Calculating the Product of 6 7/8 and 5/6: A Step-by-Step Guide in Simplest Form

Calculating the Product of 6 7/8 and 5/6: A Step-by-Step Guide in Simplest Form

When performing mathematical calculations, it's important to follow the proper steps to ensure accuracy. This guide will walk you through the process of finding the product of 6 7/8 and 5/6. We will express the result in both improper fraction and mixed number formats for clarity.

Step 1: Convert the Mixed Number to an Improper Fraction

To begin, we need to convert the mixed number 6 7/8 into an improper fraction. This is done by following these steps:

Multiply the whole number (6) by the denominator (8):
6 x 8 48 Add the numerator (7) to this product:
48 7 55 Now, place this sum over the original denominator (8):
6 7/8 55/8

Step 2: Multiply the Improper Fraction by the Second Fraction

The next step is to multiply the improper fraction 55/8 by the second fraction 5/6. Perform the multiplication as follows:

Multiply the numerators: 55 x 5 275 Multiply the denominators: 8 x 6 48 Write the product as a new fraction: 275/48

Step 3: Simplify the Fraction (if necessary)

The resulting fraction, 275/48, is already in its simplest form. To check if it can be simplified further, we need to find if the numerator (275) and the denominator (48) share any common factors. The prime factorization of these numbers is:

275 5^2 x 11 48 2^4 x 3

Since 275 and 48 do not have any common factors, the fraction cannot be simplified. Therefore, the product in simplest form is:

275/48

Alternative Representations

The fraction 275/48 can also be expressed as a mixed number with a whole number and a fractional part. To convert it, divide the numerator by the denominator:

55 goes into 48 0 times with a remainder of 35. The whole number part is 5, and the remaining fraction is 35/48.

Conclusion

The product of 6 7/8 and 5/6, when expressed in simplest form, is 275/48, or as a mixed number, 5 35/48. This step-by-step process can be applied to other similar problems to ensure accurate results. Understanding these calculations is fundamental in mathematics and can be useful in various applications including science, engineering, and everyday problem-solving.

References:

Math is Fun: Improper Fractions Math is Fun: Mixed Numbers