Simplify the expression: 8 ¹¹⁄₁₈ + 6 ¹⁄₃ + ¹⁄₂

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Step 1: Add Whole Numbers Together When you have two mixed numbers, you add the whole numbers together first. 8 ¹¹⁄₁₈ + 6 ¹⁄₃ + ¹⁄₂→ 14 ¹¹⁄₁₈ + ¹⁄₃ + ¹⁄₂ *Since this an addition problem, you are able to pull out the whole numbers to add together first. This is not the case with all operations. Step 2: Find the least common denominator for both fractions. In order to determine the least common denominator, find the least common multiple between the three denominators (18, 3, and 2). To find the least common multiple: List the multiples of each number until you find one in common. 18: 18, 36, 54… 3: 3, 6, 9, 12, 15, 18, 21… 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20… In this case, the least common denominator between ¹¹⁄₁₈ , ¹⁄₃ , ¹⁄₂ is 18. Step 3: Make the two denominators the same as the least common denominator. First, determine what number needs to multiply each denominator in order to get to the least common denominator. In the case of ¹¹⁄₁₈ , the denominator is already the lowest common denominator. For ¹⁄₃ , we would need to multiply the denominator (3) by 6 to get to the least common denominator (18). In order to make the denominator equal to 18, we multiply both the numerator and denominator by the same number (6). ^{1 • 6} / _{3 • 6} → ⁶⁄₁₈ For ¹⁄₂ , we would need to multiply the denominator (2) by 9 to get to the least common denominator (18). In order to make the denominator equal to 18, we multiply both the numerator and denominator by the same number (9). ^{1 • 9} / _{2 • 9} → ⁹⁄₁₈ Now, we have: 14 + ¹¹⁄₁₈ + ⁶⁄₁₈+ ⁹⁄₁₈ Step 4: Add the fractions. 14 + ¹¹⁄₁₈ + ⁶⁄₁₈+ ⁹⁄₁₈= 14 + ^{11 + 6 +9}⁄₁₈ Step 5: Simplify 14 + ^{11 + 6 +9}⁄₁₈ = 14 + ²⁶⁄₁₈ Step 6: Convert Improper Fractions to Mixed Numbers Next, we change the improper fraction to a mixed number. We do this by first dividing the numerator by the denominator. 26 ÷ 18 = 1 r8 (1 with a remainder of 8) Then, we identify the whole number. In this example, the whole number of the answer is 1. This means that the whole number in our fractional answer will be 1. Next, we determine what our fraction will be by placing the remainder (8) over the denominator from the original fraction (18). So we now have: 14 + 1 ⁸⁄₁₈ Step 7: Simplify. 14 + 1 ⁸⁄₁₈= 15 + ⁸⁄₁₈ Finally, if possible, we reduce the fraction. In this example, we can reduce ⁸⁄₁₈by dividing both the numerator and denominator by the greatest common factor. In order to find the greatest common factor, list all the factors of both the numerator and denominator. 8: 1, 2, 4, 8 18: 1, 2, 3 ,6, 9, 18 Now we divide both the numerator and denominator by the greatest common factor, 2, and simplify to find the final answer. 15 + ^8÷2⁄_18÷2= 15 + ⁴⁄₉= 15 ⁴⁄₉ Note: Another way to solve this equation is to turn both mixed numbers into improper fractions at the beginning, then follow the same steps outlined in this problem explanation.

Simplify the Expression: 8 11⁄18 + 6 1⁄3 + 1⁄2

Simplify the Expression: 8 ¹¹⁄₁₈ + 6 ¹⁄₃ + ¹⁄₂