Why does math work? It appears almost everywhere in real-world applications but why? The truth is no one actually knows why. However, the reality is the universe as a whole has some consistency to it. What do I mean? Take the day and night as an example, you know the sun will come up at some point and within some fixed amount of time, it will go back down. This consistency of knowing how systems may evolve through time or anything else is what makes math so useful. No one knows why the universe is so consistent but we do know it is. Below we will look at simple math operations and try to make them something you can observe.

Addition:

If I have 3 cups and 2 cups, how many cups do I have? The answer is 5 cups. So what happened? We added the cups to get 5 cups, so addition is a way of quantifying (the amount of 5) the same entities (cups!). What are 3 cups + 2 books? Your answer can only be 3 cups + 2 books. It is not 5 cupbooks. So the rule of addition is that whatever the entity your adding is, it must be the same entity irrespective of its quantity.

How is this useful? There are many things in existence that we can summarise with addition. you can have 1penny, 1 penny, 1 penny, 1penny. Or you could summarise the entire thing as 4 pennies. Much easier.

In physics, we discovered there are two types of energy in existence. An object can have energy due to its motion ( this is called kinetic energy). An object can also have energy due to its position in a field (a field is anything which varies through space). This is known as potential energy! Gravitational potential energy is an example of potential energy. If you stood on the roof and fell, it would probably hurt, but why did you fall? When you were on the roof, because of where you were (position) in earth's gravitational field, you possessed gravitational potential energy. When you leave the roof, that energy turns into kinetic energy. So the 2 energies that exist are kinetic and potential energy. So we can say the total energy in our universe is kinetic energy and potential energy or mathematically because there both the same entity (energy): total energy = Kinetic energy + Potential energy.

Subtraction:

Another thing that happens in our universe is that we may lose or reduce some entity. What if you had 5 cups of water and lost 2 cups? you would only have 3 cups. That is subtraction, the removal of a specific amount of entity. Another way to see it is by holding your hand out. Look at all 5 fingers, give them a gentle wiggle, then stop and just wiggle your pinky. If you were to subtract your pinky from your 5 fingers, you would have 4 fingers. But not only have you lost your pinky, but if you think about it carefully, you will also realise between your 5 and 1 fingers, there are 4 fingers. Subtraction is also a way of seeing what is between things of the same entity. Quick rule to notice, 5cups-1 banana is not 4 cupbanana, it can only be left at 5 cup- 1 banana.

Acceleration has a formula: Acceleration = (final velocity-initial velocity)/time taken. Where more interested in the subtraction part for now, so we will focus on the final velocity - initial velocity). Velocity is just a speed with a known direction, acceleration is the gain or loss of velocity. So now, if I'm subtracting a fixed final velocity from an initial velocity, I'm not just subtracting mathematically, but intuitively I'm asking what is between the initial and final velocity and this is a way to work out the amount of gain in velocity ( knowing the change between the initial and final velocity).

Multiply:

First, I will show what multiplying does before demonstrating its real-world application. What is 5x3? the answer is 15, and the multiply means repeat 5, 3 times i.e. 5x3=5+5+5=15. More interesting is the fact it does not matter which order you repeat the calculation; you can repeat 5, 3 times or you could repeat 3, 5 times, and it will give you the same answer. This disregard for the order of calculation is called the associative law. Multiplying is useful for many reasons, to understand one of the crucial reasons, picture the case scenario after this sentence. You buy crisps for £5, and you want 3 packets of crisps, which means you need to repeat the £5 a total of 3 times to get £15 worth of crisps (which is 3 packets). Look more closely at this example; the only reason we had to multiply the crisps price by 3 is that the business created a unit with a particular amount of crisps (the £5 one). The reality is that we need multiplication because we need units. If that's a confusing picture the following analogy, how much do you weigh? Chances are you gave me your weight in some unit (maybe the kilogram, pounds or stone). Why do we create units? We create units so we can have a universal way of measuring things. If we did not do this, how would you actually define your weight to someone else, in the example of crisps, if the packet did not exist and only crisps existed there would be no way for you to picture how many crisps your getting.

Now I'm sure you have heard of Newton's famous net force formula, Force=Mass x Acceleration. Now with our acquired knowledge, we can actually understand how to visualise this formula. Mass is the amount of matter something contains, acceleration in layman terms is the ability to gain or lose speed, and Force is a quantity that measures the change in motion of an object when it is not resisted by another force. Lets plug some numbers, 3kg is accelerating at 2ms^2, and putting that into the above formula gives 6 newtons. Multiply means repeat, so if a 3kg object is accelerating, multiply means repeat the 2ms-2 acceleration for each kg in the 3 kg.

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