HOW MUCH DO YOU HAVE TO ADD TO 3/4 TO GET 6/7? - MATHS - 2025

To find out how much to add to 3/4 to obtain 6/7, the equation "3/4 + x = 6/7" can be formulated and then performed the necessary operation to solve it.

You can use operations between rational numbers or fractions, or you can perform the corresponding divisions and then solve through decimal numbers.

The image above shows an approach that can be given to the question posed. There are two equal rectangles, which are divided into two different ways:

- The first is divided into 4 equal parts, of which 3 are chosen.

- The second is divided into 7 equal parts, of which 6 are chosen.

As can be seen in the figure, the rectangle below has more shaded area than the rectangle above. Therefore, 6/7 is greater than 3/4.

How to know how much to add to 3/4 to get 6/7?

Thanks to the image shown above you can be sure that 6/7 is greater than 3/4; that is, 3/4 is less than 6/7.

Therefore, it is logical to wonder how far 3/4 is from 6/7. Now it is necessary to pose an equation whose solution answers the question.

Statement of the equation

According to the question posed, it is understood that 3/4 must be added a certain amount, called "x", so that the result is equal to 6/7.

As seen above, the equation that models that question is: 3/4 + x = 6/7.

By finding the value of "x" you will be finding the answer to the main question.

Before trying to solve the above equation, it is convenient to remember the operations of addition, subtraction and product of fractions.

Operations with fractions

Given two fractions a / b and c / d with b, d ≠ 0, then

- a / b + c / d = (a * d + b * c) / b * d.

- a / bc / d = (a * db * c) / b * d.

- a / b * c / d = (a * c) / (b * d).

Solution of the equation

To solve the equation 3/4 + x = 6/7, it is necessary to solve for "x". To do this, different procedures can be used, but they will all return the same value.

1- Clear the "x" directly

To solve directly for "x", add -3/4 to both sides of the equality, obtaining x = 6/7 - 3/4.

Using the operations with fractions, we obtain:

x = (6 * 4-7 * 3) / 7 * 4 = (24-21) / 28 = 3/28.

2- Apply operations with fractions on the left side

This procedure is more extensive than the previous one. If the operations with fractions are used from the beginning (on the left side), it is obtained that the initial equation is equivalent to (3 + 4x) / 4 = 6/7.

If the equality on the right is multiplied by 4 on both sides, we get 3 + 4x = 24/7.

Now add -3 to both sides, so you get:

4x = 24/7 - 3 = (24 * 1-7 * 3) / 7 = (24-21) / 7 = 3/7

Finally, multiply by 1/4 on both sides to get that:

x = 3/7 * 1/4 = 3/28.

3- Make the divisions and then clear

If the divisions are made first, it is obtained that 3/4 + x = 6/7 is equivalent to the equation: 0.75 + x = 0.85714286.

Now we solve for «x» and we obtain that:

x = 0.85714286 - 0.75 = 0.10714286.

This last result appears to be different from cases 1 and 2, but it is not. If you divide 3/28, you will get exactly 0.10714286.

An equivalent question

Another way to ask the same title question is: How much should 6/7 take to get 3/4?

The equation that answers this question is: 6/7 - x = 3/4.

If the "x" is passed to the right side in the previous equation, we will obtain just the equation with which we worked before.

References

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