Dividing Fractions Cheat Sheet

Division as 'How many groups?'

Dividing by a fraction asks how many of that fraction fit into the number you're dividing.

Example: 6 ÷ (1/2) asks: How many halves are in 6? Answer: 12

Reciprocal

The reciprocal of a fraction is found by swapping the numerator and denominator. The product of a number and its reciprocal is always 1.

Example: The reciprocal of 2/3 is 3/2. (2/3) * (3/2) = 1

Dividing by a Whole Number

Dividing a fraction by a whole number is the same as multiplying the denominator by that whole number.

Example: (1/4) ÷ 2 = 1/(4*2) = 1/8

Keep

Keep the first fraction as it is.

Example: In (1/2) ÷ (3/4), keep 1/2.

Change

Change the division sign (÷) to a multiplication sign (×).

Example: Change (1/2) ÷ (3/4) to (1/2) × (3/4).

Flip

Flip the second fraction (find its reciprocal).

Example: Flip 3/4 to 4/3. Now we have (1/2) × (4/3).

Multiply

Multiply the numerators and the denominators.

Example: (1/2) × (4/3) = (1*4)/(2*3) = 4/6

Simplify

Simplify the resulting fraction to its lowest terms.

Example: 4/6 simplifies to 2/3.

Convert to Improper Fractions

First, convert any mixed numbers to improper fractions.

Example: 2 1/2 = (2*2 + 1)/2 = 5/2

Apply 'Keep, Change, Flip'

Then, use the 'Keep, Change, Flip' method as described above.

Example: 2 1/2 ÷ 1/4 becomes 5/2 ÷ 1/4, then 5/2 * 4/1 = 20/2 = 10