Joey walked away from home for 21/34 meters. Then, he walked back in the direction of his home for 15/23 meters. How far was Joey from home? Write your answer as a mixed number.

Answer 1

To determine Joey's distance from home, we need to find the difference between the distances he walked away from home and the distance he walked back towards home.

1. First, let’s denote Joey's distances:

   • Distance walked away from home: $\frac{21}{34}$ meters
   • Distance walked back towards home: $\frac{15}{23}$ meters

2. To find out how far he is from home, we need to compute: $$\text{Distance from home}=\frac{21}{34}-\frac{15}{23}$$

3. To subtract these fractions, we first find a common denominator. The denominators are 34 and 23. The least common multiple (LCM) of 34 and 23 is $34\times 23=782$.

4. Now we convert each fraction to have this common denominator:

   • For $\frac{21}{34}$: $$\frac{21}{34}=\frac{21\times 23}{34\times 23}=\frac{483}{782}$$
   • For $\frac{15}{23}$: $$\frac{15}{23}=\frac{15\times 34}{23\times 34}=\frac{510}{782}$$

5. Now we can perform the subtraction: $$\frac{21}{34}-\frac{15}{23}=\frac{483}{782}-\frac{510}{782}=\frac{483-510}{782}=\frac{-27}{782}$$

Since the result is negative, this indicates that Joey walked back more than he walked away from home:

6. Compute the absolute value to find the distance from home: $$\left|\frac{-27}{782}\right|=\frac{27}{782}$$

7. Now we convert $\frac{27}{782}$ into a mixed number.

   • 27 is less than 782, so it is already a proper fraction. The mixed number representation is simply $0\frac{27}{782}$.

Hence, as a mixed number, Joey is $\frac{27}{782}$ meters from home.

Final answer: $$\frac{27}{782}$$