Simplify the expression: 6 ²⁄₃ - 2 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 6 ²⁄₃= ^{(6 • 3) + 2}/₃ = ^{18 + 2}/₃ = ²⁰/₃ So, our new expression is: ²⁰/₃- 2 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 2 ⁵⁄₆= ^{(2 • 6) + 5}/₆ = ^{12 + 5}/₆ = ¹⁷/₆ So, our new expression is: ²⁰/₃- ¹⁷⁄₆ 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 (3 and 6). To find the least common multiple: List the multiples of each number until you find one in common. 3: 3, 6, 9, 12… 6: 6, 12, 18… In this case, the least common denominator between ²⁰/₃and ¹⁷⁄₆ 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 ²⁰⁄₃ , we would need to multiply the denominator (3) by 2 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 (2). ^{20 • 2} / _{3 • 2} → ⁴⁰⁄₆ In the case of ¹⁷⁄₆ , the denominator is already the lowest common denominator. Now, we have: ⁴⁰⁄₆ - ¹⁷⁄₆ Step 5: Subtract the fractions. ⁴⁰⁄₆ - ¹⁷⁄₆ = ^{40 - 17}⁄₆ Step 6: Simplify ^{40 - 17}⁄₆ = ²³⁄₆ 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. 23 ÷ 6 = 3 r5 (3 with a remainder of 5) Then, we identify the whole number. In this example, the whole number of the answer is 3. This means that the whole number in our fractional answer will be 3. Next, we determine what our fraction will be by placing the remainder (5) over the denominator from the original fraction (6). So we now have: 3 ⁵⁄₆ Finally, if possible, we reduce the fraction. In this case, that is not necessary.

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

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