The Correct Answer and Explanation is:
To solve the subtraction of mixed fractions 615−4166 \frac{1}{5} – 4 \frac{1}{6}651−461, follow these steps:
- Convert the mixed fractions to improper fractions:
- For 6156 \frac{1}{5}651, convert it to an improper fraction: 615=(6×5+1)÷5=3156 \frac{1}{5} = \left( 6 \times 5 + 1 \right) \div 5 = \frac{31}{5}651=(6×5+1)÷5=531
- For 4164 \frac{1}{6}461, convert it to an improper fraction: 416=(4×6+1)÷6=2564 \frac{1}{6} = \left( 4 \times 6 + 1 \right) \div 6 = \frac{25}{6}461=(4×6+1)÷6=625
- Find a common denominator:
The denominators are 5 and 6. The least common denominator (LCD) of 5 and 6 is 30. Now, rewrite each fraction with 30 as the denominator:- 315\frac{31}{5}531 becomes 31×65×6=18630\frac{31 \times 6}{5 \times 6} = \frac{186}{30}5×631×6=30186
- 256\frac{25}{6}625 becomes 25×56×5=12530\frac{25 \times 5}{6 \times 5} = \frac{125}{30}6×525×5=30125
- Subtract the fractions:
Now that both fractions have the same denominator, subtract the numerators: 18630−12530=186−12530=6130\frac{186}{30} – \frac{125}{30} = \frac{186 – 125}{30} = \frac{61}{30}30186−30125=30186−125=3061 - Convert the improper fraction back to a mixed number:
To convert 6130\frac{61}{30}3061 to a mixed number, divide 61 by 30: 61÷30=2 remainder 161 \div 30 = 2 \text{ remainder } 161÷30=2 remainder 1 So, 6130=2130\frac{61}{30} = 2 \frac{1}{30}3061=2301.
Thus, the result of 615−4166 \frac{1}{5} – 4 \frac{1}{6}651−461 is 21302 \frac{1}{30}2301.
