SETAS Math Practice: Simplifying Fractions

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: $4.8 \div \frac{1}{5} = 4.8 \times 5 = 24$

Practice math problems for students in the School of Engineering Technology and Applied Science, focusing on simplifying fractions and solving multiple-choice questions.