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Which expression has the same value as 7(1)/(6)+3(2)/(3) ? -3(2)/(3)-7(1)/(6) 3(2)/(3)-7(1)/(6) 7(1)/(6)-(-3(2)/(3)) 3(2)/(3)+(-7(1)/(6))

Which expression has the same value as 716+323 7 \frac{1}{6}+3 \frac{2}{3} ?\newline−323−716 -3 \frac{2}{3}-7 \frac{1}{6} \newline323−716 3 \frac{2}{3}-7 \frac{1}{6} \newline716−(−323) 7 \frac{1}{6}-\left(-3 \frac{2}{3}\right) \newline323+(−716) 3 \frac{2}{3}+\left(-7 \frac{1}{6}\right)

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Q. Which expression has the same value as 716+323 7 \frac{1}{6}+3 \frac{2}{3} ?\newline−323−716 -3 \frac{2}{3}-7 \frac{1}{6} \newline323−716 3 \frac{2}{3}-7 \frac{1}{6} \newline716−(−323) 7 \frac{1}{6}-\left(-3 \frac{2}{3}\right) \newline323+(−716) 3 \frac{2}{3}+\left(-7 \frac{1}{6}\right)
  1. Convert to Improper Fractions: First, convert mixed numbers to improper fractions.\newline716=426+16=4367\frac{1}{6} = \frac{42}{6} + \frac{1}{6} = \frac{43}{6}\newline323=93+23=1133\frac{2}{3} = \frac{9}{3} + \frac{2}{3} = \frac{11}{3}
  2. Add Improper Fractions: Now, add the two improper fractions.\newlineTo add fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert 113\frac{11}{3} to a fraction with a denominator of 66.\newline113=(11×2)(3×2)=226\frac{11}{3} = \frac{(11\times2)}{(3\times2)} = \frac{22}{6}
  3. Check First Choice: Add the two fractions with the common denominator. 436+226=43+226=656\frac{43}{6} + \frac{22}{6} = \frac{43 + 22}{6} = \frac{65}{6}
  4. Check Second Choice: Now, let's check each answer choice to see which one equals 656\frac{65}{6} when simplified.\newlineStart with the first choice: −3(23)−7(16)-3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)\newlineConvert to improper fractions.\newline−3(23)=−(93+23)=−113-3\left(\frac{2}{3}\right) = -\left(\frac{9}{3} + \frac{2}{3}\right) = -\frac{11}{3}\newline−7(16)=−(426+16)=−436-7\left(\frac{1}{6}\right) = -\left(\frac{42}{6} + \frac{1}{6}\right) = -\frac{43}{6}
  5. Check Third Choice: Now, subtract the two improper fractions.\newlineTo subtract fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert −113-\frac{11}{3} to a fraction with a denominator of 66.\newline−113=(−11×2)/(3×2)=−226-\frac{11}{3} = \left(-11\times 2\right) / \left(3\times 2\right) = -\frac{22}{6}
  6. Check Fourth Choice: Subtract the two fractions with the common denominator.\newline−226−436=−22−436=−656-\frac{22}{6} - \frac{43}{6} = \frac{-22 - 43}{6} = -\frac{65}{6}\newlineThis is the negative of our original sum, so this choice is incorrect.
  7. Check Fourth Choice: Subtract the two fractions with the common denominator.\newline−226−436=(−22−43)6=−656-\frac{22}{6} - \frac{43}{6} = \frac{(-22 - 43)}{6} = -\frac{65}{6}\newlineThis is the negative of our original sum, so this choice is incorrect.Check the second choice: 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)\newlineConvert to improper fractions.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}\newline7(16)=(426+16)=4367\left(\frac{1}{6}\right) = \left(\frac{42}{6} + \frac{1}{6}\right) = \frac{43}{6}
  8. Check Fourth Choice: Subtract the two fractions with the common denominator.\newline−226−436=(−22−43)6=−656-\frac{22}{6} - \frac{43}{6} = \frac{(-22 - 43)}{6} = -\frac{65}{6}\newlineThis is the negative of our original sum, so this choice is incorrect.Check the second choice: 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)\newlineConvert to improper fractions.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}\newline7(16)=(426+16)=4367\left(\frac{1}{6}\right) = \left(\frac{42}{6} + \frac{1}{6}\right) = \frac{43}{6}Now, subtract the two improper fractions.\newlineTo subtract fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert 113\frac{11}{3} to a fraction with a denominator of 66.\newline113=(11×23×2)=226\frac{11}{3} = \left(\frac{11\times2}{3\times2}\right) = \frac{22}{6}
  9. Check Fourth Choice: Subtract the two fractions with the common denominator.\newline−226−436=(−22−43)6=−656-\frac{22}{6} - \frac{43}{6} = \frac{(-22 - 43)}{6} = -\frac{65}{6}\newlineThis is the negative of our original sum, so this choice is incorrect.Check the second choice: 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)\newlineConvert to improper fractions.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}\newline7(16)=(426+16)=4367\left(\frac{1}{6}\right) = \left(\frac{42}{6} + \frac{1}{6}\right) = \frac{43}{6}Now, subtract the two improper fractions.\newlineTo subtract fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert 113\frac{11}{3} to a fraction with a denominator of 66.\newline113=(11×23×2)=226\frac{11}{3} = \left(\frac{11\times2}{3\times2}\right) = \frac{22}{6}Subtract the two fractions with the common denominator.\newline3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)00\newlineThis does not equal 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)11, so this choice is incorrect.
