Detailed solutions and explanations to fractions and percentages practice problems.
"One third of 300" is mathematically translated as:
\[ \frac{1}{3} \times 300 \]Simplify:
\[ = \frac{300}{3} = 100 \]"Two-sevenths of \( x \) is equal to 6" is translated as:
\[ \frac{2}{7} \times x = 6 \]Solve for \( x \):
\[ 2x = 42 \] \[ x = 21 \]"15% of 45% of 1.4" is translated as:
\[ 15\% \times (45\% \times 1.4) \]Simplify:
\[ = \frac{15}{100} \times \left( \frac{45}{100} \times 1.4 \right) \] \[ = \frac{15 \times 45 \times 1.4}{10,000} \] \[ = \frac{945}{10,000} = 0.0945 \]"Two-thirds of one-fifth of 12,000" is translated as:
\[ \frac{2}{3} \times \left( \frac{1}{5} \times 12,000 \right) \]Simplify step-by-step:
\[ = \frac{2}{3} \times \frac{12,000}{5} \] \[ = \frac{2}{3} \times 2,400 \] \[ = \frac{2 \times 2,400}{3} = 1,600 \]"\( x\% \) of 23 is 9.2" is translated as:
\[ \frac{x}{100} \times 23 = 9.2 \]Solve for \( x \):
\[ 23x = 9.2 \times 100 \] \[ 23x = 920 \] \[ x = 40 \]Algebra questions correct: \( 60\% \times 10 = 6 \)
Geometry questions correct: \( 80\% \times 10 = 8 \)
Trigonometry questions correct: \( 60\% \times 5 = 3 \)
Total correct: \( 6 + 8 + 3 = 17 \)
Percentage correct: \( \frac{17}{25} = 0.68 = 68\% \)
"25% of \( y \) is \( x \)" is translated as:
\[ \frac{25}{100} y = x \]Solve for \( y \):
\[ 25y = 100x \] \[ y = \frac{100x}{25} \] \[ y = 4x \]Let \( x \) be the fraction to subtract:
\[ \left( \frac{1}{2} + \frac{4}{5} \right) - x = 1 \]Solve for \( x \):
\[ x = \left( \frac{1}{2} + \frac{4}{5} \right) - 1 \]Common denominator (10):
\[ x = \left( \frac{5}{10} + \frac{8}{10} \right) - \frac{10}{10} \] \[ x = \frac{13}{10} - \frac{10}{10} = \frac{3}{10} \]One out of 5 as a fraction: \( \frac{1}{5} \)
As a percentage: \( 20\% \)
Percentage taking history:
\[ 100\% - 20\% - 28\% = 52\% \]"One-fifth of \( y + 1 \) equals 2" is translated as:
\[ \frac{1}{5}(y + 1) = 2 \]Multiply both sides by 5:
\[ y + 1 = 10 \]Add 1 to both sides:
\[ y + 1 + 1 = 10 + 1 \]Simplify:
\[ y + 2 = 11 \]