Adding and subtracting fraction

Mathematics
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A regular size chocolate bar was 10(3)7 inches long. If the king size bar was 6(1)2 inches longer, what is the length of the king size bar?

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Solving Mixed Numbers in Fractions

Answer: To solve the problem involving mixed numbers, we need to understand how to add them correctly. Mixed numbers consist of a whole number and a fraction. Here, we need to add two mixed numbers: (10 \frac{3}{7}) and (6 \frac{1}{2}).

Step 1: Convert Mixed Numbers to Improper Fractions

First, let’s convert the mixed numbers into improper fractions. An improper fraction has a numerator larger than its denominator and can be calculated by using the formula:

\text{Improper Fraction} = (\text{Whole Number} \times \text{Denominator}) + \text{Numerator}

For (10 \frac{3}{7}):

  • The whole number is (10),
  • The fraction is (\frac{3}{7}).

Using the formula:

(10 \times 7) + 3 = 70 + 3 = 73

Therefore, (10 \frac{3}{7}) as an improper fraction is (\frac{73}{7}).

For (6 \frac{1}{2}):

  • The whole number is (6),
  • The fraction is (\frac{1}{2}).

Using the same formula:

(6 \times 2) + 1 = 12 + 1 = 13

Thus, (6 \frac{1}{2}) as an improper fraction is (\frac{13}{2}).

Step 2: Find a Common Denominator

To add fractions, they must have the same denominator. We need to find the least common denominator for (\frac{73}{7}) and (\frac{13}{2}).

The denominators are 7 and 2. The least common multiple (LCM) of 7 and 2 is (14).

Step 3: Convert Fractions to Have the Same Denominator

Convert each fraction to have a denominator of 14:

For (\frac{73}{7}):

Multiply both the numerator and the denominator by 2 to get a denominator of 14:

\frac{73}{7} \times \frac{2}{2} = \frac{146}{14}

For (\frac{13}{2}):

Multiply both the numerator and the denominator by 7:

\frac{13}{2} \times \frac{7}{7} = \frac{91}{14}

Step 4: Add the Fractions

Now that both fractions have a common denominator, add them:

\frac{146}{14} + \frac{91}{14} = \frac{237}{14}

Step 5: Convert the Result Back to a Mixed Number

Convert the improper fraction back to a mixed number by dividing the numerator by the denominator:

  • Divide 237 by 14. The whole number part of the quotient is the whole number of the mixed number, and the remainder becomes the numerator of the fractional part.

Perform the division:

237 \div 14 = 16 \text{ remainder } 13

So, (\frac{237}{14}) as a mixed number is (16 \frac{13}{14}).

Thus, the length of the king size bar is (16 \frac{13}{14}) inches.

Summary: By converting mixed numbers to improper fractions, finding a common denominator, and then performing the addition before converting back to a mixed number, we found that the king size bar measured (16 \frac{13}{14}) inches in length. This approach ensures accuracy when dealing with mixed numbers in mathematical calculations. @jaMall_Lambert