• Denominator: \( \frac{5}{8} + \frac{1}{8} = \frac{6}{8} = \frac{3}{4} \)
• Quotient: \( \frac{1}{4} \div \frac{3}{4} = \frac{1}{3} \)
Exact Value: \(\frac{1}{3}\)
Rational Precision I • Answer Key Page 1 Solutions 1–8
Educator Reference • Solutions Guide
Form A Key
9 Integers
\( 25 - 3 \times \left[ (-2)^4 - 11 \right] \)
• Exponent: \( (-2)^4 = 16 \)
• Inside brackets: \( 16 - 11 = 5 \)
• Multiply & Subtract: \( 25 - 3(5) = 25 - 15 = 10 \)
Exact Value: 10
10 Integers
\( (-5)^2 - (-4) \times (-3) + (-48) \div (-2)^3 \)
• Powers: \( (-5)^2 = 25 \), \( (-2)^3 = -8 \)
• Operations: \( (-4)(-3) = 12 \), \( -48 \div (-8) = 6 \)
• Combine: \( 25 - 12 + 6 = 19 \)
Exact Value: 19
11 Fractions
\( \left(-\frac{3}{4}\right)^2 - \frac{7}{8} \times \frac{2}{3} \)
• Exponent: \( (-\frac{3}{4})^2 = \frac{9}{16} \)
• Product: \( \frac{7}{8} \times \frac{2}{3} = \frac{7}{12} \)
• Subtract: \( \frac{27}{48} - \frac{28}{48} = -\frac{1}{48} \)
Exact Value: \(-\frac{1}{48}\)
12 Decimals
\( (-0.4)^2 \div 0.2 - 1.5 \times (-3) \)
• Exponent & Div: \( 0.16 \div 0.2 = 0.8 \)
• Product: \( -1.5 \times (-3) = 4.5 \)
• Combine: \( 0.8 + 4.5 = 5.3 \)
Exact Value: 5.3
13 Fractions & Decimals
\( -1.6 + \left(\frac{2}{5}\right)^2 \times 15 \)
• Exponent: \( (\frac{2}{5})^2 = \frac{4}{25} \)
• Product: \( \frac{4}{25} \times 15 = \frac{12}{5} = 2.4 \)
• Sum: \( -1.6 + 2.4 = 0.8 = \frac{4}{5} \)
Exact Value: \(0.8 \text{ or } \frac{4}{5}\)
14 Fractions & Decimals
\( \left(\frac{1}{4} - 0.75\right)^2 \div \left(-\frac{1}{8}\right) \)
• Inside Parens: \( 0.25 - 0.75 = -0.5 \)
• Exponent: \( (-0.5)^2 = 0.25 = \frac{1}{4} \)
• Divide: \( \frac{1}{4} \times (-8) = -2 \)
Exact Value: -2
15 Fractions & Decimals
\( 2.5 - \left(-\frac{1}{2}\right)^3 \times 3.2 + \frac{3}{5} \)
• Power: \( (-\frac{1}{2})^3 = -\frac{1}{8} \)
• Product: \( -\frac{1}{8} \times 3.2 = -0.4 \)
• Combine: \( 2.5 - (-0.4) + 0.6 = 2.9 + 0.6 = 3.5 \)
Exact Value: \(3.5 \text{ or } \frac{7}{2}\)
16 Complex Fraction
\( \dfrac{1.2 - \left(-\frac{3}{5}\right)}{\frac{2}{3} \times (-0.9) + 1.6} \)
• Numerator: \( 1.2 + 0.6 = 1.8 \)
• Denominator: \( \frac{2}{3}(-0.9) + 1.6 = -0.6 + 1.6 = 1.0 \)
• Quotient: \( 1.8 \div 1.0 = 1.8 = \frac{9}{5} \)
Exact Value: \(1.8 \text{ or } \frac{9}{5}\)
Rational Precision I • Answer Key Page 2 Solutions 9–16
• Denominator: \( \frac{2}{8} - \frac{5}{8} = -\frac{3}{8} \)
