Question Types for Fraction Quiz and Fraction Four

In Fraction Quiz and Fraction Four, questions are designed to help the user practice simplifying, converting, and multiplying decimals, percentages, and fractions and to prepare them for questions of various levels of difficulty. Questions are categorized by a combination of level (which determines the difficulty) and by types of problems listed. These different categories are defined in two different organizational structures. The first organization looks at problem types, then considers how problems vary by level within that type. The second organization considers the difficulty level first, then looks at different problem types within that level. All number ranges are inclusive. Both are provided below.

Descriptions by Problem Type:

Percentage:

• Level 1: Express an unreduced fraction as a percentage. Possible answers are: 10, 20, 25, 30, 33.333, 40, 50, 60, 66.667,70, 75, 80, or 90 percent.
• Level 2: Express an unreduced fraction as a percentage or find a certain percentage (multiple of 5) of a whole number less than 300. Fractions will not be in reduced form, but can be reduced to fractions with denominators equal to 2, 3, 4, 5, 6, 9 or 10.
• Level 3: Express a fraction as a percentage or find a whole number percentage of a number less than 300. Fractions will not be in reduced form, but can be reduced to fractions with denominators between 2 and 12.

Fraction <-> Decimal:

• Level 1: Convert between fractions and decimals. Fractions may not be in reduced form, but can be reduced to fractions with denominators equal to 2, 3, 4, 5, or 10.
• Level 2: Convert between fractions and decimals. Fractions will not be in reduced form, but can be reduced to fractions with denominators equal to 2, 3, 4, 5, 6, 9, or 10.
• Level 3: Convert between fractions and decimals. Fractions may not be in reduced form, but can be reduced to fractions with denominators between 2 and 12.

Fraction <-> Percentage:

• Level 1: Convert between fractions and percentages. Fractions may not be in reduced form, but can be reduced to fractions with denominators equal to 2, 3, 4, 5, or 10.
• Level 2: Convert between fractions and percentages. Fractions may not be in reduced form, but can be reduced to fractions with denominators equal to 2, 3, 4, 5, 6, 9, or 10.
• Level 3: Convert between fractions and percentages. Fractions may not be in reduced form, but are based on fractions with denominators between 2 and 12.

Algebra:

• Level 1: Find x by combining like terms or dividing by a coefficient. Fractional terms to be combined may not have the same denominator and answer (x) will be a positive whole number or fraction. Denominators of fractions will be between 2 and 20.
• Level 2: Find x by combining like terms or dividing by the coefficient of x. Fractional terms may not have the same denominator and answer will be a positive whole number or fraction. Denominators of the fractions will be between 2 and 50.
• Level 3: Find x by combining like terms or eliminating the coefficient of x. Fractional terms may have different denominators and answers may be negative.

Comparing Fractions:

• Level 1: Determine the fraction with a greater value. Fractions may not be in reduced form, but can be reduced to fractions with denominators equal to 2, 3, 4, 5, or 10.
• Level 2: Determine the fraction with a greater value. Fractions may not be in reduced form, but can be reduced to fractions with denominators equal to 2, 3, 4, 5, 6, 9, or 10.
• Level 3: Determine the fraction with a greater value. Fractions may not be in reduced form, but can be reduced to fractions with denominators between 2 and 12.

Reducing Fractions:

• Level 1: Reduce a fraction and express it in lowest terms. Fractions will reduce to a fraction with a denominator of 2, 3, 4, 5, or 10.
• Level 2: Reduce a fraction and express it in its lowest terms. The fraction will reduce to a fraction with a denominator of 2, 3, 4, 5, 6, 9, or 10.
• Level 3: Reduce a fraction and express it in lowest terms. The fraction will reduce to a fraction with a denominator of between 2 and 12.