  10. Check Fourth Choice: Subtract the two fractions with the common denominator.\newline−226−436=(−22−43)6=−656-\frac{22}{6} - \frac{43}{6} = \frac{(-22 - 43)}{6} = -\frac{65}{6}\newlineThis is the negative of our original sum, so this choice is incorrect.Check the second choice: 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)\newlineConvert to improper fractions.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}\newline7(16)=(426+16)=4367\left(\frac{1}{6}\right) = \left(\frac{42}{6} + \frac{1}{6}\right) = \frac{43}{6}Now, subtract the two improper fractions.\newlineTo subtract fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert 113\frac{11}{3} to a fraction with a denominator of 66.\newline113=(11×23×2)=226\frac{11}{3} = \left(\frac{11\times2}{3\times2}\right) = \frac{22}{6}Subtract the two fractions with the common denominator.\newline3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)00\newlineThis does not equal 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)11, so this choice is incorrect.Check the third choice: 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)22\newlineConvert to improper fractions.\newline7(16)=(426+16)=4367\left(\frac{1}{6}\right) = \left(\frac{42}{6} + \frac{1}{6}\right) = \frac{43}{6}\newline3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)44
  11. Check Fourth Choice: Subtract the two fractions with the common denominator.\newline−226−436=(−22−43)6=−656-\frac{22}{6} - \frac{43}{6} = \frac{(-22 - 43)}{6} = -\frac{65}{6}\newlineThis is the negative of our original sum, so this choice is incorrect.Check the second choice: 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)\newlineConvert to improper fractions.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}\newline7(16)=(426+16)=4367\left(\frac{1}{6}\right) = \left(\frac{42}{6} + \frac{1}{6}\right) = \frac{43}{6}Now, subtract the two improper fractions.\newlineTo subtract fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert 113\frac{11}{3} to a fraction with a denominator of 66.\newline113=(11×23×2)=226\frac{11}{3} = \left(\frac{11\times2}{3\times2}\right) = \frac{22}{6}Subtract the two fractions with the common denominator.\newline226−436=(22−436)=−216\frac{22}{6} - \frac{43}{6} = \left(\frac{22 - 43}{6}\right) = -\frac{21}{6}\newlineThis does not equal 65/665/6, so this choice is incorrect.Check the third choice: 7(16)−(−3(23))7\left(\frac{1}{6}\right)-(-3\left(\frac{2}{3}\right))\newlineConvert to improper fractions.\newline7(16)=(426+16)=4367\left(\frac{1}{6}\right) = \left(\frac{42}{6} + \frac{1}{6}\right) = \frac{43}{6}\newline3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)00Now, subtract the two improper fractions.\newlineTo subtract fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)11 to a fraction with a denominator of 66.\newline3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)22
  12. Check Fourth Choice: Subtract the two fractions with the common denominator.\newline−226−436=(−22−43)6=−656-\frac{22}{6} - \frac{43}{6} = \frac{(-22 - 43)}{6} = -\frac{65}{6}\newlineThis is the negative of our original sum, so this choice is incorrect.Check the second choice: 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)\newlineConvert to improper fractions.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}\newline7(16)=(426+16)=4367\left(\frac{1}{6}\right) = \left(\frac{42}{6} + \frac{1}{6}\right) = \frac{43}{6}Now, subtract the two improper fractions.\newlineTo subtract fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert 113\frac{11}{3} to a fraction with a denominator of 66.\newline113=(11×23×2)=226\frac{11}{3} = \left(\frac{11\times2}{3\times2}\right) = \frac{22}{6}Subtract the two fractions with the common denominator.\newline3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)00\newlineThis does not equal 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)11, so this choice is incorrect.Check the third choice: 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)22\newlineConvert to improper fractions.\newline7(16)=(426+16)=4367\left(\frac{1}{6}\right) = \left(\frac{42}{6} + \frac{1}{6}\right) = \frac{43}{6}\newline3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)44Now, subtract the two improper fractions.\newlineTo subtract fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)88 to a fraction with a denominator of 66.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}00Subtract the two fractions with the common denominator.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}11\newlineThis equals our original sum, so this choice is correct.
