Unit 3.2 Notes - 9A.pdf

Unit 3 – Rational Numbers Grade 9 Mathematics Section 3.2 – Adding Rational Numbers A number line can sometimes be useful when adding decimal numbers. Example 1: Use a number line to add (−1.3) + (+2.1)....

Unit 3 – Rational Numbers Grade 9 Mathematics Section 3.2 – Adding Rational Numbers A number line can sometimes be useful when adding decimal numbers. Example 1: Use a number line to add (−1.3) + (+2.1). +2.1 -2 -1 0 1 2 −1.3 Example 2: Write an addition equation for the following number line. -1 0 1 2 3 4 5 1.4 Example 3: For each of the following:  Determine if the sum is positive or negative.  Estimate the answer.  Check the answer with a calculator. a. (−1.5) + (−0.6) b. (−1.8) + 2.6 c. 3.8 + (−1.2) d. 1.3 + (−3.5) e. 4.1 + 3.5 f. (−8.3) + 0.4 L. Clemens - Brenton P a g e | 10 Unit 3 – Rational Numbers Grade 9 Mathematics Example 4: A guardrail needs to be exactly 19.77 meters long. A contractor has 3 pieces measuring 2.21m, 9.14m and 3.21m. Does he have enough to complete the guardrail? Before fractions can be added, a common denominator is needed. Once a common denominator is found, we add the numerators only. If the fraction is negative, keep the negative with the numerator. Example 5: Find each sum. 1  5 3  3 7 1 (a)  (b)    (c)   2 4 8  4 12 6  4  2 6  2  1 4 (d)        (e)    (f)      5  3 7  3  2 9 When adding mixed numbers, it’s a good idea to first change the mixed numbers into improper fractions. Remember, to change a mixed number to an improper fraction, multiply the denominator with the whole number and add the numerator. If there was a negative sign, place the negative with the numerator. 3  5  2  3  13 2   5 5 5 L. Clemens - Brenton P a g e | 11 Unit 3 – Rational Numbers Grade 9 Mathematics Example 6: Change each mixed number to an improper fraction. 3 2 1 2 (a) 4 (b)  3 (c)  4 (d)  6 7 5 3 3 Example 7: Find each sum. 5 3 3  1  1  2 (a)  1 3 (b) 2    1  (c)   2     1  16 8 5  4  2  3  2 3 2 1 1  1 (d)   2   (e)  2 (f)  4    2   5 4  3  6 5  3 1 1 Example 8: Peter estimates that it takes him ℎ to prepare the dough, ℎ to grate the 4 10 1 2 cheese, ℎ to prepare the toppings, and 5 ℎ to bake the pizza. 3 a) What fraction of time did it take Peter in total to prepare the pizza? b) What was the actual time it took to prepare the pizza? L. Clemens - Brenton P a g e | 12