Maths

• What is the result of $5.92 \div 0.16$?


  $37$
• How can division be represented as a fraction?

  By writing the numerator over the denominator
• What happens when you multiply the numerator and denominator of a fraction by the same number?

  The value of the fraction remains unchanged
• What is $592 \div 16$ simplified to?


  $37$
• What is the prime factorization of $324$?


  $2^2 \times 3^4$
• How do you convert a mixed number to an improper fraction?

  Multiply the whole number by the denominator and add the numerator
• What is $2 \frac{2}{3} +$$1 \frac{3}{5}$ as a mixed number?


  $4 \frac{4}{15}$
• Why do we need a common denominator to add fractions?

  To ensure the fractions are comparable
• What is the reciprocal of $\frac{3}{4}$?


  $\frac{4}{3}$
• What is $\frac{2}{3} \div \frac{3}{4}$?


  $\frac{8}{9}$
• What is the rule for multiplying indices?

  Add the powers when multiplying the same base
• What is $5^{-3} \times 5^{7} \div 5$ simplified?


  $5^{3}$
• How do you find the ratio of $a$, $b$, and $c$ given $a:b =$$3:5$ and $a:c =$$4:7$?


  Make the $a$ values the same and combine the ratios
• What is the combined ratio of $a:b:c$ if $a:b =$$3:5$ and $a:c =$$4:7$?


  $12:20:21$
• If $e =$$1$, what are the values of $d$ and $f$ if $d =$$2e$ and $f =$$3d$?


  $d =$$2, f =$$6$
• What is the total number of counters if the ratio of red, blue, and yellow counters is $4:5:8$ and yellow is 24 more than blue?


  136
• What is the relationship between angles in a triangle?

  The sum of the angles in a triangle is always 180°
• What is the value of angle $c a b$ if $c d =$$122°$ and $abc =$$59°$?


  $63°$
• What is the formula for pressure?

  Pressure equals force divided by area
• What is the force if the pressure is $25 \text{ N/m}^2$ and the area is $7 \text{ m}^2$?


  $175 \text{ N}$
• How do you estimate the probability of getting a five on a spinner?

  By dividing the number of fives by the total spins
• What is the estimated probability of getting a five twice if the probability of getting a five once is $\frac{1}{3}$?


  $\frac{1}{9}$
• How do you solve simultaneous equations?

  By eliminating one variable to solve for the other
• What is the value of $y$ if $2x - 5y =$$20$ and $10x +$$4y =$$14$?


  $y =$$-\frac{2}{3}$
• What are the steps to convert a mixed number to an improper fraction?

  1. Multiply the whole number by the denominator.
  2. Add the numerator to the result.
  3. Write the result over the original denominator.
• What are the rules for adding fractions?

  • Find a common denominator.
  • Convert each fraction to have that denominator.
  • Add the numerators and keep the common denominator.
• What are the properties of ratios?

  • Ratios compare quantities.
  • They can be simplified.
  • They can be expressed in different forms.
• What is the relationship between pressure, force, and area?

  • Pressure = Force / Area
  • To find force, rearrange to Force = Pressure × Area.
• What is the significance of corresponding angles in parallel lines?

  • Corresponding angles are equal.
  • They occur when a transversal crosses parallel lines.
• What is the significance of angles in a triangle?

  • The sum of the angles in a triangle is always 180°.
  • This is a fundamental property of triangles.
• What is the method for solving simultaneous equations?

  • Eliminate one variable.
  • Substitute back to find the other variable.
  • Solve for both variables.
• What can be done to eliminate variables in a system of equations?

  We can add or subtract equations after manipulating them to have matching coefficients.
• If you double the top equation and have a negative and positive Y, what is the result?

  You can add the two equations together to eliminate the Y's.
• What happens when you multiply the top equation by five and the bottom one by two?

  You will have matching coefficients of $10x$ in both equations.
• What is the result of subtracting the bottom equation from the top equation after manipulation?

  The result is $-9y =$$6$.
• How do you find the value of $y$ from $-9y =$$6$?


  By dividing both sides by -9, you find $y =$$-\frac{2}{3}$.
• How do you substitute $y =$$-\frac{2}{3}$ back into the top equation?


  You replace $y$ in $2x - y =$$4$ to get $2x +$$\frac{2}{3} =$$4$.
• What does the expression $2x +$$\frac{2}{3} =$$4$ simplify to?


  It simplifies to $x =$$\frac{5}{3}$.
• How can you verify the solution $x =$$\frac{5}{3}$ in the second equation?


  By substituting $x =$$\frac{5}{3}$ and $y =$$-\frac{2}{3}$ into the second equation.
• What is the value of $8^{\frac{4}{3}} +$$\left(\frac{1}{3}\right)^{-3}$?


  The value is $43$.