## 3/4 divided by 7/8?

To divide 3/4 by 7/8, you can multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 7/8 is 8/7.

So, (3/4) ÷ (7/8) is the same as (3/4) * (8/7), which simplifies to (3 * 8) / (4 * 7) = 24/28.

You can simplify the fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 4:

(24/4) / (28/4) = 6/7.

Therefore, 3/4 divided by 7/8 equals 6/7.

## Dividing Fractions

Dividing fractions is a mathematical operation that involves determining how many times one fraction “fits into” another fraction. The process is similar to multiplying fractions but involves finding the reciprocal or inverse of the divisor fraction.

To divide any two fractions a/b and c/d:

- Invert the divisor fraction – find its reciprocal. To invert a fraction, flip the numerator and denominator.
- Multiply the dividend fraction by the inverted divisor fraction.
- Simplify the resulting fraction if possible.

For example, to divide 3/4 by 7/8:

- Invert 7/8 to get its reciprocal: 7/8 becomes 8/7
- Multiply the dividend and inverted divisor: 3/4 * 8/7 = 24/28
- Simplify the result: 24/28 can be reduced to 6/7

Therefore, 3/4 ÷ 7/8 = 6/7

## Understanding Division of Fractions

Dividing by a fraction is essentially the same as multiplying by its reciprocal. The reciprocal of 7/8 is 8/7.

When we multiply 3/4 * 8/7, we are determining how many 8/7’s are in 3/4. This gives us the same result as dividing 3/4 by 7/8.

The fundamental relationship between division, fractions, and reciprocals allows us to perform the division by multiplication instead. This makes the process easier and more straightforward compared to traditional long division with remainders.

## Checking the Solution

To check fraction division, we can multiply the result by the original divisor to see if it gives the original dividend:

6/7 * 7/8 = ? (Multiply) 6/7 * 7/8 = 3/4 ✅

Since the product equals the original 3/4 dividend, this confirms that dividing 3/4 by 7/8 results in 6/7.

In summary, dividing fractions requires finding the reciprocal of the divisor and multiplying it by the dividend fraction. Checking your work by multiplying the result by the divisor is a good way to confirm the accuracy of the division. Mastering fraction division provides a fundamental skill for more advanced math concepts down the road.

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