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Avi and Micah are teammates on a track and field team. Avi's best long jump is 1(1)/(6) times as long as Micah's. Avi's best long jump is 3(1)/(2) meters. How long is Micah's best long jump? meters

Avi and Micah are teammates on a track and field team. Avi's best long jump is 116 1 \frac{1}{6} times as long as Micah's. Avi's best long jump is 312 3 \frac{1}{2} meters.\newlineHow long is Micah's best long jump?\newlinemeters

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Q. Avi and Micah are teammates on a track and field team. Avi's best long jump is 116 1 \frac{1}{6} times as long as Micah's. Avi's best long jump is 312 3 \frac{1}{2} meters.\newlineHow long is Micah's best long jump?\newlinemeters
  1. Understand Relationship: Understand the relationship between Avi's and Micah's long jumps. Avi's best long jump is 1161\frac{1}{6} times as long as Micah's. This means that to find Micah's best long jump, we need to divide Avi's best long jump by 1161\frac{1}{6}.
  2. Convert to Improper Fraction: Convert the mixed number 1(16)1\left(\frac{1}{6}\right) to an improper fraction to make the division easier.\newline1(16)=(66+16)=761\left(\frac{1}{6}\right) = \left(\frac{6}{6} + \frac{1}{6}\right) = \frac{7}{6}\newlineNow we can express the relationship as Avi's long jump = (76)×\left(\frac{7}{6}\right) \times Micah's long jump.
  3. Write Avi's Length: Write down Avi's best long jump length. Avi's best long jump is 3(12)3\left(\frac{1}{2}\right) meters.
  4. Convert to Improper Fraction: Convert Avi's mixed number 3(12)3\left(\frac{1}{2}\right) to an improper fraction.\newline3(12)=(62+12)=723\left(\frac{1}{2}\right) = \left(\frac{6}{2} + \frac{1}{2}\right) = \frac{7}{2} meters
  5. Set Up Equation: Set up the equation to find Micah's best long jump.\newlineLet Micah's best long jump be xx meters. According to the relationship, we have:\newline72=(76)×x\frac{7}{2} = \left(\frac{7}{6}\right) \times x
  6. Solve for x: Solve for x by dividing both sides of the equation by (76)(\frac{7}{6}).\newlinex=7276x = \frac{\frac{7}{2}}{\frac{7}{6}}
  7. Perform Division: Perform the division by multiplying by the reciprocal of (76)(\frac{7}{6}).\newlinex=(72)×(67)x = (\frac{7}{2}) \times (\frac{6}{7})
  8. Simplify Equation: Simplify the equation by canceling out the common factors.\newlinex=7×62×7x = \frac{7 \times 6}{2 \times 7}\newlineThe 77s cancel out, so we are left with:\newlinex=62x = \frac{6}{2}
  9. Calculate Final Value: Calculate the final value for Micah's best long jump. x=62=3x = \frac{6}{2} = 3 meters

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