Mixed Number Division Worksheets
When you first are required to divide or equally share two mixed number values it can be a bit overwhelming. Students will try to separate the whole number value and the fraction, but there is such an easier way to do this if we just remember that a mixed number is just a different representation of an improper fraction. So in order to process these operations we begin by converting the mixed number values to improper fractions. All you need to do is multiply the whole number by the denominator and add that value to the numerator. From there, when it comes to division, just follow the steps that we chart out for you in the lesson. Students learn how to divide top heavy fractions and mixed numbers in these worksheets and lessons.
Aligned Standard: 5.NF.B.7b
- Improper Fraction Quotients Step-by-Step Lesson- We present students with improper fractions instead of mixed numbers to get them comfortable.
- Guided Lesson - We start to turn up the heat on number three.
- Guided Lesson Explanation - Make sure students understand reciprocals before walking into this task.
- Practice Worksheet - I mostly gave them the same denominators, and only in a few situations that doesn't hold true.
- Matching Worksheet - I actually saw a student do this one in under a minute. That impressed me!
- Answer Keys - These are for all the unlocked materials above.
The denominators are different. Don't let that trip you up on these.
- Homework 1 - Find the inverse of 8/4 by swapping the numerator and the denominator.
- Homework 2 - It's all about flipping the numbers here.
- Homework 3 - Watch out for those zeroes.
I would highly recommend that you have students reduce the fractions, if possible.
- Practice 1 - Multiply the numerators. Then, multiply the denominators.
- Practice 2 - 5/1 ÷ 8/3
- Practice 3 - See is the denominators make sense first.
Math Skill Quizzes
I kept all the denominators as close as possible to the factors to see if students would take the bait. The best way to learn is from your mistakes.
- Quiz 1 - These are some thick values.
- Quiz 2 - These are a bit odd.
- Quiz 3 - The denominators sit well with me.
How do you Divide Mixed Numbers?
The concept of division is the same; either you are dividing mixed numbers, proper fraction, improper fraction or whole numbers. The only difference that makes the division process a little bit complicated or different is that of the numbers that are being divided. The process of diving mixed numbers is very similar to that of multiplying them. Let’s explore this concept and look at the steps you need to follow to divide a mixed number.
When we are working with mixed numbers, we have to realize that they are just converted improper fractions. By this time, we are very confident with our fractional operations. So, why don’t we just convert them back to fractions and go that route. Change the mixed number you have into an improper fraction (top heavy). You next step is to convert this to a workable problem by finding the reciprocal of the divisor (second fraction) and then multiply. You can then simplify it if there is a need. Make sure to give the answers in the lowest terms. Cross-check to make sure that the answers make sense.
The following example will make it easier for you to learn the operation.
Example: 30 divided by 1 1/2.
1) Convert the Mixed Number to an Improper Fraction - This is 30 divided by 3/2.
2) Take the Reciprocal of the Divisor - The divisor is fraction (3/2). The reciprocal just means that we replace the numerator with the denominator and the denominator with the numerator. They just switch places. So the reciprocal of 3/2 is 2/3.
3) Make it a Multiplication Problem - So the math would appear as: 30/1 (2/3). We multiply the numerators (30 x 2 = 60) and the denominators (1 x 3 = 3). So this product is 60/3.
4) Reduce the Fraction - They both have a common multiple of 3. So, if we divide them evenly into the numerator and denominator we will be left with: 60/3 = 20/1 or 20.