Adding and Subtracting Fractions:

• Level 1: Add or subtract fractions with a common denominator and express the answer in lowest terms. Answers may be proper fractions, improper fractions or equal to one, but will not be negative.
• Level 2: Add or subtract two fractions with different denominators between 0 and 50 and express it in lowest terms. Answer may be a proper fraction, an improper fraction, or equal to one, but will not be negative.
• Level 3: Add or subtract two fractions with denominators between 2 and 100 and express answer in lowest terms. Answer may be a proper fraction, an improper fraction, and/or negative.

Multiplying and Dividing Fractions:

• Level 1: One of three question types:
  • Multiply two fractions with denominators less than 20.
  • Divide two fractions with denominators less than 20.
  • Find a fractional portion of a whole number. Answer will be a whole number.
• Level 2: One of three problem types:
  • Multiply two fractions with denominators less than 50 and report in lowest terms.
  • Divide two fractions with denominators less than 50 and report in lowest terms.
  • Find a fractional portion of a whole number less than 100. The denominator of the fraction will be less than 10, but may not be a common factor of the whole number, resulting in decimal answers to be rounded to the thousandths place.
• Level 3: One of three problem types:
  • Multiply two fractions and report in lowest terms.
  • Divide two fractions and report in lowest terms.
  • Find a fractional portion of a whole number less than 200. The denominator of the fraction will be less than 20, but may not be a factor of the whole number, resulting in decimal answers to be rounded to the thousandths place.

Rounding Decimals:

• Level 1: Round a decimal with one decimal place to the nearest whole number or a decimal with two decimal places to the nearest tenth place.
• Level 2: Round a number with three decimal places to the nearest tenth place.
• Level 3: Round a decimal with four decimal places to the nearest hundredth place or a decimal with five decimal places to the nearest thousandth place.

Improper Fractions <-> Mixed Numbers:

• Level 1: Convert between improper fractions and their mixed number equivalents or vice versa. The denominators of all fractions will be between 2 and 5, and the whole number portion will be either 1 or 2.
• Level 2: Convert between improper fractions and their mixed number equivalents and report in lowest terms. The denominators of all fractions will be between 2 and 10 and the whole number portion will be between 1 and 3.
• Level 3: Convert between improper fractions and their mixed number equivalents and report answer in lowest terms. The denominators of all fractions will be between 2 and 20, and the whole number portion will be less than 5.

Descriptions by Difficulty Level:

Level 1:

• Percentage: Express an unreduced fraction as a percentage. Possible answers are: 10, 20, 25, 30, 33.333, 40, 50, 60, 66.667,70, 75, 80, or 90 percent.
• Fraction <-> Decimal: Convert between fractions and decimals. Fractions may not be in reduced form, but can be reduced to fractions with denominators equal to 2, 3, 4, 5, or 10.
• Fraction <-> Percentage: Convert between fractions and percentages. Fractions may not be in reduced form, but can be reduced to fractions with denominators equal to 2, 3, 4, 5, or 10.
• Algebra: Find x by combining like terms or dividing by a coefficient. Fractional terms to be combined may not have the same denominator and answer (x) will be a positive whole number or fraction. Denominators of fractions will be between 2 and 20.
• Comparing Fractions: Determine the fraction with a greater value. Fractions may not be in reduced form, but can be reduced to fractions with denominators equal to 2, 3, 4, 5, or 10.
• Reducing Fractions: Reduce a fraction and express it in lowest terms. Fractions will reduce to a fraction with a denominator of 2, 3, 4, 5, or 10.
• Adding and Subtracting Fractions: Add or subtract fractions with a common denominator and express the answer in lowest terms. Answers may be proper fractions, improper fractions or equal to one, but will not be negative.
• Multiplying and Dividing Fractions: One of three question types:
  • Multiply two fractions with denominators less than 20.
  • Divide two fractions with denominators less than 20.
  • Find a fractional portion of a whole number. Answer will be a whole number.
• Rounding Decimals Round a decimal with one decimal place to the nearest whole number or a decimal with two decimal places to the nearest tenth place.
• Improper Fractions <-> Mixed Numbers: Convert between improper fractions and their mixed number equivalents or vice versa. The denominators of all fractions will be between 2 and 5, and the whole number portion will be either 1 or 2.

