Chapter 5: Problem 24

Without using a calculator find the value of $$ 3 \frac{13}{17}+\frac{4-\frac{1}{3}}{3 / 7} $$

Short Answer

Expert verified

Question: Simplify the given expression without using a calculator: $$3 \frac{13}{17}+\frac{4-\frac{1}{3}}{3 / 7}$$ Answer: $$\frac{1885}{153}$$

Step by step solution

Convert the mixed number into an improper fraction

Convert the mixed number $$3 \frac{13}{17}$$ into an improper fraction by multiplying the whole number by the denominator, then adding the numerator and placing that value over the denominator. So we get: $$ 3 \frac{13}{17} = \frac{3 \cdot 17 + 13}{17} = \frac{51 + 13}{17} = \frac{64}{17} $$

Simplify the expression within the parenthesis of the second part

Next, we will simplify the expression inside the parenthesis $$4-\frac{1}{3}$$ by finding a common denominator and then subtracting the fractions: $$ 4-\frac{1}{3} = \frac{12}{3}-\frac{1}{3} = \frac{11}{3} $$

Replace the parenthesis with the simplified expression

Now, we need to substitute the simplified expression found in Step 2 into the original expression. So we get: $$ 3 \frac{13}{17}+\frac{4-\frac{1}{3}}{3 / 7} = \frac{64}{17} + \frac{\frac{11}{3}}{3 / 7} $$

Simplify the complex fraction

In this step, we will simplify the complex fraction in the second part. To do this, we will multiply the numerator by the reciprocal of the denominator: $$ \frac{\frac{11}{3}}{3 / 7} = \frac{11}{3} \cdot \frac{7}{3} = \frac{11 \cdot 7}{3 \cdot 3} = \frac{77}{9} $$

Add the simplified fractions

Finally, we will add the two simplified fractions found in Steps 1 and 4. To do this, we need to first find the common denominator, which in this case is $$17 \cdot 9$$: $$ \frac{64}{17} + \frac{77}{9} = \frac{64 \cdot 9}{17 \cdot 9} + \frac{77 \cdot 17}{9 \cdot 17} = \frac{576 + 1309}{153} = \frac{1885}{153} $$ So the simplified value of the given expression is $$\frac{1885}{153}$$.

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Without using a calculator find the value of $$ 3 \frac{13}{17}+\frac{4-\frac{1}{3}}{3 / 7} $$

Short Answer

Step by step solution

Convert the mixed number into an improper fraction

Simplify the expression within the parenthesis of the second part

Replace the parenthesis with the simplified expression

Simplify the complex fraction

Add the simplified fractions

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