Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for 6th grade dividing fractions? Then this Grade 6 lesson on Dividing Fractions with Models and Reciprocals explains each idea step by step, with worked examples.
Quick answer: To divide by a fraction, multiply by its reciprocal, which is the fraction flipped over. Fraction division answers how many groups fit or how big one group is. Visual models show why it works, and mixed numbers become improper fractions before dividing.
Standards: 6.NS.A.1 · Level: Grade 6
What does it mean to divide by a fraction?
Dividing asks how many groups fit, or how big one group is. In 3 ÷ 14, the question is how many quarter-cup scoops fit into 3 cups.
Each cup holds 4 quarters, so 3 cups hold 3 × 4 = 12 quarters. Dividing by 14 gave the same result as multiplying by 4.
What is a reciprocal?
Two numbers are reciprocals when their product is 1. Swap the numerator and denominator: the reciprocal of 34 is 43, and the reciprocal of 5 (which is 51) is 15.
How do you divide one fraction by another?
To divide by a fraction, multiply by its reciprocal.
ab ÷ cd = ab × dc
- Rewrite any mixed numbers or whole numbers as fractions.
- Keep the first fraction and flip the second.
- Multiply, then simplify.
- Check by multiplying the answer by the divisor.
Find 23 ÷ 45.
23 × 54 = 1012 = 56.
How do you divide mixed numbers?
Change each mixed number to an improper fraction first. For 2 12 ÷ 34, write 52 × 43 = 206 = 3 13.
Dividing a whole number by a fraction below 1 gives a larger number, because many small groups fit. This is the opposite of dividing by a whole number, which makes the result smaller. A quick estimate before you calculate catches most flipping errors.
What are the two kinds of word problems?
In a how-many-groups problem you know the size of each group and want the number of groups, such as the number of scoops in a bag of rice. In a how-much-in-one-group problem you know the number of groups and want the size of one, such as the share of pizza each friend gets. Both are divisions, and a picture or tape diagram shows which is which.
Flipping the wrong fraction. Only the divisor (the second fraction) is flipped. Writing 23 ÷ 14 as 32 × 14 gives the wrong answer.
Make a quick estimate: dividing by a fraction less than 1 must give a bigger number than you started with.
- Reciprocals multiply to 1: 3/4 and 4/3.
- a/b ÷ c/d = a/b × d/c.
- Dividing by a fraction less than 1 gives a larger number.
- Turn mixed numbers into improper fractions first.
- Check a quotient by multiplying it by the divisor.
Dividing Fractions with Models and Reciprocals: frequently asked questions
What is a reciprocal?
A reciprocal is the number that multiplies with another to make 1. You find it by swapping the numerator and denominator, so the reciprocal of 3/4 is 4/3.
Why does dividing by a fraction make the answer bigger?
A fraction less than 1 is a small group, so many of those groups fit into the amount. In 3 ÷ 1/4 there are 12 quarter-cup scoops in 3 cups.
How do you divide mixed numbers?
Write each mixed number as an improper fraction, flip the second one, and multiply. Then simplify and, if needed, write the answer as a mixed number.
How do you divide a fraction by a whole number?
Write the whole number as a fraction over 1 and multiply by its reciprocal. For example, 3/4 ÷ 6 = 3/4 × 1/6 = 1/8.
How can you check a fraction division answer?
Multiply the quotient by the divisor. If 2/3 ÷ 4/5 = 5/6, then 5/6 × 4/5 must equal 2/3.