NON CALC

• What is the first step in solving the problem "three-fifths of a number is 48"?

  The first step is to recognize that three-fifths of a number equals 48.
• How do you find the original number when three-fifths of it is 48?

  You divide 48 by 3 to find the value of one part, which is 16.
• Why do you divide by the numerator when finding the original number in the problem?

  You divide by the numerator because you want to find the value of one part of the total.
• What is the process for adding mixed numbers?

  1. Convert mixed numbers to improper fractions.
  2. Find a common denominator.
  3. Add the numerators.
  4. Simplify if necessary.
• What is the first step in adding the mixed numbers three and four-fifths and three-sevenths?

  The first step is to convert the mixed number three and four-fifths to an improper fraction.
• How do you convert three and four-fifths to an improper fraction?

  You multiply 3 by 5 and add 4 to get 19-fifths.
• What is the lowest common multiple of 5 and 7?

  The lowest common multiple of 5 and 7 is 35.
• How do you create equivalent fractions with a common denominator of 35 for 19-fifths and three-sevenths?

  You multiply 19-fifths by 7/7 and three-sevenths by 5/5.
• What do you do after obtaining the equivalent fractions 133/35 and 15/35?

  You add the numerators to get 148/35.
• How do you convert 148/35 to a mixed number?

  You divide 148 by 35 to find how many times it fits, which is 4, with a remainder of 8.
• What is the final answer for the mixed number from 148/35?

  The final answer is 4 and 8/35.
• What is the process for dividing mixed numbers?

  1. Convert mixed numbers to improper fractions.
  2. Keep the first fraction as it is.
  3. Flip the second fraction to its reciprocal.
  4. Multiply the fractions.
  5. Simplify if necessary.
• How do you convert one and one-fifth to an improper fraction?

  You convert it to six-fifths.
• What do you do when dividing six-fifths by three-quarters?

  You multiply six-fifths by the reciprocal of three-quarters, which is four-thirds.
• What is the result of multiplying the numerators 6 and 4 when dividing mixed numbers?

  The result is 24.
• What is the denominator when multiplying the fractions five and three?

  The denominator is 15.
• How do you convert 24/15 to a mixed number?

  You divide 24 by 15 to get 1 with a remainder of 9, resulting in 1 and 9/15.
• What is the simplified form of 9/15?

  The simplified form is 3/5.
• What is the final answer for the division of one and one-fifth by three-quarters?

  The final answer is 1 and 3/5.
• How do you write 0.47 with a recurring dot as a fraction?

  You set x equal to 0.47 and multiply by 10 to eliminate the recurring decimal.
• What happens when you subtract the two equations formed from the recurring decimal?

  The recurring decimals cancel out, allowing you to solve for x.
• What is the result of subtracting 0.47 from 4.77?

  The result is 4.3.
• What is the final step to express x as a fraction after finding 9x = 4.3?

  You divide both sides by 9 to solve for x.
• Why is it important to eliminate decimals when expressing a number as a fraction?

  It is important because fractions should not contain decimal values.
• What is the significance of the recurring decimal in the context of fractions?

  The recurring decimal indicates that the fraction cannot be expressed as a finite decimal.
• What is the result of $4.77 - 0.47$?


  $4.3$
• When subtracting $10x - 1x$, what is the simplified result?


  $9x$
• Why is it necessary to multiply both sides by 10 when converting $4.3$ into a fraction?


  To eliminate the decimal before forming the fraction
• What is the fraction representation of $x$ after multiplying both sides by 10?


  $x =$$\frac{43}{90}$
• How do you determine if the fraction $\frac{43}{90}$ can be simplified?


  By checking if both the numerator and denominator have common factors
• What is the prime factorization of $525$?


  $3 \times 5^2 \times 7$
• What does a negative exponent indicate in $25^{-1/2}$?


  It indicates the reciprocal of the base
• What is the first step to evaluate $25^{-1/2}$?


  Calculate the square root of $25$
• What is the cube root of $8$?


  $2$
• What is the cube root of $27$?


  $3$
• What is the final result of $\left(\frac{8}{27}\right)^{\frac{2}{3}}$?


  $\frac{4}{9}$
• How can $\sqrt{80}$ be expressed in the form $k\sqrt{5}$?


  $4\sqrt{5}$
• Why is it important to identify the largest square number that divides into $80$ when simplifying $\sqrt{80}$?


  To ensure the expression is in its simplest form
• What is the result of $\sqrt{40} +$$\sqrt{90}$ after simplification?


  $5\sqrt{10}$
• How do you convert $5600$ into standard form?


  $5.6 \times 10^3$