What is 6 divided by 1/5 1/5 as a FRACTION
The Correct Answer and Explanation is:
Answer (as a fraction): 30 ⁄ 1
Dividing a whole number by a fraction may feel counter-intuitive at first, because the operation literally asks “how many copies of that fraction fit into the whole?” In our problem we are asked to divide 6 by 1⁄5. In fractional notation that is 6 ÷ 1⁄5. A reliable way to work with division by fractions is to rewrite the division as multiplication by the reciprocal. The reciprocal of a non-zero fraction is obtained by swapping its numerator and denominator—so the reciprocal of 1⁄5 is 5⁄1.
Multiplying a whole number by a fraction is straightforward: multiply the whole number by the numerator and keep the denominator unchanged. Here that gives (6 × 5) ⁄ 1 = 30 ⁄ 1. A fraction with denominator 1 equals its numerator, so the simplified answer is 30. Expressed strictly as a fraction, 30 is written 30 ⁄ 1.
Why does this reciprocal rule work? Division asks for the factor that turns the divisor into the dividend. If x ÷ y = z, then z × y must equal x. Replacing y with 1⁄5, we want a number that multiplied by 1⁄5 yields 6. Since 1⁄5 of 30 is indeed 6 (because 30 × 1⁄5 = 30⁄5 = 6), we know 30 is the correct quotient.
In everyday terms, slicing something into fifths makes each piece five times smaller; consequently it takes five of those pieces to reconstitute one original unit. Six originals therefore contain 6 × 5 = 30 such pieces. Visually, you could lay out thirty identical 1⁄5-length bars end to end and see them align perfectly with six full-length bars.
Stated differently, thirty is the exact count of one-fifth units within six, altogether. This alignment between arithmetic and geometry reinforces the reciprocal principle. Hence, dividing by a fraction enlarges the result instead of shrinking unexpectedly.
