Final answer:
To determine the missing fractions, we apply knowledge of multiplication and division. A fraction greater than 1/3 multiplied by 11 will result in a number greater than 11. A fraction less than 8/8 multiplied by 5 will yield a number less than 5, and for the last equation, the denominator must be 2 for 6×2/_ to equal 6.
Step-by-step explanation:
To solve the problems _/3×11 > 11, 5×_/8 < 5, and 6×2/_ = 6, let's apply some basic knowledge about multiplication and division of fractions and whole numbers.
For the first inequality _/3×11 > 11, we need to find a fraction that when multiplied by 11 results in a number greater than 11. Since multiplying by 1 would give us 11, the fraction must be greater than 1/3. An example of such a fraction could be 4/3, because 4/3×11 = 44/3, which is greater than 11.
For the second inequality 5×_/8 < 5, we are looking for a fraction that when multiplied by 5 results in a number less than 5. Since multiplying by 1 (or 8/8) would yield 5, the fraction must be less than 8/8. A fraction like 3/8 works because 5×3/8 = 15/8, which is less than 5.
Lastly, for the equation 6×2/_ = 6, we want to find the denominator of a fraction that will make the statement true. By simplifying 6 on both sides, we find that 2/_ must be equal to 1, and thus the denominator should be 2 since 2/2 equals 1.
These problems illustrate how intuition about basic multiplication and division can guide us in identifying the missing numerator or denominator to make given mathematical sentences true.