Final answer:
To solve for what 4/9 divided by equals 12, you multiply 12 by the reciprocal of 4/9. This gives you the answer that 4/9 divided by 27 equals 12.
Step-by-step explanation:
To find what number 4/9 should be divided by to equal 12, you would set up an equation as follows:
4/9 ÷ x = 12.
To solve this equation, you need to take the reciprocal of 12 and multiply it by 4/9. This is because dividing by a number is the same as multiplying by its reciprocal.
The reciprocal of 12 is 1/12. So you would multiply:
(4/9) × (1/12)
This would give you the reciprocal of the unknown number x that when 4/9 is divided by, would result in 12:
x = (4/9) ÷ 12
Therefore, we need to multiply both sides of the equation by 12 to get rid of the fraction on the left side:
x × 12 = (4/9)
Now, we divide both sides of the equation by the 4/9 to isolate x on one side:
x = 12 ÷ (4/9)
Finally, multiplying 12 by the reciprocal of 4/9:
x = 12 × (9/4)
x = 27
So, 4/9 must be divided by 27 to equal 12.