Question 4 Simplify the following without using a calculator. 4.1. \( 1 \frac{2}{3}: 2 \frac{2}{3} \) 4.2. \( 2(\sqrt{64}+\sqrt{25}) \) 4.3. \( \left(3.6 \times 10^{6}\right)-\left(5.2 \times 10^{5}\right) \) 4.4. \( \frac{1}{2}+2 \frac{3}{4}-\frac{3}{8} \) GRAND TOTAL: 50
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When simplifying mixed numbers, it’s often helpful to convert them to improper fractions first! For example, \( 1 \frac{2}{3} \) becomes \( \frac{5}{3} \), and \( 2 \frac{2}{3} \) becomes \( \frac{8}{3} \). Then, dividing fractions turns into multiplying by the reciprocal, so you would have \( \frac{5}{3} \div \frac{8}{3} = \frac{5}{8} \). In \( 2(\sqrt{64}+\sqrt{25}) \), remember that the square roots can be simplified to whole numbers, with \( \sqrt{64} = 8 \) and \( \sqrt{25} = 5 \). Adding those gives you \( 8 + 5 = 13 \), and multiplying by 2 results in \( 2 \times 13 = 26 \). An easy path to success!
