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Questions and Answers
Simplify $\frac{3}{4} \div \frac{2}{3}$, provide your answer in lowest terms
Simplify $\sqrt{15^2 - 9^2}$
Simplify -5(3)^2
(6 x 3) + (-2 x 4) =
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Solve $\frac{10^5}{10^3}$
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How many thirds are there in 7.5?
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Simplify $\sqrt{20^2 - 3^2}$
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Study Notes
Simplifying Expressions
- To simplify a fraction division, multiply by the reciprocal: $\frac{1}{2} \div \frac{4}{5} = (\frac{1}{2}) \times (\frac{5}{4})$
- Simplify numerator and denominator separately: $\frac{1}{2} \div \frac{4}{5} = \frac{1 \times 5}{2 \times 4} = \frac{5}{8}$
Simplifying Radicals
- To simplify a square root, simplify the expression inside the radical: $\sqrt{10^2 - 6^2} = \sqrt{100 - 36} = \sqrt{64} = 8$
- Evaluate the expression inside the radical first: $\sqrt{10^2 - 6^2} = \sqrt{64} = 8$
Evaluating Exponents
- Follow the order of operations (PEMDAS): evaluate exponents, then multiply: $-3(4)^2 = -3(16) = -48$
- Evaluate the exponent first, then multiply: $-3(4)^2 = -3(16) = -48$
Evaluating Expressions
- Follow the order of operations (PEMDAS): evaluate expressions inside brackets first: $(4 x 2) + (-5 x 3) = (2)(4) + (-5)(3) = 8 - 15 = -7$
- Simplify each bracket separately: $(4 x 2) + (-5 x 3) = (2)(4) + (-5)(3) = 8 - 15 = -7$
Dividing Exponents
- To divide exponents, subtract the exponents: $\frac{10^6}{10^4} = 10^{6 - 4} = 10^2$
- Use the rule for dividing exponents: $\frac{10^6}{10^4} = 10^{6 - 4} = 10^2$
Dividing Decimals
- To find the number of fifths in a decimal, divide by a fifth: $4.8 \div \frac{1}{5} = 4.8 \times 5 = 24$
- Divide the decimal by a fifth to find the number of fifths: $4.8 \div \frac{1}{5} = 4.8 \times 5 = 24$
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Description
Practice math problems for students in the School of Engineering Technology and Applied Science, focusing on simplifying fractions and solving multiple-choice questions.
