3 Work these out. Give each answer as a mixed number in its lowest terms. Cancel before you do any calculations. \( \begin{array}{lll}\text { a } \frac{3}{4} \times 18 & \text { (c) } \frac{5}{8} \times 22\end{array} \)
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The Deep Dive
To solve these problems, it's all about simplifying before multiplying. For the first one, \( \frac{3}{4} \times 18 \): We can rewrite 18 as \( \frac{18}{1} \). Now, let's find a common factor: the 18 can be simplified by dividing it by 2, giving us 9, and the 4 simplifies down to 2. So, \( \frac{3 \times 9}{2 \times 1} = \frac{27}{2} \). As a mixed number, that’s \( 13 \frac{1}{2} \). Now, for the second one, \( \frac{5}{8} \times 22 \): Similarly, we rewrite 22 as \( \frac{22}{1} \) and notice that both 22 and 8 can be divided by 2. This gives us \( \frac{5 \times 11}{4 \times 1} = \frac{55}{4} \). Converting this to a mixed number gives us \( 13 \frac{3}{4} \). So, we have: \( \frac{3}{4} \times 18 = 13 \frac{1}{2} \) and \( \frac{5}{8} \times 22 = 13 \frac{3}{4} \).
