Solving One-Step Equations with Mixed Numbers
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Solving One-Step Linear Equations with Mixed Numbers
A mixed number is a number expressed as the sum of a whole number and a fractions , such as 3 1 4 .
It is usually easier to do calculations with improper fractions than mixed numbers, but mixed numbers give a better idea of the size of a number. So you should know how to convert back and forth.
To solve an equation that has a mixed number coefficient, we convert the mixed number to an improper fraction as the first step.
Some linear equations can be solved with a single operation. For this type of equation, use the inverse operation to solve. The easiest type involves only an addition or a subtraction.
3 4 + p = 1 1 4
Rewrite the mixed number as an improper fraction.
3 4 + p = 5 4
The inverse operation of addition is subtraction. Use the subtraction property of equality to subtract 3 4 from both sides.
3 4 + p − 3 4 = 5 4 − 3 4
Divide the numerator and the denominator by the GCF, 2 .
Also, we can solve linear equations when only multiplication or division is involved. If there's a coefficient in front of the variable, multiply by the reciprocal of that number to get a coefficient of 1 .
2 1 4 x = 7 1 6
Rewrite the mixed numbers as improper fractions.
9 4 x = 43 6
The inverse operation of division is multiplication.
To isolate the variable x (to get a coefficient of 1 ), multiply both sides by 4 9 which is the reciprocal of 9 4 .
4 9 ⋅ ( 9 4 x ) = 4 9 ⋅ 43 6
You can cancel common factors before you multiply.
x = 4 2 9 ⋅ 43 6 2 x = 86 27
Finally, write the improper fraction as a mixed number. 27 goes into 86 three times with a remainder of 5 . So:
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Equations with Mixed Numbers/Improper Fractions
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Mixed Fractions
(Also called " Mixed Numbers ")
A Mixed Fraction is a whole number and a proper fraction combined. Such as 1 3 4
See how each example is made up of a whole number and a proper fraction together? That is why it is called a "mixed" fraction (or mixed number).
We can give names to every part of a mixed fraction:
Three Types of Fractions
There are three types of fraction:
Mixed Fractions or Improper Fractions
We can use either an improper fraction or a mixed fraction to show the same amount.
For example 1 3 4 = 7 4 , as shown here:
Converting Improper Fractions to Mixed Fractions
To convert an improper fraction to a mixed fraction, follow these steps:
- Divide the numerator by the denominator.
- Write down the whole number answer
- Then write down any remainder above the denominator.
Example: Convert 11 4 to a mixed fraction.
Write down the 2 and then write down the remainder (3) above the denominator (4).
That example can be written like this:
Example: Convert 10 3 to a mixed fraction.
Converting mixed fractions to improper fractions.
To convert a mixed fraction to an improper fraction, follow these steps:
- Multiply the whole number part by the fraction's denominator.
- Add that to the numerator
- Then write the result on top of the denominator.
Example: Convert 3 2 5 to an improper fraction.
Multiply the whole number part by the denominator:
Add that to the numerator:
Then write that result above the denominator:
We can do the numerator in one go:
Example: Convert 2 1 9 to an improper fraction.
Are improper fractions bad .
NO, they aren't bad!
For mathematics they are actually better than mixed fractions. Because mixed fractions can be confusing when we write them in a formula: should the two parts be added or multiplied?
But, for everyday use , people understand mixed fractions better.
Example: It is easier to say "I ate 2 1 4 sausages", than "I ate 9 4 sausages"
We Recommend:
- For Mathematics: Improper Fractions
- For Everyday Use: Mixed Fractions
How Do You Solve an Equation Where You're Multiplying Fractions?
Solving an equation with multiple fractions in different forms isn't so bad. This tutorial shows you how to convert a mixed fraction to an improper fraction in order to solve the equation. Then, you'll see how to convert the answer back to a mixed fraction to make sense of it. Follow along with this tutorial to see how it's done!
- 1 step solution
- solve by division
- division property of equality
- mixed fraction
- improper fraction
Background Tutorials
Converting decimals and fractions.
How Do You Turn an Improper Fraction Into a Mixed Fraction?
In math, it's often important to change a fraction from one type to another. It can help you work with the fraction in an equation or help make more sense of an answer. This tutorial shows you how to convert an improper fraction to a mixed fraction.
Multiplying Fractions
How Do You Multiply Fractions?
Working with fractions can be intimidating, but if you arm yourself with the right tools, you'll find that working with fractions is no harder than working with basic numbers. In this tutorial you'll see the process for multiplying 3 very simple fractions. Enjoy!
Dividing Fractions
What's a Reciprocal?
Reciprocals are important when it comes to dividing fractions, finding perpendicular lines, dealing with inverse proportions, and so much more! In this tutorial you can review the basics about reciprocals.
What's an Improper Fraction?
Fractions come in all sorts of flavors, and in this tutorial you'll learn how to recognize improper fractions.
Evaluating Expressions
How Do You Evaluate an Algebraic Expression?
Plugging variables into an expression is essential for solving many algebra problems. See how to plug in variable values by watching this tutorial.
What is a Variable?
You can't do algebra without working with variables, but variables can be confusing. If you've ever wondered what variables are, then this tutorial is for you!
Solving Equations by Multiplying
What's the Multiplication Property of Equality?
Solving equations can be tough, especially if you've forgotten or have trouble understanding the tools at your disposal. One of those tools is the multiplication property of equality, and it lets you multiply both sides of an equation by the same number. Watch the video to see it in action!
Further Exploration
Solving one-step fraction equations.
How Do You Solve a Word Problem Using an Equation Where You're Multiplying Fractions?
Working with word problems AND fractions? This tutorial shows you how to take a word problem and translate it into a mathematical equation involving fractions. Then, you'll see how to solve and get the answer. Check it out!
