Reviewing 6th Grade Mathematics The Number System CCGPS.NS6.1-7

Reviewing 6th Grade Math: The Number System Using your notes and the Holt textbook, and one side of a sheet of notebook paper, create notes on the following topics that you would use on a test. Factors and Multiples Dividing Whole Numbers Integers Absolute Value Rational Numbers Compare and Order Rational Numbers Add and Subtract Decimals Multiply and Divide Decimals Divide Fractions and Mixed Numbers The Coordinate Plane Solve Problems in the Coordinate Plane

Factors and Multiples Factor (p.169): A number that is multiplied by another number to get a product. e.g. The factors of 10 are 1, 2, 5, and 10. The GCF (p.173) of 12 and 36 is 12.

Factors and Multiples Multiple (p.228, 234): A multiple of a number is the product of the number and any nonzero whole number. e.g. Multiples of 5 include 5, 10, 15, 20… The LCM (p.228) of 5 and 10 is 10. To find the LCM, start listing multiples of the largest number first until all numbers share this multiple.

Dividing Whole Numbers Divisible (p.164): A number is divisible by another number if the quotient is a whole number with no remainder. e.g. 42 ÷ 6 = 7 42 is the dividend 6 is the divisor 7 is the quotient

Integers Integers (p.602): A member of the set of whole numbers and their opposites. e.g. {-3, -2, -1, 0, 1, 2, 3} 0 is an integer. Fractions and decimals are NOT integers but can be negative. Numbers to the left of 0 on a number line are negative. Numbers to the right of 0 on a number line are positive. Zero is neither positive or negative.

Absolute Value Absolute Value (p.762): The distance of a number from zero on a number line; shown by the symbol . e.g. −5 =5 , 5 =5 The absolute value of negative 5 and 5 is 5 because they both have a distance of 5 from zero. Absolute value is always positive.

Rational Numbers Rational (p.763): A number that can be expressed as the ratio of two integers in the form 𝑎 𝑏 , where b is not equal to 0. Fractions Decimals Percents Integers p.180-193 p.380 p.381 p.602

Compare and Order Rational Numbers Fractions (p.198): (1) Get common denominators, (2) create equivalent fractions, (3) compare numerators. Decimals: (1) Line them up by its decimal point, (2) fill in empty spaces with zero, (3) compare from left to right. Integers: The number farthest right on a number line has the most value. The number farthest left on a number line has the least value.

Add and Subtract Decimals p.118 Line up the numbers by its decimal point Subtract or add Bring your decimal down

Divide Fractions Multiplying Fractions (p.254 - 264): (1) Rename mixed numbers as improper fractions and write whole numbers as fractions with 1 as the denominator, (2) multiply straight across; multiply numerators, multiply denominators, (3) write answer in simplest form Dividing Fractions (p.270): (1) Rename mixed numbers as fractions and write whole numbers as fractions with 1 as the denominator, (2) Keep, change, flip (keep chicken fried)

Divide Fractions When checking a solution from a division problem, remember that the quotient is one of two factors needed to get the original dividend: Keep, Change, Flip (multiply by the reciprocal) If you don’t use the original fraction 2/3, the product will not be ½.

The Coordinate Plane Coordinate Plane (p.610): A plane formed by the intersection of a horizontal number line called the x-axis and a vertical number line called the y-axis. The two axes divide the coordinate plane into four quadrants. The point where the axes intersect is called the origin. The ordered pair for the origin is (0,0). The numbers in an ordered pair are called coordinates. The first number is called the x-coordinate. The second number is called the y-coordinate.

The Coordinate Plane C

The Coordinate Plane When finding distance between points on a coordinate plane, add the absolute values of each point from zero. From Point E to the origin, the distance is 2. From the origin to Point H, the distance is 3. Therefore, the distance from Point E to Point H is 2 + 3 = 5.

When the point is reflected across the x-axis: x-coordinate stays the same y-coordinate changes sign (becomes the opposite) D C Rectangle ABCD Points Reflection across the x-axis A B A(-5, -2) B(-3, -2) C(-3, -5) D(-5, -5) A’(-5, 2) B’(-3, 2) A B C’(-3, 5) D’(-5, 5) D C

When the point is reflected across the y-axis: y-coordinate stays the same x-coordinate changes sign (becomes the opposite) Rectangle ABCD Points Reflection across the y-axis A(-5, -2) B(-3, -2) C(-3, -5) D(-5, -5) A’(5, -2) B’(3, -2) C’(3, -5) D’(5, -5) A B B A D C C D