(1) $ \frac{3 x}{4 y}+\frac{5 x}{6 y} $

Ask by Sullivan Coleman.

Nov 22,2024 10:47

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Answer

$ \frac{19xy}{12} $

Solution

Calculate or simplify the expression $ 3*x/4*y+5*x/6*y $. Simplify the expression by following steps: - step0: Solution: $\frac{3x}{4}y+\frac{5x}{6}y$ - step1: Multiply the terms: $\frac{3xy}{4}+\frac{5x}{6}y$ - step2: Multiply the terms: $\frac{3xy}{4}+\frac{5xy}{6}$ - step3: Reduce fractions to a common denominator: $\frac{3xy\times 3}{4\times 3}+\frac{5xy\times 2}{6\times 2}$ - step4: Multiply the numbers: $\frac{3xy\times 3}{12}+\frac{5xy\times 2}{6\times 2}$ - step5: Multiply the numbers: $\frac{3xy\times 3}{12}+\frac{5xy\times 2}{12}$ - step6: Transform the expression: $\frac{3xy\times 3+5xy\times 2}{12}$ - step7: Multiply the terms: $\frac{9xy+5xy\times 2}{12}$ - step8: Multiply the terms: $\frac{9xy+10xy}{12}$ - step9: Add the terms: $\frac{19xy}{12}$ The simplified form of the expression $ \frac{3x}{4y} + \frac{5x}{6y} $ is $ \frac{19xy}{12} $.

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To combine the fractions $ \frac{3 x}{4 y} $ and $ \frac{5 x}{6 y} $, you first need a common denominator. The least common multiple of 4 and 6 is 12. Rewriting both fractions with a denominator of 12 gives: \[ \frac{3 x}{4 y} = \frac{3 x \cdot 3}{4 y \cdot 3} = \frac{9 x}{12 y} \] \[ \frac{5 x}{6 y} = \frac{5 x \cdot 2}{6 y \cdot 2} = \frac{10 x}{12 y} \] Now combine them: \[ \frac{9 x}{12 y} + \frac{10 x}{12 y} = \frac{(9 x + 10 x)}{12 y} = \frac{19 x}{12 y} \] So, the final answer is $ \frac{19 x}{12 y} $. Now let’s sprinkle in some fun facts! The concept of common denominators has been around since ancient civilizations, where traders needed to understand fractional values to ensure fairness in transactions. Imagine merchants in bustling bazaars attempting to weigh goods accurately, all while shouting over one another! In real life, mastering fractions is essential not just in academia but also in situations like cooking or mixing paint colors. For instance, if you’re doubling a recipe and you need to add $ \frac{3}{4} $ of a cup of sugar, understanding how to manipulate fractions ensures your cake doesn’t turn out overly sweet—or worse, flavorless!