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Add 17+35+210\frac{1}{7} + \frac{3}{5} + \frac{2}{10}

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Add and subtract rational numbersright chevron icon

Full solution

Q. Add 17+35+210\frac{1}{7} + \frac{3}{5} + \frac{2}{10}
  1. Find Common Denominator: Find a common denominator for 17\frac{1}{7}, 35\frac{3}{5}, and 210\frac{2}{10}. The least common multiple of 77, 55, and 1010 is 7070, so we will use 7070 as the common denominator.
  2. Convert to Equivalent Fractions: Convert each fraction to an equivalent fraction with a denominator of 7070. \newline1/7=(1×10)/(7×10)=10/701/7 = (1\times10)/(7\times10) = 10/70\newline3/5=(3×14)/(5×14)=42/703/5 = (3\times14)/(5\times14) = 42/70\newline2/10=(2×7)/(10×7)=14/702/10 = (2\times7)/(10\times7) = 14/70
  3. Add Fractions: Add the fractions with the common denominator. 1070+4270+1470=(10+42+14)70\frac{10}{70} + \frac{42}{70} + \frac{14}{70} = \frac{(10 + 42 + 14)}{70}
  4. Perform Addition: Perform the addition.\newline10+42+14=6610 + 42 + 14 = 66\newlineSo, 1070+4270+1470=6670\frac{10}{70} + \frac{42}{70} + \frac{14}{70} = \frac{66}{70}
  5. Simplify Fraction: Simplify the fraction 6670\frac{66}{70} if possible.\newlineBoth 6666 and 7070 are divisible by 22.\newline6670=(66/2)(70/2)=3335\frac{66}{70} = \frac{(66/2)}{(70/2)} = \frac{33}{35}

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