Question

Perform the indicated operation. \(14 \frac{3}{4}-6 \frac{5}{12}\)

Short answer

Question: Subtract the following mixed numbers: \(14\frac{3}{4} - 6\frac{5}{12}\). Answer: \(8\frac{1}{3}\)

Step-by-step solution

Separate whole numbers and fractions

First, let's separate the whole number parts and the fraction parts of each mixed number: \(14\) and \(\frac{3}{4}\), \(6\) and \(\frac{5}{12}\).

Subtract the whole numbers

Subtract the whole numbers: \(14 - 6 = 8\).

Find a common denominator for the fractions

In order to subtract the fractions, we need a common denominator. The least common multiple (LCM) of \(4\) and \(12\) is \(12\). So, our common denominator is \(12\).

Convert the fractions to equivalent fractions with the common denominator

Now, we need to find equivalent fractions for \(\frac{3}{4}\) and \(\frac{5}{12}\) with the common denominator of \(12\). We do this as follows: \(\frac{3}{4} \times \frac{3}{3} = \frac{9}{12}\) \(\frac{5}{12}\) already has the common denominator, so we don't need to change it.

Subtract the fractions

Now we can subtract the fractions: \(\frac{9}{12} - \frac{5}{12} = \frac{9-5}{12} = \frac{4}{12}\)

Simplify the fraction

It's always a good idea to simplify fractions when possible. We can see that the numerator and denominator of \(\frac{4}{12}\) share a common factor of \(4\). Therefore, the fraction simplifies to: \(\frac{4 \div 4}{12 \div 4} = \frac{1}{3}\)

Combine the whole number and the fraction

Finally, we combine the whole number from Step 2 and the simplified fraction from Step 6: \(8 \frac{1}{3}\) Hence, the result of the subtraction \(14\frac{3}{4} - 6\frac{5}{12}\) is \(8\frac{1}{3}\).