Final answer:
Joe ate 5/9 of the whole pizza for lunch after consuming 2/3 of the 5/6 that was remaining.
Step-by-step explanation:
The student asked how much of the whole pizza Joe had for lunch if he ate 2/3 of the 5/6 of a pizza that was left over. To find the fraction of the whole pizza that Joe ate for lunch, we multiply the two fractions: 5/6 × 2/3. Multiplying the numerators together (5 × 2) gives us 10, and multiplying the denominators together (6 × 3) gives us 18. Simplifying the resulting fraction (10/18) by dividing both the numerator and denominator by their greatest common divisor, which is 2, we get 5/9. Therefore, Joe had 5/9 of the whole pizza for lunch.