AI Tutor
Imagine you have 3123\frac{1}{2} cups of flour, and each mini cake recipe needs 1161\frac{1}{6} cups. How many mini cakes can you bake?
To find out, we need to divide one mixed number by another: 312÷1163\frac{1}{2} \div 1\frac{1}{6}.

Step 1: Change to Improper Fractions

You cannot divide mixed numbers directly by dividing the whole numbers and the fractions separately. First, convert both mixed numbers into improper fractions, which are fractions where the top number is equal to or greater than the bottom number.
Now our problem looks like regular fraction division: 72÷76\frac{7}{2} \div \frac{7}{6}. How do we divide fractions again?

Step 2: Multiply by the Reciprocal

Dividing by a fraction is the same as multiplying by its reciprocal, which is the fraction flipped upside down. The reciprocal of 76\frac{7}{6} is 67\frac{6}{7}.
So 312÷116=33\frac{1}{2} \div 1\frac{1}{6} = 3. You can make exactly 33 complete mini cakes.
What happens if the answer does not divide evenly into a whole number? Let's look at another example.

Worked Example: Fraction Quotients

Let's solve 223÷1142\frac{2}{3} \div 1\frac{1}{4} step by step.