Level 2:

• Percentage: Express an unreduced fraction as a percentage or find a certain percentage (multiple of 5) of a whole number less than 300. Fractions will not be in reduced form, but can be reduced to fractions with denominators equal to 2, 3, 4, 5, 6, 9 or 10.
• Fraction <-> Decimal: Convert between fractions and decimals. Fractions will not be in reduced form, but can be reduced to fractions with denominators equal to 2, 3, 4, 5, 6, 9, or 10.
• Fraction <-> Percentage: Convert between fractions and percentages. Fractions may not be in reduced form, but can be reduced to fractions with denominators equal to 2, 3, 4, 5, 6, 9, or 10.
• Algebra: Find x by combining like terms or dividing by the coefficient of x. Fractional terms may not have the same denominator and answer will be a positive whole number or fraction. Denominators of the fractions will be between 2 and 20.
• Comparing Fractions: Determine the fraction with a greater value. Fractions may not be in reduced form, but can be reduced to fractions with denominators equal to 2, 3, 4, 5, 6, 9, or 10.
• Reducing Fractions: Reduce a fraction and express it in its lowest terms. The fraction will reduce to a fraction with a denominator of 2, 3, 4, 5, 6, 9, or 10.
• Adding and Subtracting Fractions: Add or subtract two fractions with different denominators between 0 and 50 and express it in lowest terms. Answer may be a proper fraction, an improper fraction, or equal to one, but will not be negative.
• Multiplying and Dividing Fractions: One of three problem types:
  • Multiply two fractions with denominators less than 50 and report in lowest terms.
  • Divide two fractions with denominators less than 50 and report in lowest terms.
  • Find a fractional portion of a whole number less than 100. The denominator of the fraction will be less than 10, but may not be a common factor of the whole number, resulting in decimal answers to be rounded to the thousandths place.
• Rounding Decimals Round a number with three decimal places to the nearest tenth place.
• Improper Fractions <-> Mixed Numbers: Convert between improper fractions and their mixed number equivalents and report in lowest terms. The denominators of all fractions will be between 2 and 10 and the whole number portion will be between 1 and 3.

Level 3:

• Percentage: Express a fraction as a percentage or find a whole number percentage of a number less than 300. Fractions will not be in reduced form, but can be reduced to fractions with denominators between 2 and 12.
• Fraction <-> Decimal: Convert between fractions and decimals. Fractions may not be in reduced form, but can be reduced to fractions with denominators between 2 and 12.
• Fraction <-> Percentage: Convert between fractions and percentages. Fractions may not be in reduced form, but are based on fractions with denominators between 2 and 12.
• Algebra: Find x by combining like terms or eliminating the coefficient of x. Fractional terms may have different denominators and answers may be negative.
• Comparing Fractions: Determine the fraction with a greater value. Fractions may not be in reduced form, but can be reduced to fractions with denominators between 2 and 12.
• Reducing Fractions: Reduce a fraction and express it in lowest terms. The fraction will reduce to a fraction with a denominator of between 2 and 12.
• Adding and Subtracting Fractions: Add or subtract two fractions with denominators between 2 and 100 and express answer in lowest terms. Answer may be a proper fraction, an improper fraction, and/or negative.
• Multiplying and Dividing Fractions: One of three problem types:
  • Multiply two fractions and report in lowest terms.
  • Divide two fractions and report in lowest terms.
  • Find a fractional portion of a whole number less than 200. The denominator of the fraction will be less than 20, but may not be a factor of the whole number, resulting in decimal answers to be rounded to the thousandths place.
• Rounding Decimals: Round a decimal with four decimal places to the nearest hundredth place or a decimal with five decimal places to the nearest thousandth place.
• Improper Fractions <-> Mixed Numbers: Convert between improper fractions and their mixed number equivalents and report answer in lowest terms. The denominators of all fractions will be between 2 and 20, and the whole number portion will be less than 5.