Integers and Rational Numbers

Unit Review Sheet

Facts and Definitions

Lesson 1: Fraction Addition and Subtraction

• Equivalent fractions have the same value. To make an equivalent fraction, multiply or divide the numerator and denominator by the same number. For example, 9/12 and 3/4 are equivalent fractions.
• When you simplify a fraction, the fraction will have the smallest possible denominator and numerator. For example, 2/4 simplifies to 1/2.
• To convert an improper fraction to a mixed number, divide the numerator by the denominator, write the whole number answer, and then write any remainder above the original denominator. For example, 13/3 = 13 ÷ 3 = 4 1/3
• To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator to the product of the whole number and the denominator, and then place this number over the original denominator. For example, 3 1/2 = 3 × 2 + 1 = 7/2
• Easiest common denominator (ECD) method — multiply the denominators together and then convert each fraction to an equivalent fraction. For example, 1/2 and 3/4 (4 × 2 = 8) = 4/8 and 6/8
• Least common denominator (LCD) method — find the lowest common multiple and then convert each fraction to an equivalent fraction. For example, 1/2 and 3/4 (LCD is 4) = 2/4 and 3/4

Lesson 2: Fraction Multiplication

• To multiply a fraction by a whole number, multiply the numerator by the whole number and leave the denominator the same. For example, 2/7 × 3 = 6/7
• To multiply two or more fractions, multiply the numerators to find the numerator of the product, and multiply the denominators to find the denominator of the product. For example, 1/2 × 3/4 = 3/8
• To multiply by a mixed number, first convert the mixed number(s) into improper fraction(s). Cancel or reduce when possible before multiplying, and convert the product to a mixed number as needed. For example, 2 1/4 × 3 = 9/4 × 3 = 27/4 = 6 3/4
• The word "of" in a math problem often means to multiply. For example, 2/3 of 6 = 2/3 × 6.

Lesson 3: Fraction Division

• The reciprocal of a fraction flips the numerator and the denominator. For example, the reciprocal of 2/1 is 1/2, and the reciprocal of 3/4 is 4/3.
• To divide fractions, find the reciprocal of the divisor, and then multiply the two fractions. For example, 3/4 ÷ 2/3 = 3/4 × 3/2 = 6/8 or 3/4
• To divide mixed numbers, first convert the mixed numbers to improper fractions. Note that you may need to convert the answer back to a mixed number. For example, 3 1/2 ÷ 2 3/4 = 7/2 ÷ 11/4 = 7/2 × 4/11 = 28/22
  or 1 6/22 or 1 3/11

Lesson 4: Negative Numbers and Integers

• A negative number is a number that is less than zero.
• Natural numbers are the set of counting numbers starting at 1 (1, 2, 3, etc.), and whole numbers are the set of natural numbers as well as zero.
• An integer is a number with no fractional part. Integers include the natural (counting) numbers, zero, and the negatives of the counting numbers.
• A rational number is a number that can be written as a fraction or decimal; all integers as also rational numbers.
• All numbers are understood to have a sign, either positive (indicating the number is greater than zero) or negative (indicating the number is less than zero). Zero is neither positive nor negative.
• The additive inverse of a number is what you have to add to that number to get zero. The additive inverse is sometimes referred to as the opposite of a number.

Lesson 5: Absolute Value and Inequalities

• Absolute value is the value of a number without regard to its sign, or the distance of a number from zero. It is also called the magnitude of a number.
• The sign of a number refers to whether a number is positive (greater than zero) or negative (less than zero). Zero is neither positive nor negative.
• An inequality is a number statement that has a "greater than" or "less than" symbol in it.

Lesson 6: The Coordinate Plane

• A plane is a two-dimensional space.
• A coordinate plane is a two-dimensional number line system used to show the location of specific points in a plane.
• The x-axis is the horizontal axis (i.e., number line) in the coordinate plane.
• The y-axis is the vertical axis (i.e., number line) in the coordinate plane.
• A coordinate is a number used to indicate the location of a point.
• An ordered pair is a pair of numbers (i.e., a pair of coordinates), written (a, b), that indicates the location of a point on the coordinate plane.
• The origin is the point where the x-axis and y-axis cross; its coordinates are (0, 0).
• The x-coordinate is the first coordinate listed in an ordered pair.
• The y-coordinate is the second coordinate listed in an ordered pair.
• The coordinate plane is divided into 4 quadrants, or regions. Quadrants are labeled with Roman numerals.
• Changing just the sign of a coordinate will cause the point to reflect across one of the axes (line of reflection).

Lesson 7: Coordinate Problem Solving

• Horizontal distances measure distance along the x-axis. Vertical distances measure distance along the y-axis.

Lesson 8: Unit 2 Test

• [none]

Final Project: Coordinate Game

• [none]