Add or subtract the fractions below and simplify your result. x 4 + x 10 − x 5 \frac{x}{4}+\frac{x}{10}-\frac{x}{5}

This problem asks us to add or subtract the fractions below and simplify our result. So notice we have X over 4 + X over 10 minus X over 5. Now, right off the bat, I can clearly see we do not have a common denominator. These are not like fractions. So when that happens, my first step is finding the least common denominator. Now, we know a couple of different methods for finding the LCD, but since I'm dealing with three fractions here, I'm going to use prime factorization. So the denominators I can see are 4. 10 And 5. Now, I can break each of these down into prime factors. 4 is 2 times 2, 10 is 2 times 5, and 5 is already a prime factor itself. So, I just need to go ahead and collect the unique prime factors, and remember, the product of unique prime factors gives us our LCD. Well, I can see that we have 2 2s being multiplied, then I can see we have a 2 down here, so I don't need to include it since we We already have 2 2's up here for the 4, but I do need to include this 5, but I don't need to include this other 5 since we already have a 5 up here. So those are all the unique prime factors, meaning we get 2 times 2 times 5, and 2 times 2 times 5 gives us 20. So 20 is the least common denominator. Now that I've identified my least common denominator, I can recognize all of these fractions. I need to write as equivalent fractions, each having a denominator of 20. So what I need to do is think about what constant I need to multiply by the denominator and the numerator to give me 20. Well, we'll start with this first fraction. I can recognize 5 times 4 gives me 20. So if I need to multiply the denominator by 5, I should also multiply the numerator by 5, giving me 5 times x or 5 x. Now keep in mind we're adding these fractions and subtracting these, and next, what I can do is move to my second fraction, which is x over 10. Well, I know that 2 times 10 would give me 20, this denominator, so you need to multiply the numerator by 2, giving me 2 x. Now moving to my third fraction, I can recognize 4 times 5 gives me 20, and so I can multiply this numerator by 4, giving me 4 x as well. Remember, to get equivalent fractions, we multiply the numerator and denominator by the same constant, which is what we did across the board. So notice now I have equivalent fractions all with the same denominator of 20. And since we have these like fractions now, I can just combine the numerators and keep the same denominator. So we have 5 x. Plus 2 X minus 4 X all over the common denominator of 20. Now, 5 X + 2 X is 7 X, and if we subtract off 4 X, we end up getting 3 X and then all of this will be over the common denominator of 20. We cannot simplify 3 X over 20 any farther, so this is the final answer to the problem.

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1. Whole Numbers2h 43m

Adding Whole Numbers
27m

Subtracting Whole Numbers
21m

Multiplying Whole Numbers
46m

Dividing Whole Numbers
21m

Long Division
36m

Exponents
10m

2. Integers1h 7m

Introduction to Integers
16m

Multiplying Integers
24m

Exponential Expressions
10m

Dividing Integers
16m

3. Introduction to Solving Equations and Problem Solving1h 11m

Simplifying Expressions
13m

Translating Word Phrases to Algebraic Expressions
6m

Introduction to Solving Equations
41m

Translating Sentences to Algebraic Equations
9m

4. Fractions3h 29m

Intro To Fractions and Mixed Numbers
44m

Simplifying Fractions
45m

Adding And Subtracting Fractions
31m

Finding The Least Common Denominator
33m

Adding And Subtracting Unlike Fractions
34m

Ordering Fractions
19m

5. Decimals1h 20m

Introduction to Decimals
26m

Rounding Decimals
12m

Adding And Subtracting Decimals
41m

6. Ratio, Proportion, and Percent2h 1m

Ratios and Rates
35m

Proportions
33m

Solving Percent Problems With Equations
16m

Applications of Percent
36m

7. Graphing and Introduction to Statistics31m

Tables
3m

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3m

Frequency Distributions and Histograms
5m

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14m

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4m

8. Geometry49m

Square Roots and The Pythagorean Theorem
29m

The Circle
20m

9. Measurement58m

US Units of Length
25m

Metric Units of Length
33m

10. Linear Equations and Inequalities6h 29m

The Distributive Property
17m

Evaluating Expressions
15m

Review: Addition and Subtraction Properties of Equality
41m

Review: Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Introduction to Problem Solving
37m

Formulas
21m

Review: Percent Problem Solving
59m

Mixture Problem Solving
43m

Linear Inequalities in One Variable
46m

11. Graphing Linear Equations and Inequalities4h 58m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

Linear Inequalities in Two Variables
28m

Introduction to Relations and Functions
57m

Function Notation
15m

12. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

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15m

Solving Systems of Linear Equations by Elimination
45m

13. Exponents and Polynomials3h 55m

Review: Evaluating Exponents
29m

The Product Rule
10m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

The Quotient Rule
13m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

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20m

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33m

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34m

14. Factoring Polynomials2h 42m

Factoring by Greatest Common Factor & Grouping
38m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
20m

Sum & Difference of Cubes
12m

Quadratic Equations & Applications
41m

15. Rational Expressions and Equations3h 40m

Simplifying Rational Expressions
39m

Multiplying And Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

Direct & Inverse Variation
27m

16. Roots and Radicals2h 46m

Introduction to Radical Expressions
47m

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46m

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19m

Multiplying, Dividing, and Rationalizing Radicals
53m

17. Quadratic Equations1h 55m

The Square Root Property
17m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
30m

4. Fractions

Adding And Subtracting Unlike Fractions

Prealgebra & Beginning Algebra

4. Fractions

Adding And Subtracting Unlike Fractions

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Multiple Choice

Add or subtract the fractions below and simplify your result.
$\frac{x}{4} + \frac{x}{10} - \frac{x}{5}$

$\frac{x}{10}$

$\frac{3x}{10}$ a

$\frac{3x}{20}$

$\frac{11x}{20}$

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Struggling with Prealgebra & Beginning Algebra?

Add or subtract the fractions below and simplify your result.x4+x10−x5\(\frac{x}{4}\)+\(\frac{x}{10}\)-\(\frac{x}{5}\)

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Add or subtract the fractions below and simplify your result.
$\frac{x}{4} + \frac{x}{10} - \frac{x}{5}$