Subtract

Subtract: 7 7/10-3 4/5 =

A.
4 3/5

B.
4 1/10

C.
3 9/10

D.
11 5/10

The correct answer and Explanation is :

To solve the subtraction (7 \frac{7}{10} – 3 \frac{4}{5}), follow these steps:

1. Convert Mixed Numbers to Improper Fractions: For (7 \frac{7}{10}):

• The whole number part is 7, and the fraction part is (\frac{7}{10}).
• Convert to an improper fraction:
  [
  7 \frac{7}{10} = 7 + \frac{7}{10} = \frac{70}{10} + \frac{7}{10} = \frac{77}{10}
  ] For (3 \frac{4}{5}):
• The whole number part is 3, and the fraction part is (\frac{4}{5}).
• Convert to an improper fraction:
  [
  3 \frac{4}{5} = 3 + \frac{4}{5} = \frac{15}{5} + \frac{4}{5} = \frac{19}{5}
  ]

1. Find a Common Denominator: The denominators are 10 and 5. The least common multiple of 10 and 5 is 10. Convert (\frac{19}{5}) to have this denominator:
   [
   \frac{19}{5} = \frac{19 \times 2}{5 \times 2} = \frac{38}{10}
   ]
2. Subtract the Fractions: Subtract (\frac{38}{10}) from (\frac{77}{10}):
   [
   \frac{77}{10} – \frac{38}{10} = \frac{77 – 38}{10} = \frac{39}{10}
   ]
3. Convert the Result to a Mixed Number: Divide 39 by 10:

• 39 divided by 10 gives 3 with a remainder of 9.
• Thus, (\frac{39}{10} = 3 \frac{9}{10}).

So the result of (7 \frac{7}{10} – 3 \frac{4}{5}) is (3 \frac{9}{10}), which corresponds to option C.

Explanation:

1. Conversion: We first converted mixed numbers to improper fractions to make subtraction straightforward.
2. Common Denominator: We found a common denominator to perform the subtraction easily.
3. Subtraction: We performed the subtraction operation on the numerators and maintained the common denominator.
4. Conversion Back: Finally, we converted the improper fraction result back to a mixed number for clarity.

This approach ensures accuracy and clarity in handling fraction operations, providing a step-by-step solution for mixed number subtraction.