Home » Math Vocabulary » Simplify Mixed Numbers – Definition, Parts, Examples, FAQs
What is Simplify in Math?
Simplify means to make it simple. In mathematics, to simplify or simplification is to reduce the expression/fraction/problem in a simpler form. It makes the problem easy for calculations and solving.
Begin here
Make 10 Strategy
Add 1-Digit Numbers Game
Add 2-digit number to 1-digit
Add 2-Digit and 1-Digit Numbers Game
Regroup and add 2-digit numbers
Add 2-Digit Numbers By Regrouping Game
Add Three Whole Numbers
Add 3 Numbers Game
Add Three Whole Numbers
Add 3 Numbers in Any Order Game
Introduction to Addition
Add 3 Numbers Using Groups of Objects Game
Add Three Whole Numbers
Add 3 Numbers using Model Game
Add within 1000 without Regrouping
Add 3-Digit and 1-Digit Numbers and Match Game
Add 3-digit number to 1-digit
Add 3-Digit and 1-Digit Numbers Game
Add within 1000 with Regrouping
Add 3-Digit and 1-Digit Numbers with Regrouping Game
Mixed Numbers
A mixed number is a combination of a whole number, and a proper fraction. It generally represents a number between any two whole numbers.
Look at the given image, it represents a fraction that is greater than 1 but less than 2. It is thus a mixed number.
![Simplifying Mixed Numbers? Definition, Method, Calculation, Facts (12) Simplifying Mixed Numbers? Definition, Method, Calculation, Facts (12)](https://i0.wp.com/www.splashlearn.com/math-vocabulary/wp-content/uploads/2022/08/Simplify-mixed-numbers-1.png)
Some other examples of mixed numbers are:
![Simplifying Mixed Numbers? Definition, Method, Calculation, Facts (13) Simplifying Mixed Numbers? Definition, Method, Calculation, Facts (13)](https://i0.wp.com/www.splashlearn.com/math-vocabulary/wp-content/uploads/2022/08/Simplify-mixed-numbers-2.png)
Related Worksheets
Parts of a Mixed Number
A mixed number is formed by combining three parts: a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number.
![Simplifying Mixed Numbers? Definition, Method, Calculation, Facts (24) Simplifying Mixed Numbers? Definition, Method, Calculation, Facts (24)](https://i0.wp.com/www.splashlearn.com/math-vocabulary/wp-content/uploads/2022/08/Simplify-mixed-numbers-3.png)
Simplify Mixed Numbers
Simplify mixed numbers is to convert a mixed number into reduced form. A mixed number is said to be in its simplest form if the highest common factor, i.e., the HCF of its fractional part is 1.
On simplifying mixed numbers, the value of the fraction remains the same. We can say that the simplified mixed number and the actual mixed number are equivalent fractions.
Converting Mixed Numbers into Improper Fractions
Suppose the mixed number is $2\frac{1}{3}$.
Step 1: We will multiply the denominator with the whole number part.
Here, 3 × 2 = 6.
Step 2: We will add the numerator to the product obtained in step 1.
Here, 6 + 1 = 7.
Step 3: We will write the value obtained in step 2 over the denominator. This will be the new numerator while the denominator will remain the same.
Here, we get $\frac{7}{3}$.
How to Simplify Mixed Numbers Step by Step
Let the fraction be $9\frac{4}{8}$.
Step 1: We will look at the fractional part.
In this example, we will look at $\frac{4}{8}$ and will keep the whole part as it is.
The factors of 4 and 8 are
Factors of 4: 1, 2 and 4
Factors of 8: 1, 2, 4 and 8.
Step 2: Determine the highest common factors of numerator and denominator. The highest common factor of 4 and 8 is 4.
Step 3: Divide the numerator and denominator by the highest common factor. The fraction obtained by dividing is in the simplest form. Let’s divide by 4, then
$\frac{4 \div 4}{8 \div 4}$ = $\frac{1}{2}$.
Hence, the mixed number is $9\frac{1}{2}$.
Let the fraction be $4\frac{12}{15}$.
Step 1: The first step is to write the factors of numerator and denominator of the fractional part keeping the whole number aside.
The factors of 12 and 15 are
Factors of 12: 1, 2, 3, 4, 6 and 12.
Factors of 15: 1, 3, 5 and 15.
Step 2: The next step is to determine the HCF of the numerator and denominator. The greatest common factor of 12 and 15 is 3.
