University:
High School
Course:
High School Mathematics
Academic year:

2023
Views:

462

Pages:

3
Author:

anon

Adding & Subtracting Rational Numbers To add/subtract rational numbers, 1. Find the lowest common denominator (LCD, also known as the least common multiple (LCM, for the fractions 2. Add/Subtract the numerators 3. Simplify (reduce to lowest terms if needed) What is a Lowest Common Denominator (LCD)? The lowest common denominator is the smallest number that is a multiple of all denominators. What is the lowest common multiple (LCM) of 2, 3, and 4? 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, … 3: 3, 6, 9, 15, 18, 21, 24, 27, … 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, … LCM (2,3,4)=12 ∴ The lowest common. multiple of 2,3 and 4 is 12 What is the lowest common multiple of 10 and 25? 10: 10, 20, 30, 40, 50, 60, 70,... 25: 25, 50, 75, 100, 125,… ∴ LCM (10,25)=50 Example 1: Identify 2 equivalent rationals for each of the following. Explain how you calculated them. −2 7 −2×2 7×2 −2×3 7×3 a) b) = = −4 14 −6 21 −18 −144 = 18÷2 9 = 72 144÷2 18÷18 1 = 144÷18 8 18 144 OR 9÷9 72÷9 = 1 8 Example 2: Convert the following mixed fractions into improper fractions? 2 3 3+2 3 5 3 a) 1 = = (3×1)+2 3 = 2 b) -5 7 = =− =− (7×5)+2 7 35+2 7 37 7 Example 3: Evaluate a) −2 3 + 4 −5 = = (−2)×5 3×5 − 4×3 5×3 = −10 15 12 15 = −10−12 15 = −22 15 =− b) − The LCD(3,5)=15 ← 𝑠𝑢𝑏𝑡𝑟𝑎𝑐𝑡 𝑡ℎ𝑒 𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟𝑠 −5 6 − =− 11×1 12×1 =− 11 12 = −1 12 + 5 6 ← LCD(6,12)=12 10 12 + −11+10 12 11 12 =− 5×2 6×2 + = c) 4 5 − 22 15 11 −12 =− −2 3 ← add the numerators 1 12 5 −8 −1 −6 + =− 5×3 8×3 =− 15 24 + + − 2 −3 =− 1×4 6×4 + 2×8 3×8 4 24 = −15+4+16 24 = −15+20 24 + 16 24 5 8 + 1 6 + 2 3 ←simplify ←LCD(3,6,8)=24 ←simplifying = 5 24 d) − 1 ( 3 4 + −1 1 5 )− −5 2 =− 7 4 ( + − to improper fraction =− 7 4 =− 7×5 4×5 =− 35 20 6 5 − − − 6×4 5×4 24 20 = −35−24−50 20 = −59 50 = −9 20 2 1 4 2 1 5 5 5 1 5 2 + + ← simplify + 50 20 2 2 5 2 × 2 × 5 = 20 So LCD(2,4,5)=20 5×10 2×10 ← LCD(2,4,5) 6 5 )+ 5 2 ←change mixed numbers