Question - Solving Fractions in an Expression using PEMDAS/BODMAS Rules
Solution:
To solve the expression provided in the image, we must first understand the order of operations, which usually follows the PEMDAS/BODMAS rules (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).In this case, we have an expression involving fractions, subtraction, and addition.Here is the expression from the image:\[ \frac{3}{4} - \frac{2}{8} + \frac{1}{2} \]To add or subtract fractions, we need a common denominator. The numbers 4, 8, and 2 all have a common multiple, which is 8. So we convert all fractions to have the denominator of 8. The first fraction already has a common denominator with the second:\[ \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \]The second fraction is already over 8, so it remains:\[ \frac{2}{8} \]For the third fraction:\[ \frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8} \]Now we can rewrite the entire expression with a common denominator of 8:\[ \frac{6}{8} - \frac{2}{8} + \frac{4}{8} \]Perform the operations:\[ \frac{6 - 2 + 4}{8} = \frac{4 + 4}{8} = \frac{8}{8} \]And $$\frac{8}{8}$$ simplifies to 1 since any number divided by itself is 1. Therefore, the solution to the given expression is 1.
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