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Understanding Rational Numbers and Operations with Integers

This comprehensive guide covers the essentials of rational numbers and integer operations. A rational number is defined as any number that can be expressed as a quotient (a/b), where (a) and (b) are integers, and (b <br>eq 0). Examples and a number line graphing activity are included. The addition and subtraction of integers are also detailed, with key rules outlined for combining positive and negative numbers. Practice problems are provided, encouraging mastery of these fundamental concepts in mathematics.

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Understanding Rational Numbers and Operations with Integers

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  1. Ch. 8 Integers

  2. Understanding Rational Numbers • A rational number is any number that can be written as a quotient a/b, where a and b are integers and b is NOT equal to 0. • Examples: 3 1/8, -0.28 and 5 are all rational numbers because they can be written as 25/8, -28/100, and 5/1.

  3. Graph the rational numbers on the number line. 1) -1 3/8 2) 0.75 3) -7/8 4) -1/8

  4. Adding Integers • IMPORTANT THINGS TO REMEMBER: • When adding two negative numbers the answer will always be negative. Ex. -5 + -7= -12 • If you are adding a positive and a negative number. Look to see which number is larger. The larger number’s sign (+, -) will decide if the answer will be positive or negative. Ex. 5+ -7 = 7 is the bigger number so the answer will be a negative number. Ex. -6 + 11= 11 is the bigger number so the answer will be a positive number.

  5. Problems • -4 + -18 = • 17 + -29= • -4 + -5 = • -8+ -5 + 6= • -18+ 18= • -20+ 4= • -3+ 2+ 2=

  6. Subtracting Integers • IMPORTANT THINGS TO REMEMBER! • When subtracting two positive numbers look at the 1st number. If it is less than the second number the answer will be negative. Ex. 10-12= -2 • When you are subtracting a negative and a positive number your answer is essentially adding two negative numbers and your answer will be negative. Ex. -12-6= or -12+-6= -18

  7. Subtracting continued • IMPORTANT THINGS TO REMEMBER! • When you have two negatives in a row (a subtraction sign and a negative sign) it cancels each other out and changes to a positive. Ex. 6-(-4)= There are two negatives in a row so it changes to 6+4=10 Just like English- you cannot have a double negative in a sentence! What about -2-(-7)?

  8. Problems • -6-3= • -8-(-8)= • 7-12= If n=-3 evaluate each expression. 4. n-(-19)= 5. -1-n= 6. 7- l n l –(-11)=

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