Divide with Unit Fractions - Practice 2

Distinguish the number of equal-size groups from the size of an equal share.

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A unit fraction has numerator 1. A whole number divided by a unit fraction asks how many groups of that size fit. A unit fraction divided by a positive whole number shares that fraction equally. Keep the reference whole fixed. Check every result by multiplication. Never divide by zero.

Worked example

2 divided by 1/3 = 6 groups: each of two wholes contains three thirds. But 1/3 divided by 2 = 1/6 per share: split the third into two equal parts. Check: 6 x 1/3 = 2 and 2 x 1/6 = 1/3. The diagram shows these examples, not the questions.

Top: two same-sized wholes each have three equal pieces numbered one through six, showing 2 divided by 1/3 = 6 groups. Bottom: one whole has six equal pieces; the first two make one third and are numbered as two equal shares. Each share is one sixth, so 1/3 divided by 2 = 1/6. Practice questions use different amounts. — Group numbers distinguish equal groups. Each whole has the same size, even when partitioned differently.

Would you believe it?

Changing the unit can change the count without changing the amount: one whole contains two halves or four quarters. Division counts the groups named by its divisor. Check by multiplying the group count by the group size.

OpenStax: dividing fractions

Question 1 2 divided by 1/5 = ? 2/5 5/2 10

Question 2 1/3 divided by 4 = ? 1/12 4/3 1/7

Question 3 1/2 divided by 1 = ? 2 1/2 1

Question 4 Share 1/6 equally among 3 people. Each share is 1/__. What denominator fills the blank? Answer

Question 5 Can 1/4 divided by 0 have a defined number answer? Yes, the answer is zero Yes, the answer is four No, zero times any number cannot give 1/4

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