Integers & Exponents
Mathematics, Grade 8
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Integers Exponents Example Rule If the signs of the integers are the same, add the absolute values. The sum will have the same sign as the integers you are adding. If the signs of the integers are different, subtract the absolute values. The difference will have the same sign as the integer with the larger absolute value. 6 + 4 = 10 -6 + (-4) = -10 -6 + 4 = -2 6 + (-4) = 2 • Integers are a set of whole numbers and their opposites. • Positive integers are whole numbers greater than zero. • Negative integers are whole numbers less than zero. • The integer 0 is neither positive nor negative. • Integers have either a positive (+) or negative (–) sign, except zero, which has no sign. • An exponent tells how many times to multiply a number, called the base, by itself. Scientific Notation • Scientific notation is used to express very large or very small numbers. Adding Integers Example Rule If the factors have different signs, the product is negative. If the factors have the same sign, the product is positive. If one factor is zero, the product is zero. -7 x 4 = -28 -4 x 0 = 0 5 x -3 = -15 6 x 2 = 12 -8 x -9 = 72 Multiplying Integers Example Rule To subtract an integer, add its opposite by changing the subtraction sign to addition and changing the sign of the second integer. Subtracting Integers 6 – (-2) = 6 + 2 = 8 6 – 2 = 6 + (-2) = 4 Example Property Properties of Exponents a x • a y = a x + y 50 = 1 ; (-5)0 = 1 42 • 43 = 42 + 3 = 45 Example Rule If the dividend and divisor have different signs, the quotient is negative. If the dividend and divisor have the same signs, the quotient is positive. Zero divided by any integer equals zero. -12 ÷ 4 = -3 15 ÷ (-3) = -5 32 ÷ 4 = 8 -21 ÷ (-3) = 7 = 0 = 0 Dividing Integers 0 9 0 -8 a 0 = 1 , if a = 0 a x = a x – y, if a = 0 a y 25 = 25 – 2 = 2 3 22 Example Definition Negative Exponents a-x = , if a = 0 a x 1 64 1 (-4)-3 = = = (-4)3 1 (-4) (-4) (-4) 1 • • 5-2 = = = 5 2 1 25 1 5•5 1 5 = 5 x 5 x 5 = 125 3 base exponent scientific notation standard form 2.58 x 10 2,580,000 6 0.00012 1.2 x 10 -4 © Copyright NewPath Learning. All Rights Reserved. 93-4802 www.newpathlearning.com Integers & Exponents
Example Rule If the signs of the integers are the same, add the absolute values. The sum will have the same sign as the integers you are adding. If the signs of the integers are different, subtract the absolute values. The difference will have the same sign as the integer with the larger absolute value. • Integers are • Positive integers are • Negative integers are • The integer 0 is neither positive nor negative . • Integers have either a or sign, except zero, which none. • An exponent tells how many times to multiply a number, called the base, by itself. Scientific Notation • Scientific notation is used to express very large or very small numbers. Adding Integers Example Rule If the factors have different signs, the product is negative. If the factors have the same sign, the product is positive. If one factor is zero, the product is zero. Multiplying Integers Example Rule To subtract an integer, add its opposite by changing the subtraction sign to addition and changing the sign of the second integer. Subtracting Integers Example Property Properties of Exponents a x • a y = a x + y Example Rule If the dividend and divisor have different signs, the quotient is negative. If the dividend and divisor have the same signs, the quotient is positive. Zero divided by any integer equals zero. Dividing Integers a 0 = 1 , if a = 0 a x = a x – y, if a = 0 a y Example Definition Negative Exponents a-x = , if a = 0 a x 1 scientific notation standard form 2,580,000 0.00012 Integers Exponents . . . Key Vocabulary Terms • absolute value • difference • dividend • divisor • exponent • factor • integer • negative integer • positive integer • quotient • scientific notation • sum © Copyright NewPath Learning. All Rights Reserved. 93-4802 www.newpathlearning.com Integers & Exponents \|xiBAHBDy01670qzZ
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