Step 3: The final step is to divide the numerator and denominator by the HCF. The fraction obtained after dividing is in the simplest form.
$\frac {12 \div 3}{15 \div 3}$ = $\frac{4}{5}$
Thus, we get $4 \frac{4}{5}$.
Solved Examples
Solution: Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24
Example 1: Simplify $2 \frac{24}{36}$.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18 and 36
HCF of 24 and 36 = 12
$\frac {24 \div 12}{36 \div 12}$ = $\frac{2}{3}$
So, $ 2 \frac{24}{36}$ = $2 \frac{2}{3}$
Example 2: Add: $ 1 \frac {4}{8} $ and $ 4 \frac {16}{32}$.
Solution: $ 1 \frac{4}{8}$
HCF (4, 8) = 4
$ \frac {4 \div 4}{8 \div 4} $= $ \frac {1}{2}$ , So we get $ 1 \frac{1}{2}$ = $ \frac{3}{2}$
$ 4 \frac {16}{32}$
HCF (16, 32) = 16
$ \frac {16 \div 16}{32 \div 16}$ = $ \frac {1}{2} $, So we get $ 4 \frac{16}{32} $ = $4 \frac{1}{2}$ = $ \frac {9}{2}$
$ \frac {3}{2}$ + $ \frac {9}{2}$ = $ \frac {3 + 9}{2}$ = $\frac{12}{2}$ = 6
Example 3: Write the mixed number for the following shaded part and simplify it.
![Simplifying Mixed Numbers? Definition, Method, Calculation, Facts (25) Simplifying Mixed Numbers? Definition, Method, Calculation, Facts (25)](https://i0.wp.com/www.splashlearn.com/math-vocabulary/wp-content/uploads/2022/08/Solved-Examples-3.png)
Solution: There are 3 whole shaded parts and the fraction shaded in fourth figure is $ \frac {2}{4}$.
So, the mixed number = $ 3 \frac {2}{4}$
HCF (2, 4) = 2 $ \frac {2 \div 2} {4 \div 2}$ = $ \frac {1}{2}$ , So we get $ 3 \frac{2}{4}$ = $ 3 \frac {1}{2}$
Practice Problem
1What should replace the blank? $7\frac{18}{30}$ ____ $7\frac{20}{25}$
$\gt$
$\lt$
=
None of these
CorrectIncorrect
Correct answer is: $\lt$
$7\frac{18}{30} = 7\frac{3}{5}$ and $7\frac{20}{25} = 7\frac{4}{5}$
On comparing $\frac{3}{5}$ and $\frac{4}{5}$, we get $\frac{3}{5}$ $\lt$ $\frac{4}{5}$
We get 7$\frac{18}{30}$ $\lt$ 7$\frac{20}{25}$
2What is the product of $10\frac{3}{6}$ by $1\frac{22}{33}$?
$ 12 \frac {1}{2}$
$ 17 \frac {2}{3}$
$ 17 \frac {1}{2}$
$ 15 \frac {2}{3}$
CorrectIncorrect
Correct answer is: $ 17 \frac {1}{2}$
$ 10 \frac {3}{6}$ = $ 10 \frac{1}{2}$ = $ \frac{21}{2}$
$ 1 \frac {22}{33}$ = $ 1 \frac{2}{3}$ = $ \frac{5}{3}$
$ \frac {21}{2} x {5}{3}$ = $ \frac{35}{2}$ = $ 17 \frac{1}{2}$
3Which of the following is not true for a mixed number?
It is also called mixed fraction.
It is always greater than 1.
It consists of a whole and a part.
None of these
CorrectIncorrect
Correct answer is: None of these
None of these
Frequently Asked Questions
Why do we use mixed numbers?
Mixed numbers are helpful when we count the whole things and parts of things together. For example, Jamie ordered four pepperoni pizzas for her and two friends to enjoy for her slumber party Friday night. Aunt Marie ate half of one of the pizzas without knowing they were for the girls. So, the pizza left for girls is $ 3 \frac{1}{2}$.
Can a proper fraction be written as a mixed number?
No, we cannot write the proper fraction as a mixed number as the numerator is less than the denominator in the proper fraction.
Can we simplify mixed number by converting it to an improper fraction?
Yes, we can also simplify a mixed number by first converting it to an improper fraction and then again by converting the simplified improper fraction into a mixed number.