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How to plot inequalities on a number line | Pre-Algebra | Khan Academy

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Constructing and solving a one-step inequality | Linear inequalities | Algebra I | Khan Academy

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Multiplying and dividing with inequalities example | Linear inequalities | Algebra I | Khan Academy

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Constructing and solving a two-step inequality | Linear inequalities | Algebra I | Khan Academy

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Solving a two-step inequality | Linear inequalities | Algebra I | Khan Academy

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Algebra: Linear equations 4 | Linear equations | Algebra I | Khan Academy

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Algebra: Linear equations 3 | Linear equations | Algebra I | Khan Academy

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Algebra: Linear equations 2 | Linear equations | Algebra I | Khan Academy

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Khan Academy: Algebra Linear Equations Level 1

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Khan Academy: Algebra Linear Equations Level 1

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Algebra: Linear equations 1 | Linear equations | Algebra I | Khan Academy

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Understanding Solutions to Linear Equations

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Understanding Solutions to Linear Equations

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Understanding Solutions to Linear Equations | PBS LearningMedia

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In this video, explore linear equations in one variable with one solution, infinitely many solutions, or no solutions. In the accompanying classroom activity, students watch the video and then write and solve three equations: one with one solution, one with infinitely many solutions, and one with no solutions. They trade with a partner and solve each other’s equations. To get the most from this lesson, students should be comfortable solving linear equations in one variable with one solution.

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How to Multiply Fractions |  Basic Fractions and Mixed Fractions with Whole Numbers

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Solving Inequalities is similar to solving equations, but where an equation has one unique solution, an inequality has a range of solutions.

To solve an inequality we calculate the values that an unknown variable can be in that inequality.

Multiplying or dividing by a negative number changes the direction of the inequality.

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How To Solve Linear Inequalities, Basic Introduction, Algebra

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How To Solve Linear Equations In Algebra

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Comparing and Ordering Rational Numbers Using a Number Line | Math with Mr. J

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One of the easiest ways to order rational numbers is to turn them all into decimals and then put them in order. If we want to turn a percentage into a decimal, all we do is turn the percent sign into a decimal point and move it two places to the left. So 13% becomes 0.13, and 213% becomes 2.13.

Another way to order rational numbers: If you want arrange rational numbers in descending order then, take the LCM and make denominators of all rational numbers equal. Then rational number whose numerator is greater will be the largest rational number and rational number whose numerator is small that will be smallest.

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Ordering Rational Numbers using decimals

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Calculate a Discount (Percent) without a Calculator

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Calculate a Discount (Percent) without a Calculator

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How to Calculate a Discount without a Calculator | Calculating Discounts by Hand | Math with Mr. J

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Calculate Percent (with a calculator) | Finding a Percentage

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Finding a Percent of a Number | Calculating Percentages

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What are Square Roots? | Math with Mr. J

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This animated Math Shorts video from UEN explains the term scientific notation and provides several examples in converting extreme numbers to and from scientific notation. It also demonstrates how to multiply numbers using scientific notation. In the accompanying classroom activity, students practice writing numbers in scientific notation and develop real-world problems for each other to solve.

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Simplifying Exponents with Fractions, Variables, Negative Exponents, Multiplication & Division

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Simplifying Exponents with Fractions, Variables, Negative Exponents, Multiplication & Division

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Simplifying Exponents With Fractions, Variables, Negative Exponents, Multiplication & Division, Math

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Simplifying exponents is a method of simplifying the algebraic expressions involving exponents into a simpler form such that they cannot further be simplified. There are rules in algebra for simplifying exponents with different and same bases that we can use. Various arithmetic operations like addition, subtraction, multiplication, and division can be applied to simplify exponent algebraic expressions, exponents in fractions, and negative exponents using the laws of exponents.

In this article, we will learn how to simplify exponents in algebraic expressions, fractions, negative exponents, and with different bases using the simplifying exponents' rules. We will also solve various examples related to the concept for a better understanding.

What is Simplifying Exponents?

Let us first recall the concept of exponents before learning to simplify exponents. The exponent of a number shows how many times the number is multiplied by itself. When we apply arithmetic operations on exponents, we use the laws of exponents for simplifying exponent expressions. Simplifying exponents is a simple process of reducing the mathematical expressions involving exponents into a simpler form such that they cannot further be simplified. Let us first go through some of the important rules for simplifying exponents in the next section.

Simplifying Exponents Rules

Given below is a list of rules that we for simplifying exponents in algebraic expressions. These rules are also known as the laws of exponents and are named as per the operation involved. Let us have a look at these rules that we will use later for simplifying exponents:

Simplifying Exponents With Different Bases

When we multiply exponents or divide exponents with different bases, there can be two cases: i) when the exponents are the same, ii) when the exponents are different. Let us discuss each of these cases and understand the process of simplifying exponents in such cases with the help of examples.

