15 3/4 divided by 2 1/4: Simplify Your Calculation

When it comes to dividing fractions, the concept can sometimes seem daunting. But don't worry, we're here to make it simple and clear. Let's break down the operation of dividing 15 3/4 by 2 1/4 step-by-step.

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To begin, it's crucial to understand that dividing fractions is essentially the same as multiplying. The only difference is that instead of a multiplication sign, we use a division sign. Now, dive into the world of mixed numbers and their division.

Inverting and Multiplying: The Key to Dividing Fractions

As previously mentioned, dividing fractions involves multiplying by the reciprocal of the divisor. So, we'll first invert the divisor (2 1/4) and then perform the multiplication.

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Let's convert our mixed numbers into improper fractions before we proceed. This will make the process smoother and less prone to errors.

Converting Mixed Numbers to Improper Fractions

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The first step involves converting 15 3/4 to an improper fraction. Multiply the whole number (15) by the denominator of the fraction (4) and add the numerator (3): 15*4 + 3 = 60 + 3 = 63.

Now, we'll place this in the form of an improper fraction with a denominator of 4: 63/4.

Converting the Divisor (2 1/4) to an Improper Fraction

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Following the same process, convert 2 1/4 to an improper fraction. Multiply the whole number (2) by the denominator of the fraction (4) and add the numerator (1): 2*4 + 1 = 8 + 1 = 9.

Now, we'll convert it to an improper fraction with a denominator of 4: 9/4.

With our fractions now converted, let's find the reciprocal of the divisor (9/4) to proceed with the division.

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To find the reciprocal, simply flip the numerator and denominator of the fraction: 4/9.

Dividing the Fractions: Performing the Calculation

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Now that we have the reciprocal (4/9), we can multiply the two fractions (63/4) * (4/9) to divide 15 3/4 by 2 1/4.

Using our multiplication of fractions formula, we multiply the numerators together and the denominators together: (63 * 4) / (4 * 9) = 252/36.

Simplifying the Fraction

Finally, simplify the fraction 252/36. Both the numerator and the denominator are divisible by 12: 252/12 = 21 and 36/12 = 3. So, our simplified quotient is 21/3, which can then be converted back into a mixed number as 7 1/3.

And there you have it! A fundamental understanding of division with mixed numbers, leading to a clear answer for 15 3/4 divided by 2 1/4.

Practice this method with other mixed numbers to get comfortable with the process. Keep exploring fractions and their operations – the more you practice, the more confident you'll become!