Question

To divide two fractions with common denominators, divide the first numerator by the second numerator, ignoring the denominators. Rewrite this division problem as the division of two integers.

Answer 1

To divide two fractions with common denominators, simply divide the numerators, ignoring the denominators. The result is the division of two integers.

Step-by-step explanation:

When dividing two fractions with common denominators, the process involves dividing the numerators and keeping the common denominator unchanged. This is due to the property of fractions where, with the same denominator, the ratio of two quantities is directly related to the ratio of their numerators. Mathematically, for fractions a/b and c/b, where "b" is the common denominator:

`\[ (a)/(b) / (c)/(b) = (a)/(b) * (b)/(c) \]`

Here, the "b" in the numerator and denominator cancels out, leaving us with the result of
`\( (a)/(c) \)`. When the denominators are the same, the division reduces to the division of the numerators.

Expressing this result as the division of two integers, we have
`\( (a)/(c) \),`where both "a" and "c" are integers. This is because the numerator and denominator of the original fraction, having been divided by the common denominator, are both integers.

Therefore, dividing two fractions with common denominators indeed yields the division of two integers. This simplification facilitates easier computation and understanding of the relationship between the two quantities being divided.

Answer 2

To divide two fractions with common denominators, divide the first numerator by the second numerator, ignoring the denominators. Rewrite this division problem as the division of two integers.

Step-by-step explanation:

When dividing fractions with common denominators, you can simplify the process by dividing the numerators directly, ignoring the denominators. Let's consider the fractions
`\( (a)/(c) ÷ (b)/(c) \)`. The result is
`\( (a)/(b) \)`, where a is the numerator of the first fraction, b is the numerator of the second fraction, and c is the common denominator. In a more mathematical sense,
`\( (a)/(c) ÷ (b)/(c) = (a)/(b) \)`. This is because when you divide by a fraction, it is equivalent to multiplying by its reciprocal. The common denominator cancels out, leaving you with the division of the numerators.

For example, let's take
`\( (5)/(2) ÷ (2)/(2) \)`. Directly dividing the numerators, we get
`\( (5)/(2) ÷ (2)/(2) = (5)/(2) × (2)/(2) = (5)/(2) × 1 = (5)/(2) \). So, \( (5)/(2) ÷ (2)/(2) = (5)/(2) \).`

In summary, dividing two fractions with common denominators involves simply dividing the numerators, as the common denominators cancel out. This shortcut makes the process more straightforward and can be applied to any similar fractions with a common denominator.