Simplifying Exponents With Different Bases and Same Power

When simplifying exponents with different bases and the same power, we follow the rules:

Let us simplify the following exponents: i) 2 ⁴ × 3 ⁴, ii) 4 ³ ÷ 2 ³

= 8

Simplifying Exponents With Different Bases and Different Power

When we have to simplify exponents with different bases and different power, we simplify the terms separately and then apply the arithmetic operation involved. Let us solve an example to understand this better. Simplify 23 × 52. Now, here the bases and powers both are different. So, for simplifying exponents in this expression, we will simplify the terms separately first.

= 8 × 25

= 200

Simplifying Exponents In Fractions

In this section, we will learn how to simplify exponents in fractions. When we are given algebraic expressions in fractions, we use the laws of exponents to simplify them. Let us understand this with the help of a few examples solved below:

Solution: We will simplify the given algebraic expression, using the simplifying exponents rules discussed above. So, we have

Example 2: Use simplifying exponents rules to simplify (2a ³b ⁵c) × (5ab ⁶c ²).

Solution: We will combine the like terms and simplify them separately. So, we have

Simplifying Rational Exponents

Now that we have understood how to apply simplifying exponents rules, let us now learn to simplify rational exponents. We apply the rules in the same way for simplifying rational exponents as we did for whole numbers. Some of the common rules that we will use here are:

Simplifying Negative Exponents

As we discussed in the previous section, for simplifying negative exponents, we apply the laws of exponents in the same way. Some of the common rules that we use for simplifying such exponents are:
Important Notes on Simplifying Exponents

Simplifying exponents is a simple process of reducing the mathematical expressions involving exponents into a simpler form such that they cannot further be simplified.

When we apply arithmetic operations on exponents, we use the laws of exponents for simplifying exponent expressions.

We can apply the rules of simplifying exponents for simplifying rational and negative exponents.

☛ Related Articles:
Simplifying Exponents Examples
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FAQs on Simplifying Exponents

What is Simplifying Exponents in Math?

Simplifying exponents is a method of simplifying the algebraic expressions involving exponents into a simpler form such that they cannot further be simplified. There are rules in algebra for simplifying exponents with different and same bases.

What are the Rules for Simplifying Exponents?

Given below is a list of rules that we for simplifying exponents in algebraic expressions:

What is Simplifying Exponents in Fractions?

When algebraic expressions involving exponents are given in fractions, we simplify them using the laws of exponents. For example, (35x ³y ²z) / (7xy ⁴), (5x ²y ⁷z) / (xy⁻¹), etc.

How to Simplify Negative Exponents?

For simplifying expressions with negative exponents, we use the same laws of exponents as we use for whole numbers. Some of the commonly used rules are:

How to Simplify Rational Exponents?

We apply the rules in the same way for simplifying rational exponents as we did for whole numbers. Some of the common rules that we will use here are:

What is Simplifying Exponents with Different Bases?

When we multiply exponents or divide exponents with different bases, there can be two cases: i) when the exponents are the same, ii) when the exponents are different. When simplifying exponents with different bases and the same power, we follow the rule:

When we have to simplify exponents with different bases and different power, we simplify the terms separately and then apply the arithmetic operation involved.

What is the Difference Between Simplifying Exponents and Evaluating Exponents?

Simplifying exponents means reducing an expression with an exponent to a simpler form such that it cannot further be reduced. Evaluating exponents implied determining the value of an expression by substituting the value of the variable involved or by doing the calculations involved.

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Simplifying Exponents - Rules, Different Bases, Fractions, Examples

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Simplifying exponents is a simple process of reducing the mathematical expressions involving exponents into a simpler form such that they cannot further be simplified.

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Operations

"Operations" mean things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation.

But, when you see something like ...

... what part should you calculate first?

Start at the left and go to the right?
Or go from right to left?
Warning: Calculate them in the wrong order, and you can get a wrong answer !
So, long ago people agreed to follow rules when doing calculations, and they are:

Order of Operations

Do things in Parentheses First

Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract

Multiply or Divide before you Add or Subtract

Otherwise just go left to right

How Do I Remember It All ... ? PEMDAS !

Divide and Multiply rank equally (and go left to right).

Add and Subtract rank equally (and go left to right)

So do it this way:

After you have done "P" and "E", just go from left to right doing any "M" or "D" as you find them.

Then go from left to right doing any "A" or "S" as you find them.

Pudgy Elves May Demand A Snack
Popcorn Every Monday Donuts Always Sunday
Please Eat Mom's Delicious Apple Strudels
People Everywhere Made Decisions About Sums

You may prefer GEMS ( Grouping, Exponents, Multiply or Divide, Add or Subtract).
In the UK they say BODMAS (Brackets, Orders, Divide, Multiply, Add, Subtract).
In Canada they say BEDMAS (Brackets, Exponents, Divide, Multiply, Add, Subtract).
It all means the same thing! It doesn't matter how you remember it, just so long as you get it right.

