It is important for students to work math problems mentally, as well as algorithmically, in order to become more comfortable with numbers and, over time, develop "Number Sense."

**Find a "Number Sense" way and an "Algorithmic" way to solve each of the following:**

**1/2 + 1/3 + 1/6 + 3/17**

**Number Sense:** When you add 1/2 and 1/3, the answer is 5/6. Now, notice that the next fraction to add is 1/6, so all together you have 6/6 = 1. From here, we add 1 + 3/17, making 1 3/17 the final answer.

**Algorithmic:** The least common denominator of 1/2, 1/3, 1/6, and 3/17 is 102. So, add 51/102 + 34/102 + 17/102 + 18/102 to get 120/202. Turn this improper fraction into a mixed number by solving 120 ÷ 102 = 1 r18, which becomes 1 18/102. Simplify this to get **1 3/17**.

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**1/2 x 2/3 x 3/4 x 4/5 x 5/6 x 6/7 x 7/8**

**Number Sense:** We know that when you multiply fractions where the denominator of one term and the numerator of another are the same number, they “cancel” out. So when we look at this problem, we can quickly determine in our minds that 1/2 x 2/3 x3/4 x 4/5 x 5/6 x 6/7 x 7/8 = **1/8**.

**Algorithmic:** Multiply all numerators and all denominators to arrive at the answer 5,040/40,320. Simplify this fraction and you get **1/8**.