Question - Solving Arithmetic Expression Involving Fractions
Solution:
The image shows a handwritten arithmetic expression involving fractions. Unfortunately, the image is slightly blurry, and there is a line through some of the numbers, but I will do my best to interpret and solve the expression. It seems that the expression is as follows:\[ \frac{1}{4} + \frac{6}{5} - \frac{1}{2} + \frac{1}{3} \]To add and subtract fractions, they must have a common denominator. We first find the least common multiple (LCM) of the denominators (4, 5, 2, and 3), which is 60. Then, we convert each fraction to an equivalent fraction with a denominator of 60 and perform the arithmetic:\[ \frac{1}{4} = \frac{15}{60} \]\[ \frac{6}{5} = \frac{72}{60} \]\[ \frac{1}{2} = \frac{30}{60} \]\[ \frac{1}{3} = \frac{20}{60} \]Now, we combine them:\[ \frac{15}{60} + \frac{72}{60} - \frac{30}{60} + \frac{20}{60} \]\[ = \frac{15 + 72 - 30 + 20}{60} \]\[ = \frac{77}{60} \]Since 77 and 60 have no common factors other than 1, the fraction is already in its simplest form. The result is $$\frac{77}{60}$$, which can also be written as a mixed number, $$1 \frac{17}{60}$$, since $$77 \div 60 = 1 \text{ R } 17$$.
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