Dividing by a fraction
Master dividing whole numbers by fractions in Grade 6 math using the Keep, Change, Flip method — multiply by the reciprocal to turn division into multiplication and solve confidently.
Key Concepts
Property To divide a whole number by a fraction, first find how many parts of that fraction are in 1 (its reciprocal), then multiply that result by the whole number.
Examples To solve $8 \div \frac{2}{3}$: Step 1 is $1 \div \frac{2}{3} = \frac{3}{2}$. Step 2 is $8 \times \frac{3}{2} = 12$. To solve $10 \div \frac{1}{5}$: Step 1 is $1 \div \frac{1}{5} = 5$. Step 2 is $10 \times 5 = 50$. To solve $12 \div \frac{3}{8}$: Step 1 is $1 \div \frac{3}{8} = \frac{8}{3}$. Step 2 is $12 \times \frac{8}{3} = 32$.
Explanation Dividing by a fraction sounds scary, but it’s a two step trick! First, ask how many of the fraction fit into the number 1—this is just its reciprocal. Then, multiply that answer by the big number you started with. This turns a confusing division problem into a simple multiplication, making it way easier to find your answer and avoid a fraction induced headache.
Common Questions
Why do you flip the fraction when dividing?
When you divide by a fraction, flipping it gives you its reciprocal. Multiplying by the reciprocal is mathematically equivalent to dividing by the original fraction. For example, dividing by 2/3 is the same as multiplying by 3/2.
What is the Keep, Change, Flip method?
Keep the first number as-is, Change the division sign to multiplication, and Flip the second fraction to its reciprocal. For example, 8 divided by 2/3 becomes 8 times 3/2 which equals 12.
Why does dividing by a fraction sometimes give a bigger answer?
Dividing by a fraction less than 1 gives a larger result because you are asking how many small pieces fit into the whole. For instance, 4 divided by one-half equals 8, because 8 half-pieces fit into 4 whole units.
What common mistakes do students make when dividing fractions?
The most common mistake is multiplying without flipping the second fraction first. Always find the reciprocal of the divisor before multiplying. Another error is forgetting to simplify the final answer to lowest terms.