Unit 3.3 Notes - 9A Rational Numbers PDF

Unit 3 – Rational Numbers Grade 9 Mathematics Section 3.3 – Subtracting Rational Numbers When subtracting rational numbers, KEEP-CHANGE-CHANGE or KCC is a phrase that will help us to remember to ADD THE OPPOSITE. The first number stays the...

Unit 3 – Rational Numbers Grade 9 Mathematics Section 3.3 – Subtracting Rational Numbers When subtracting rational numbers, KEEP-CHANGE-CHANGE or KCC is a phrase that will help us to remember to ADD THE OPPOSITE. The first number stays the same, the subtraction is changed to addition and the sign on the second number is changed to the opposite. Every subtraction problem can be rewritten as an addition problem. For example, (−8) – (−7) is the same as (−8) + (+7) = −1 Example 1: Subtract. a. (+5) − (+3) b. 7 − (−4) c. −4 − (−2) − (+3) The same rule for subtracting integers can be applied to decimals. 2.3 – (−1.2) is the same as 2.3 + (+1.2) = 3.5 Example 2: Subtract. a. 0.3 – 0.5 b. 1.6 – (−2.7 c. (−4.5) – 1.2 d. 1.8 – 0.5 e. 2.6 – (−1.5) f. (−6.3) – (−6.3) L. Clemens - Brenton P a g e | 16 Unit 3 – Rational Numbers Grade 9 Mathematics Like when adding fractions, a common denominator is needed when subtracting fractions as well. Once a common denominator is found, we subtract the numerators only. If the fraction is negative, keep the negative with the numerator. When subtracting mixed numbers, change the mixed numbers into improper fractions. Example 3: Find the difference. 1 7 4  2 1  1 a.   b.    c.     2 8 5  3 2  3 3 5  13 1 3 1 d. 2 e. 1 f. 2 3 4 8 15 5 8 2 5 −3 1 2 1 3 g. − h. −1 4 – (−2 3 ) i. 16 − 4 7 7 L. Clemens - Brenton P a g e | 17 Unit 3 – Rational Numbers Grade 9 Mathematics Example 4: The temperature in St. John’s is 6.5 ℃. In Corner Brook, it is 8 degrees colder. What is the temperature in Corner Brook? Example 5: A piece of pipe is 146.3 cm long. A piece 13.7 cm is cut off. How long is the remaining piece? 2 Example 6: A person climbs 12 3 meters above the water to the top of a cliff. 1 He dives into the water and reaches −3 6 meters below the surface. What is the difference in these heights? L. Clemens - Brenton P a g e | 18 Unit 3 – Rational Numbers Grade 9 Mathematics Example 7: Which expression has the same answer as −2.3 − (−3.9) ? A. −2.3 + (−3.9) B. 2.3 − (−3.9) C. −2.3 − (+3.9) D. −2.3 + (+3.9) Example 8: Determine the missing number in each subtraction equation. −3 2 a. 2.5 − = 3.8 b. − = 10 5 L. Clemens - Brenton P a g e | 19