Examples

Example: How do you work out 3 + 6 × 2 ?

Multiplication before A ddition:

Example: How do you work out (3 + 6) × 2 ?

P arentheses first:

Example: How do you work out 12 / 6 × 3 / 2 ?

Multiplication and D ivision rank equally, so just go left to right:

A practical example:

Example: Sam threw a ball straight up at 20 meters per second, how far did it go in 2 seconds?

Sam uses this special formula that includes the effects of gravity:

height = velocity × time − (1/2) × 9.8 × time ²

Sam puts in the velocity of 20 meters per second and time of 2 seconds:

height = 20 × 2 − (1/2) × 9.8 × 2 ²

Now for the calculations!
The ball reaches 20.4 meters after 2 seconds
Exponents of Exponents ...

What about this example?

Exponents are special: they go top-down (do the exponent at the top first). So we calculate this way:
And finally, what about the example from the beginning?
297, 1566, 1572, 298, 1568, 381, 1570, 3854, 3855, 383

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"Operations" mean things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation. But, when you see something like ... ... what part should you calculate first? Start at the left and go to the right? Or go from right to left?

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Multiplying and Dividing Decimals: A Step-By-Step Review | How to Multiply and Divide Decimals

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Adding and Subtracting Decimals (How to) | Math with Mr. J

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How to Simplify Ratios | Simplifying Ratios

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Equivalent Ratios | How to Find Equivalent Ratios

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Ratios and Unit Rate Examples and Word Problems!

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Once you have cookies enabled, you can click here to go to the Math Antics home page.
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Math Antics | Basic Math Videos and Worksheets

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Your browser doesn’t support HTML5 video. Here is a link to the video instead.

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Watch three friends vocalize together in this rap song about dividing fractions with the keep, change, flip method. Dividing a fraction by another fraction has never been so fun and easy to understand as they break down the meaning behind keep, change, flip, and show that even though it is a trick, it's not magic... it's mathemagic!

Song Lyrics:

CHORUS:
To divide by a fraction here's a tip: KEEP, CHANGE, FLIP!
To divide by a fraction here's a tip: KEEP, CHANGE, FLIP!

To divide one half by one sixth: KEEP, CHANGE, FLIP!
one times six is six, and two times one is two
it's an improper fraction; so we're not through.
Divide six by two and the quotient is three.
Keep, change, flip - it's all that you need.

(CHORUS)

To divide two fifths by one fifth: KEEP, CHANGE, FLIP!
Two times five is ten, and five times one is five;
it's an improper fraction, so you need to divide.
Ten divided by five equals two.
When we divide by fractions this is what we do!

(CHORUS)

"Keep - change - flip" may seem to work magically,
but it can be explained mathematically.
With the number ten, we can divide by two,
and that will leave five in each group...
Or we can find that "five" through a different path
by multiplying ten by two, "flipped" to one half.
It's the trick that never fails called "keep - change - flip."
It's real mathemagic, so use this tip!

We understand with ease these problems we love,
because we know "division" means:
"...has how many groups of..."

Let's explore that thought:
How many groups of "fourths" does one half got?
Two "fourths" fit into one half perfectly,
and we found the quotient mentally!

(DOUBLE CHORUS)

Learn More

This song targets TEKS and Common Core learning standards from both 5th Grade and 6th Grade. Look into the relevant standards here, or dig deeper into dividing fractions here. Or click here to get a conceptual/visual understanding of why one can Keep, Change, and Flip when dividing fractions as a means of obtaining the right answer.

If you are interested in getting ideas on how to plan a robust standards-aligned telling time lesson, we recommend checking out Instructure's recommendations for common core standards 5.NF.B.7, and 6.NS.A.1 . These pages help break down standard language, lay out the grade-appropriate level of rigor for each concept, and offer a variety of suggestions for activities (lesson seeds) that help students achieve their learning targets.

To continue browsing Numberock's math video content library, click here. To gain access to Numberock's growing library of premium content, click here.

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Keep, Change, Flip Video | Dividing Fractions by NUMBEROCK

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What better way to learn about the Keep, Change, Flip method to divide fractions than through an extremely catchy song!

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Prime Factorization ( Division Method and Factor Tree Method)

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Prime Factorization ( Division Method and Factor Tree Method)

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Greatest Common Factor and Least Common Multiple

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Greatest Common Factor and Least Common Multiple

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Multiplication Chart for quick reference

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Click on this link to play: https://app.legendsoflearning.com/join/YXNzaWdubWVudC0zMzYzMTEx