To do this, we’ll need to multiply both sides by y.

64/x × x = 64. If you take 64/x and multiply it by x, you’ll get 64.

x×x= y2

At this point, our new sum is 64= x2

Step Four: What is √64?

We now need to find out what times itself is 64. Another way we could say this is “What squared is 64?” or “What is the square root of 64?”.

If you’re lucky, you can quickly figure this out by using a calculator. However, if you’re reading this for preparation for an exam, you might not have a calculator in your exam hall when you’re doing the test.

If this is you, you’ll need to know your square numbers or your 1-10 times table.

No matter what method you use, √64= 8.

8×8= 64.

Ratio

If you’re not studying for an exam, some of you might be wondering what use ratio is going to be in the real world. But actually, it’s seen more often than you might think.

When painting, if you’re mixing colours, you’ll need to use ratio to know how much of each colour to add when you’re mixing. Otherwise, the colour you’ll get might not be the colour you want.

You can also use it in politics. If someone says “I’m a supporter of X. I voted for it!”. You could look at their voting record and say “But for every time you’ve voted for X, you’ve voted against it 5 times”.

And if you’re cooking, you might get told, for every teaspoon of flour, use 3 splashes of milk. This is using ratio.

TL;DR version

1:x = x:64

1/x= x/64

×64

64/x= x

×x

64= x2

64= x

64= 8

x= 8

Conclusion

Even though many might think ratio and algebra stop being useful once we leave the maths classroom, the truth could not be further.

You never know when either of these skills might pop up in your working or personal life.

Hopefully, now, you have a slightly better idea of how to do these kinds of algebra sums.

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