Grade 6 Math · Topic 09
A fraction is in simplest form when its numerator and denominator share no common factor besides 1. To simplify, find the greatest common factor (GCF) and divide both numbers by it. A simplified fraction is easier to read, compare, and use.
Lesson alignment: 6.NS.B.4 (GCF prerequisite for fraction division) · Take your time. You can return to this lesson whenever you need it.
Explore visually
Compare the same amount in two bars and at the same point on a number line. Change the fraction and watch equivalent parts regroup.
Think first: If the denominator changes but the numerator stays fixed, how will the size of each part change?
Swipe horizontally to see the full diagram.
Turn on JavaScript to adjust this model. The examples and practice below work without it.
Read each step, then cover the explanation and see if you can explain why it works.
Worked example 1
List the factors so the greatest common factor is easy to see. Factors of 18: 1,2,3,6,9,18. Factors of 24: 1,2,3,4,6,8,12,24. The greatest common factor is 6. Divide both: 18 ÷ 6 = 3 and 24 ÷ 6 = 4. So 18/24 = 3/4.
Answer: 3/4
Worked example 2
Look for the biggest factor both numbers share. GCF of 45 and 60 is 15. Now divide: 45 ÷ 15 = 3 and 60 ÷ 15 = 4. So 45/60 = 3/4.
Answer: 3/4
Work these on paper first. Open “Check” when you are ready to compare your answer.
2/3
3/4
2/3
3/4
2/5
5/8
3/4
2/3
In a 6th-grade survey, 24 out of 36 students chose pizza as their favorite lunch. Write this as a fraction in simplest form.
Answer: 2/3.
Start by writing the calculation clearly: 24/36 has GCF 12. Now divide: 24 ÷ 12 = 2 and 36 ÷ 12 = 3.
A basketball player made 35 of 50 free throws. Write his shooting percentage as a fraction in simplest form.
Answer: 7/10.
Look for the biggest factor both numbers share. GCF of 35 and 50 is 5. 35 ÷ 5 = 7 and 50 ÷ 5 = 10.
Fresh questions · saved on this device
Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.
Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.
Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.
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