How to Teach Dividing Fractions with Common Denominators in 6th Grade (Part 2)
Now that we established using common denominators to divide fractions from Part 1, we can jump into trickier problems. Here’s how I use the same strategy for answers with leftovers, mixed numbers, and whole numbers.
Quick refresher on the Part 1 and the steps:
- Find common denominators.
- Divide the numerators.
- Simplify if you need to.
What happens when the numerators don’t divide evenly?
This is where I slow down. Take 2/3 ÷ 1/4.
- Rename: 8/12 ÷ 3/12
- Divide the numerators: 8 ÷ 3 or 2 2/3
Then I ask, “How many groups of 3 twelfths fit into 8 twelfths?” Two full groups, with 2 twelfths left over. Those 2 leftover pieces are 2/3 of another group of 3. So, the answer is 2 2/3.
I pull the graph paper back out for this one. Shade 8 out of 12, circle groups of 3, and students can actually see the leftover piece.
How do students divide mixed numbers?
In order to divide mixed numbers, the mixed numbers become improper fractions (or fractions greater than one) first! Then, you can continue with the same 3 steps.
- Make mixed numbers into improper fractions.
- Find a common denominator.
- Divide the numerators.
- Simplify if needed.
2 1/2 ÷ 3/4
- Convert: 2 1/2 = 5/2
- Rename: 10/4 ÷ 3/4
- Divide the numerators 10 ÷ 3 = 3 1/3
What about whole numbers?
This will be the same. All whole numbers can be written with a denominator of 1. Once it has that denominator, you can use it to find a common denominator and complete the steps the same way.
Did you miss Part 1?
In Part 1, I show you how to introduce division with a model. It is worth a read! Click HERE to check out Part 1.
Ready to try it??
Grab some graph paper and get started!
Then, you can follow it up with my FRACTION DIVISION resources for some practice!
What mistakes should I watch for when students divide fractions?
Why do my students get stuck on mixed numbers?
They try to rename 2 1/2 without making it an improper fraction first. I keep the rule simple: convert first, every time.
What if they keep the same denominator?
This one is so common because it’s exactly what they do when adding and subtracting. They’ll write 6/8 ÷ 2/8 = 3/8. I ask, “How many 2/8s fit in 6/8?” Three. Three groups, not three eighths. The answer counts how many groups fit, so there’s no denominator to keep. A quick reasonableness check helps too: 3/8 is less than one group, and three whole groups clearly fit. If students want the math behind it, the denominators divide too, and 8 ÷ 8 = 1.
What do students need to know first?
Equivalent fractions, finding common denominators, and division are the prerequisite skills.
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