Final answer:
The values of a, b, and c that complete the division one-sixth divided by three-fifths are a = 18, b = 5, and c = 18. This is found by multiplying one-sixth by the reciprocal of three-fifths, which is five-thirds, resulting in the fraction 5/18.
Step-by-step explanation:
The question asks to find the values of a, b, and c that complete the division equation One-sixth divided by three-fifths = StartFraction 1 Over a EndFraction times StartFraction b Over c EndFraction. To divide fractions, we actually multiply by the reciprocal of the divisor. Thus, the division of one-sixth by three-fifths is the same as multiplying one-sixth by the reciprocal of three-fifths, which is five-thirds. The multiplication yields the result:
When we multiply the numerators (1 x 5), we get 5, and when we multiply the denominators (6 x 3), we get 18. Therefore, the result of the division is:
To match the given format, we then have:
So the completed division equation is:
One-sixth divided by three-fifths = StartFraction 1 Over 18 EndFraction times StartFraction 5 Over 18 EndFraction.