Simplify the expression: 11 ¹⁄₂ - 3 ⁵⁄₆

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Step 1: Convert First Mixed Number to An Improper Fraction You can use this formula to convert mixed numbers to improper fractions: a ^b/_c = ^{ac + b}/_c 11 ¹⁄₂= ^{(11 • 2) + 1}/₂ = ^{22 + 1}/₂ = ²³/₂ So, our new expression is: ²³/₂- 3 ⁵⁄₆ Step 2: Convert Second Mixed Number to An Improper Fraction You can use this formula to convert mixed numbers to improper fractions: a ^b/_c = ^{ac + b}/_c 3 ⁵⁄₆= ^{(3 • 6) + 5}/₆ = ^{18 + 5}/₆ = ²³/₆ So, our new expression is: ²³/₂- ²³⁄₆ Step 3: Find the least common denominator for both fractions. In order to determine the least common denominator, find the least common multiple between the two denominators (2 and 6). To find the least common multiple: List the multiples of each number until you find one in common. 2: 2, 4, 6, 8, 10… 6: 6, 12, 18… In this case, the least common denominator between ²³/_{2 and} ²³⁄₆ is 6. Step 4: 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. For ²³⁄₂ , we would need to multiply the denominator (2) by 3 to get to the least common denominator (6). In order to make the denominator equal to 6, we multiply both the numerator and denominator by the same number (3). ^{23 • 3} / _{2 • 3} → ⁶⁹⁄₆ In the case of ²³⁄₆ , the denominator is already the lowest common denominator. Now, we have: ⁶⁹⁄₆ - ²³⁄₆ Step 5: Subtract the fractions. ⁶⁹⁄₆ - ²³⁄₆ = ^{69 - 23}⁄₆ Step 6: Simplify ^{69 - 23}⁄₆ = ⁴⁶⁄₆ Step 7: 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. 46 ÷ 6 = 7 r4 (7 with a remainder of 4) Then, we identify the whole number. In this example, the whole number of the answer is 7. This means that the whole number in our fractional answer will be 7. Next, we determine what our fraction will be by placing the remainder (4) over the denominator from the original fraction (6). So we now have: 7 ⁴⁄₆ Finally, if possible, we reduce the fraction. In order to determine whether or not a fraction can be reduced, you look for the lowest common factor between the numerator and the denominator. You can find it by listing the factors of each number and finding the smallest on they have in common. 4: 1, 2, 4 6: 1, 2, 3, 6 In this case, you can reduce the fraction by dividing both the numerator and denominator by the lowest common factor, 2. 7 ^4÷2⁄_6÷2= 7 ²⁄₃

Simplify the Expression: 11 1⁄2 - 3 5⁄6

Simplify the Expression: 11 ¹⁄₂ - 3 ⁵⁄₆