maths foundation

• What is the first step in rounding numbers to one significant figure?

  Identify the first non-zero digit in the number.
• How do you round $6.32$ to one significant figure?


  $6$
• What is the result of rounding $6.51$ to one significant figure?


  $7$
• What is $0.503$ rounded to one significant figure?


  $0.5$
• What happens when you divide by $0.5$?


  It doubles the answer.
• What is $42 \div 0.5$?


  $84$
• How do you write $180$ as a product of prime factors?


  Using a prime factor tree.
• What is the prime factorization of $180$ in index form?


  $2^2 \times 3^2 \times 5$
• How do you calculate the total cost of a washing machine priced at $640\text{ pounds}$ with $20\%\text{ VAT}$?


  Calculate $20\%\text{ of }640\text{ pounds}$ and add it to $640\text{ pounds}$.
• What is $10\%\text{ of }640\text{ pounds}$?


  $64\text{ pounds}$
• How much does James pay in total after a $68\text{ pound}$ deposit?


  $700\text{ pounds}$
• What is the monthly payment if James pays the remaining amount in 10 equal installments?

  $70\text{ pounds}$
• What is the process for multiplying fractions?

  Multiply the numerators and multiply the denominators.
• What is $\frac{3}{4} \times \frac{2}{3}$?


  $\frac{6}{12} =$$\frac{1}{2}$
• How do you divide fractions?

  Keep the first fraction, flip the second, and multiply.
• What is $\frac{2}{3} \div \frac{1}{9}$?


  $\frac{10}{9} =$$1 \frac{1}{9}$
• What is required to add or subtract fractions?

  A common denominator is needed.
• How do you convert a mixed number to an improper fraction?

  Multiply the whole number by the denominator and add the numerator.
• How do you find the total number of counters if $\frac{2}{5}$ are blue and there are 18 blue counters?


  Set up the equation $\frac{2}{5} =$$18$ and solve for the total.
• If $\frac{2}{5}$ of the total counters equals 18, what is the total number of counters?


  45 counters.
• How do you write a number in standard form?

  Make it a number between 1 and 10, then multiply by $10^n</text{ where }n$ is the number of decimal places moved.
• What is $5600$ in standard form?


  $5.6 \times 10^3$
• How do you convert $2.3 \times 10^5$ to an ordinary number?


  Move the decimal point 5 places to the right.
• How do you multiply numbers in standard form?

  Multiply the coefficients and add the exponents.
• What is $(4 \times 10^5) \times (3 \times 10^{-2})$?


  $12 \times 10^3$
• How do you convert a percentage to a decimal?

  Divide by 100.
• What is $35\%$ as a decimal?


  $0.35$
• How do you write $35\%$ as a fraction?


  $\frac{35}{100}$
• What is the simplest form of $\frac{35}{100}$?


  $\frac{7}{20}$
• How do you simplify $\frac{35}{100}$?


  Divide both numerator and denominator by 5.
• What is the final simplified form of $\frac{7}{20}$?


  It cannot be simplified further.
• How can 35 percent be expressed as a fraction?

  35 out of 100
• What is the simplest form of the fraction representing 35 percent?

  7 over 20
• What is the first step to convert numbers into ascending order?

  Convert them all into the same format
• Why is it easier to convert numbers to percentages for ordering?

  Because percentages provide a common format for comparison
• How do you convert 0.30 into a percentage?

  Multiply by 100 to get 30 percent
• What is the percentage equivalent of the fraction 1 over 4?

  25 percent
• How do you convert the fraction 6 over 25 into a percentage?

  Multiply by 4 to get 24 percent
• What is the percentage equivalent of 0.295?

  29.5 percent
• What is the correct order of the percentages from smallest to largest?

  24 percent, 25 percent, 28 percent, 29.5 percent, 30 percent