Whole Number and Mixed Number Operations Worksheets
Math operations between values that are in combination of mixed number and whole number format happen all the time in situations where the old fashion Imperial system of measurement is being used. You will find this commonly in situations that involve construction. Standard U.S. tape measures are delineated in one-sixteenth inch increments. For a long time, financial institutions also subscribed to use this form of measure as well. Interest rates and stock quotes used to be presented as mixed numbers or fractions. While that form of math is not impossible, it is more time consuming. We will tackle this form of math on this topic. These worksheets show you how to perform all four main math operations between whole numbers and mixed numbers.
Aligned Standard: 5.NF.A.1, 5.NF.B.6
- Add / Subtract Whole Numbers and Mixed Numbers Lesson- Start with the easier operations to explain and understand.
- Multiplying and Dividing Lesson- Division is a bit tough for this level. Make sure to review it before attempting these problems.
- Guided Lesson - The problems include addition, subtraction, and division.
- Guided Lesson Explanation - Don't forget to review converting mixed number to improper fractions.
- Practice Worksheet 1 - Find the missing value of the denominators in each sum problem.
- Subtraction Worksheet 1- All the problems involve subtraction between and variety of situations.
- Answer Keys - These are for all the unlocked materials above.
Addition and Subtraction Practice Sheets
Some of the sheets work on algebra type problems.
- Addition 2 - These problems are asking you to add a whole number to a mixed number.
- Addition 3 - Missing Values - Use addition or find the missing number.
- Subtraction 2 - Write the missing values shown by the small boxes.
- Subtraction 3 - Lost Values - Subtract or write the missing numbers.
Division and Multiplication Worksheets
You might find these difficult at first, but they get easier as you practice.
- Division 1 - Start by converting all the values to fractions with the same denominator.
- Multiplication 1 - Multiply the fractions (numerators and denominators).
- Division 2 - Fill in the missing numbers.
- Multiplication 2 - Write the missing numbers.
- Division 3 - Divide or fill in the missing numbers.
- Multiplication 3 - Multiply or write the missing numbers.
Basic Operations Between Mixed and Whole Numbers
Before we go full throttle with mixed numbers lets look at how they work in operations with whole numbers. Let’s get the easy stuff out of the way first. When you are adding values in these two formats together, you simply combine or add the whole number values. Here is an example:
5 ½ + 6 = 11 ½
Subtracting these types of values just requires you to remember that a whole number can be represented as a fractional value as well. You would just convert it to that format and proceed with the operation from there. Let’s look at two examples one where the whole number serves as the subtrahend and then where it serves as the minuend, which is more complicated:
As a subtrahend: 8 ¾ - 5 = 3 ¾
We simply subtract the whole values.
As a minuend: 6 - 2 ⅔.
Start by pulling out a fraction using the same denominator as the subtrahend. We therefore can rewrite the problem as:
5 3/3 - 2 ⅔
We can now clearly see that we can subtract the whole number and fractional values, as a result:
5 – 2 = 3 and 3/3 - ⅔ = ⅓. Or 3 ⅓
What About Multiplication?
There are several steps that you need to follow when performing this operation. Let’s take look by working on this problem:
Find the product of 4 ½ and 12.
Step #1: Convert the whole number to a fraction. To do this we just have to place it over 1. We would also convert the mixed value to an improper fraction by multiplying the whole value by denominator and adding it to the numerator.
9/2 x 12/1
Step #2: Multiply the numerators and while were at it, the denominators too.v
9/2 x 12/1
Numerators: 9 x 12 = 108
Denominators: 2 x 1 = 2
This leaves us with: 108/2 or 54 when we simplify it.
How Do You Divide Whole Numbers by Mixed Numbers?
This is a skill that you will use when working with recipes in your kitchen and it is often used in many sports by coaches that use analytics to determine the best player to use on their roster at certain stages of their season.
Dividing mixed numbers is similar to multiplying them. You need to add one more step into the mix. To divide two mixed numbers, i.e., 6 2/8 ÷ 3 5/9, you need to follow the steps below.
Step #1: Convert each number to an improper fraction. Example: You would convert those values by multiplying the whole number with the denominator and then adding that value to the numerator. In this case: 6 2/8 ÷ 3 5/9 would convert to: 50/8 ÷ 32/9.
Step #2: Invert the latter improper fraction and change the sign to multiplication. Example: 50/8 × 9/32
Step #3: Multiply the two numerators together. Example: 50 × 9 = 450
Step #4: Multiply the denominators together. Example: 8 × 32 = 256
Step #5: Convert the answer back to a mixed number. Example: 450/256 = 1 194/256
Step #6: You can further simplify the mixed number if possible. Example: 1 97/128.