Solving Multi-Step Fraction Equations
How Do You Solve a Multi-Step Equation with Fractions by Multiplying Away the Fraction?
Trying to solve an equation involving a fraction? Just multiply the fraction away and then perform the order of operations in reverse! See how in this tutorial.
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Unit 2: Lesson 1
- Why we do the same thing to both sides: Variable on both sides
- Intro to equations with variables on both sides
- Equations with variables on both sides: 20-7x=6x-6
Equation with variables on both sides: fractions
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Video transcript
- Math Article
Mixed Fractions
Mixed Fractions are one of the three types of f ractions . It is also called mixed numbers. For example, 2 1 / 7 is a mixed fraction. Learn here all types of fractions in detail.
You can understand these fractions in details in this article, such as its definition, changing of the improper fraction to a mixed fraction and so on. Also, you will learn here to perform operations like multiplying, dividing, adding and subtracting fractions . Read the complete article to become well versed with all the related concepts of these types of fractions.
It is a form of a fraction which is defined as the ones having a fraction and a whole number.
Example : 2(1/7), where 2 is a whole number and 1/7 is a fraction.
How to convert Improper fraction to a mixed fraction?
- Step 1: Divide the Fraction’s numerator with the denominator, i.e. 15/7.
- Step 2: The integer part of the answer will be the integer part for a mixed fraction, i.e. 2 is an integer.
- Step 3: The Denominator will be the same as original, i.e 7.
- Step 4: So, the improper fraction 15/7 is changed to a Mixed fraction as 2 (1/7)
Read More Articles:
Mixed fraction to Improper Fraction
- Step 1: Multiply the denominator with the whole number, i.e. Multiply 7 with 2 in the given example, 2(1/7).
- Step 2: Add the numerator of the Fraction to the result in step 1. i.e., Add 1+ 14
- Step 3: Keep the Denominator same i.e. 7.
- Step 4: The Improper fraction obtained is: 15/7.
Adding Mixed Fractions
When it comes to adding Mixed or Improper fractions, we can have either the same denominators for both the fractions to be added or the denominators can differ too.
Here’s a step-wise method to add the improper fraction with same or different denominators.
Note : Before applying any operations such as addition, subtraction, multiplication, etc., change the given mixed fractions to improper fractions as shown above.
Subtracting Mixed Fractions
Here’s a step-wise explanation of how to Subtract the improper fraction with Same or Different Denominators.
Multiplying Mixed Fractions
Example : 2(⅚) × 3 (½)
Step 1 : Convert the mixed into an improper fraction. 17/6 × 7/2
Step 2 : Multiply the numerators of both the fractions together and denominators of both the fractions together. {17 × 7} {6 × 2}
Step 3 : You can convert the fraction into the simplest form or Mixed one = 119 / 12 or 9 (11/12)
Definition of Fraction
In simple words, the ratio of the two numbers is called a fraction.
For Example, 15/7 is a fraction, where 15 is a numerator and 7 is a denominator. 7 is the number of parts into which the whole number divides.
A fraction can represent part of a whole .
Kinds of Fractions
There are three types of fractions. Below given table defines all three of them.
Mixed Equivalent Fractions
How can we find mixed equivalent fractions? Let us find the answer to this question here.
Two fractions are said to be equivalent if their values are equal after simplification. Suppose ½ and 2/4 are two equivalent fractions since 2/4 = ½.
Now when two mixed fractions are equal to each other then they are equivalent in nature. Hence, if we are converting any two equivalent fractions into mixed fractions, then the quotient left, when we divide numerator by denominator, should be the same.
For example, 5/2 and 10/4 are two equivalent fractions.
5/2: when we divide 5 by 2, we get a quotient equal to 2 and the remainder equal to 1. So 5/2 could be written in the form of a mixed fraction as 2 1 / 2 .
Similarly, in the fraction 10/4, when we divide 10 by 4, we get a quotient equal to 2 and the remainder equal to 2. Therefore, 10/4 = 2 2 / 4 .
Hence, for both mixed fractions 2 1 / 2 and 2 2 / 4 , the quotient value is equal to 2.
Video Lesson on Fractions
Frequently Asked Questions – FAQs
What is a mixed fraction, how to read a fraction, how to convert an improper fraction into a mixed fraction, how to convert a mixed fraction into an improper fraction, how to add mixed fractions, how to subtract mixed fractions.
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Solving One-Step Equations with Mixed Numbers · 1. Change the mixed number to an improper fraction. · 2. Isolate the variable by multiplying both sides of the
To solve an equation that has a mixed number coefficient, we convert the mixed number to an improper fraction as the first step. Some linear equations can
Fractions #AnilKumar #GCSE #EQAO #GlobalMathInstitute https://www.youtube.com/watch?v=KMPrzZ4NTtc Contact: [email protected] or
Learn how to solve a one step equation. An equation is a statement stating that two values are equal. A one step equation is an equation
1) Convert mixed numbers to improper fractions, if applicable · 2) Multiply both sides by reciprocal of 1st mixed number or improper fraction to isolate the
Converting Mixed Fractions to Improper Fractions · Multiply the whole number part by the fraction's denominator. · Add that to the numerator · Then write the
Solving an equation with multiple fractions in different forms isn't so bad. This tutorial shows you how to convert a mixed fraction to an improper fraction
In general, the mixed number a b/c is the same as a + b/c. For instance, we can write our mixed number, 6 2/5 as 6 + 2/5. Now, if we were to pull out a
The general rule for solving equations with fractions — whether it be only on one side or both — is to try to get rid of all of them. The most common way to
Mixed Fractions · Step 1: Divide the Fraction's numerator with the denominator, i.e. 15/7. · Step 2: The integer part of the answer will be the integer part for a