• Quotient: \( \frac{1}{2} \times (-\frac{8}{3}) = -\frac{4}{3} \)
Exact Value: \(-\frac{4}{3} \text{ or } -1\frac{1}{3}\)
Rational Precision II • Answer Key Page 1 Solutions 1–8
Educator Reference • Solutions Guide
Form B Key
9 Integers
\( \left[ (-4)^2 - 25 \right] \times (-3) - (-18) \)
• Exponent: \( (-4)^2 = 16 \)
• Bracket: \( 16 - 25 = -9 \)
• Multiply & Subtract: \( -9(-3) - (-18) = 27 + 18 = 45 \)
Exact Value: 45
10 Integers
\( (-3)^3 + 4 \times (-6) - (-32) \div (-4) \)
• Exponent: \( (-3)^3 = -27 \)
• Mult & Div: \( 4(-6) = -24 \), \( -32 \div (-4) = 8 \)
• Combine: \( -27 + (-24) - 8 = -59 \)
Exact Value: -59
11 Fractions
\( \left(-\frac{2}{5}\right)^2 \times \left(-\frac{15}{8}\right) + \frac{7}{10} \)
• Exponent: \( (-\frac{2}{5})^2 = \frac{4}{25} \)
• Product: \( \frac{4}{25} \times (-\frac{15}{8}) = -\frac{3}{10} \)
• Sum: \( -\frac{3}{10} + \frac{7}{10} = \frac{4}{10} = \frac{2}{5} \)
Exact Value: \(\frac{2}{5} \text{ or } 0.4\)
12 Decimals
\( 2.8 - (-0.3)^2 \times 40 + 1.5 \)
• Exponent: \( (-0.3)^2 = 0.09 \)
• Multiply: \( 0.09 \times 40 = 3.6 \)
• Combine: \( 2.8 - 3.6 + 1.5 = 0.7 \)
Exact Value: 0.7
13 Fractions & Decimals
\( 1.25 \times \left(-\frac{4}{5}\right) - \left(-\frac{1}{3}\right)^2 \times 9 \)
• Product 1: \( \frac{5}{4} \times (-\frac{4}{5}) = -1 \)
• Power & Mult: \( \frac{1}{9} \times 9 = 1 \)
• Subtract: \( -1 - 1 = -2 \)
Exact Value: -2
14 Fractions & Decimals
\( \left(-\frac{3}{4}\right) \div 0.25 + (1.2 - 1.8)^2 \)
• Division: \( -0.75 \div 0.25 = -3 \)
• Parens & Power: \( (1.2 - 1.8)^2 = (-0.6)^2 = 0.36 \)
• Sum: \( -3 + 0.36 = -2.64 = -\frac{66}{25} \)
Exact Value: \(-2.64 \text{ or } -\frac{66}{25}\)
15 Fractions & Decimals
\( 0.8 - \left[ \frac{1}{2} + \left(-\frac{1}{2}\right)^3 \times 4 \right] \)
• Power & Mult: \( (-\frac{1}{8}) \times 4 = -\frac{1}{2} \)
• Inside Bracket: \( \frac{1}{2} + (-\frac{1}{2}) = 0 \)
• Subtract: \( 0.8 - 0 = 0.8 = \frac{4}{5} \)
Exact Value: \(0.8 \text{ or } \frac{4}{5}\)
16 Complex Fraction
\( \dfrac{(-0.4)^2 - \frac{1}{25}}{\frac{3}{10} + \left(-\frac{1}{2}\right)} \)
• Numerator: \( 0.16 - 0.04 = 0.12 \)
• Denominator: \( 0.3 - 0.5 = -0.2 \)
• Quotient: \( 0.12 \div (-0.2) = -0.6 = -\frac{3}{5} \)
Exact Value: \(-0.6 \text{ or } -\frac{3}{5}\)
Rational Precision II • Answer Key Page 2 Solutions 9–16
