Fractions Division: Simple Fractions

Dividing simple fractions is easy. All we have to do is flip (turn over) the second fraction (called the multiplier, as you learned in Basic Multiplication, Lesson 13) and then multiply the two numerators and the two denominators. However, what are we doing when we do this?

Our first example is: 1/2 ÷ 1/4:

1 / 2
White Box  plus     White Box  equals     White Box   White Box   White Box

What does this mean? How many times does 1/4 go into 1/2? How many sections of 1/4 are there in one section of 1/2?

White Box  plus     White Box  equals     White Box   White Box   White Box

As you see, the answer is 2. The equation is:

1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2.

1 times 4 is 4. The numerator is 4. 2 times 1 is 2. The denominator is 2, and the resulting fraction, 4/2 reduces to 2.
We see that there are two sections of 1/4 in one section 1/2.

Here is another example: 2/3 ÷ 1/6:

2 / 3

What does this mean? How many times does 1/6 go into 2/3? How many sections of 1/6 are there in one section of 2/3?

White Box   White Box  plus     White Box   White Box  equals     White Box   White Box   White Box   White Box   White Box

As you see, the answer is 4. The equation is:

2/3 ÷ 1/6 = 2/3 × 6/1 = 12/3 = 4.

2 times 6 is 12. The numerator is 12. 3 times 1 is 3. The denominator is 3, and the resulting fraction, 12/3 reduces to 4.
We see that there are four sections of 1/6 in one section of 2/3.

In this unit Fractions Division, you are required to enter all answers in reduced form. For example, an answer of 4/6 would be incorrect: you are required to enter 2/3.