HOW MUCH DOES 7/9 EXCEED 2/5? - MATHS - 2025

To determine by how much 7/9 exceeds 2/5, an operation is carried out, which can be applied to any pair of real numbers (rational or irrational), which consists of subtracting both numbers. You are also told to take the difference.

In mathematics, when the word "difference" is used, it does not refer to the characteristics that distinguish one object (number, set, functions, among others) from another, but rather refers to taking the subtraction of one object minus the other.

For example, in the case of functions, the difference between the functions f (x) and g (x) is (fg) (x); and in the case of real numbers, the difference between “a” and “b” is “ab”.

Does the order of the difference matter?

In the case of real numbers, when taking the difference, the order in which the numbers are subtracted is important, since the sign of the result will depend on the order in which the subtraction is made.

For example, if you want to calculate the difference between 5 and 8, two cases result:

-5-8 = -3, in this case the difference is negative.

-8-5 = 3, in this case the difference is positive.

As can be seen in the previous example, the results are different.

What does the word "exceed" mathematically mean?

When the word "exceeds" is used, it is implicitly saying that one number (object) is greater than another.

So the main title of this article is implicitly saying that 7/9 is greater than 2/5. This can be verified in two equivalent ways:

- Subtracting 7/9 minus 2/5 should obtain a positive number.

- Solving 7/9> 2/5 and verifying that the expression obtained is true.

The first case will be checked later. As for the second case, if the expression is solved, we get 35> 18, which is true. Therefore, 7/9 is greater than 2/5.

How much does 7/9 exceed 2/5?

To calculate by how much 7/9 to 2/5 exceeds two equivalent methods, which are:

- Calculate the value of 7/9 by dividing 7 by 9, and calculate the value of division 2/5 by dividing 2 by 5. Then, these two results are subtracted by first placing the value of 7/9 and then the value of 2/5.

- Directly subtract 7/9 minus 2/5, using the properties of addition and / or subtraction of fractions, and at the end perform the corresponding division to obtain the desired result.

In the first method the counts are as follows: 7 ÷ 9 = 0.77777777… and 2 ÷ 5 = 0.4. When performing the subtraction between these two numbers, the difference between 7/9 and 2/5 is 0.377777…

Using the second method the calculations are as follows: 7 / 9-2 / 5 = (35-18) / 45 = 17/45. When dividing 17 by 45, the result is 0.377777…

In any case, the same result was obtained and it is also a positive number, which implies that 7/9 exceeds (is greater) than 2/5.

Therefore, 7/9 exceeds by 0.37777… 2/5, or equivalently it can be said that 7/9 exceeds 2/5 by 17/45.

Another equivalent question

An equivalent way to ask the same question as the one in the title of this article is "How much should you add to 2/5 to get to 7/9?"

It should be noted that the previous question requires finding a number x such that 2/5 + x equals 7/9. But the recently mentioned expression is equivalent to taking the subtraction from 7 / 9-2 / 5, and this result will be the value of x.

As you can see, you will get the same value as before.

References

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