  13. Check Fourth Choice: Subtract the two fractions with the common denominator.\newline−226−436=(−22−43)6=−656-\frac{22}{6} - \frac{43}{6} = \frac{(-22 - 43)}{6} = -\frac{65}{6}\newlineThis is the negative of our original sum, so this choice is incorrect.Check the second choice: 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)\newlineConvert to improper fractions.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}\newline7(16)=(426+16)=4367\left(\frac{1}{6}\right) = \left(\frac{42}{6} + \frac{1}{6}\right) = \frac{43}{6}Now, subtract the two improper fractions.\newlineTo subtract fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert 113\frac{11}{3} to a fraction with a denominator of 66.\newline113=11×23×2=226\frac{11}{3} = \frac{11\times2}{3\times2} = \frac{22}{6}Subtract the two fractions with the common denominator.\newline3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)00\newlineThis does not equal 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)11, so this choice is incorrect.Check the third choice: 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)22\newlineConvert to improper fractions.\newline7(16)=(426+16)=4367\left(\frac{1}{6}\right) = \left(\frac{42}{6} + \frac{1}{6}\right) = \frac{43}{6}\newline3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)44Now, subtract the two improper fractions.\newlineTo subtract fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)88 to a fraction with a denominator of 66.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}00Subtract the two fractions with the common denominator.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}11\newlineThis equals our original sum, so this choice is correct.Check the fourth choice: 3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}22\newlineConvert to improper fractions.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}44
  14. Check Fourth Choice: Subtract the two fractions with the common denominator.\newline−226−436=(−22−43)6=−656-\frac{22}{6} - \frac{43}{6} = \frac{(-22 - 43)}{6} = -\frac{65}{6}\newlineThis is the negative of our original sum, so this choice is incorrect.Check the second choice: 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)\newlineConvert to improper fractions.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}\newline7(16)=(426+16)=4367\left(\frac{1}{6}\right) = \left(\frac{42}{6} + \frac{1}{6}\right) = \frac{43}{6}Now, subtract the two improper fractions.\newlineTo subtract fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert 113\frac{11}{3} to a fraction with a denominator of 66.\newline113=(11×23×2)=226\frac{11}{3} = \left(\frac{11\times2}{3\times2}\right) = \frac{22}{6}Subtract the two fractions with the common denominator.\newline3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)00\newlineThis does not equal 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)11, so this choice is incorrect.Check the third choice: 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)22\newlineConvert to improper fractions.\newline7(16)=(426+16)=4367\left(\frac{1}{6}\right) = \left(\frac{42}{6} + \frac{1}{6}\right) = \frac{43}{6}\newline3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)44Now, subtract the two improper fractions.\newlineTo subtract fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)88 to a fraction with a denominator of 66.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}00Subtract the two fractions with the common denominator.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}11\newlineThis equals our original sum, so this choice is correct.Check the fourth choice: 3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}22\newlineConvert to improper fractions.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}44Now, add the two improper fractions.\newlineTo add fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert 113\frac{11}{3} to a fraction with a denominator of 66.\newline113=(11×23×2)=226\frac{11}{3} = \left(\frac{11\times2}{3\times2}\right) = \frac{22}{6}
  15. Check Fourth Choice: Subtract the two fractions with the common denominator.\newline−226−436=(−22−43)6=−656-\frac{22}{6} - \frac{43}{6} = \frac{(-22 - 43)}{6} = -\frac{65}{6}\newlineThis is the negative of our original sum, so this choice is incorrect.Check the second choice: 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)\newlineConvert to improper fractions.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}\newline7(16)=(426+16)=4367\left(\frac{1}{6}\right) = \left(\frac{42}{6} + \frac{1}{6}\right) = \frac{43}{6}Now, subtract the two improper fractions.\newlineTo subtract fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert 113\frac{11}{3} to a fraction with a denominator of 66.\newline113=(11×23×2)=226\frac{11}{3} = \left(\frac{11\times2}{3\times2}\right) = \frac{22}{6}Subtract the two fractions with the common denominator.\newline3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)00\newlineThis does not equal 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)11, so this choice is incorrect.Check the third choice: 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)22\newlineConvert to improper fractions.\newline7(16)=(426+16)=4367\left(\frac{1}{6}\right) = \left(\frac{42}{6} + \frac{1}{6}\right) = \frac{43}{6}\newline3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)44Now, subtract the two improper fractions.\newlineTo subtract fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)88 to a fraction with a denominator of 66.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}00Subtract the two fractions with the common denominator.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}11\newlineThis equals our original sum, so this choice is correct.Check the fourth choice: 3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}22\newlineConvert to improper fractions.\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}\newline3(23)=(93+23)=1133\left(\frac{2}{3}\right) = \left(\frac{9}{3} + \frac{2}{3}\right) = \frac{11}{3}44Now, add the two improper fractions.\newlineTo add fractions, find a common denominator.\newlineThe least common multiple of 66 and 33 is 66.\newlineConvert 113\frac{11}{3} to a fraction with a denominator of 66.\newline113=(11×23×2)=226\frac{11}{3} = \left(\frac{11\times2}{3\times2}\right) = \frac{22}{6}Add the two fractions with the common denominator.\newline7(16)=(426+16)=4367\left(\frac{1}{6}\right) = \left(\frac{42}{6} + \frac{1}{6}\right) = \frac{43}{6}11\newlineThis does not equal 3(23)−7(16)3\left(\frac{2}{3}\right)-7\left(\frac{1}{6}\right)11, so this choice is incorrect.

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