Rational expression word problems

Here is a graphic preview for all of the word problems worksheets. You can select different variables to customize these word problems worksheets for your needs. The word problems worksheets are randomly created and will never repeat so you have an endless supply of quality word problems worksheets to use in the classroom or at home. Our word problems worksheets are free to download, easy to use, and very flexible.

These word problems worksheets are a great resource for children in 3rd Grade, 4th Grade, and 5th Grade. Words to Symbols Handout This Word Problems Worksheet will produce a great handout to help students learn the symbols for different words and phrases in word problems.

Addition Word Problems Worksheets Using 1 Digit with 2 Addends These addition word problems worksheets will produce 1 digit problems with two addends, with ten problems per worksheet. These word problems worksheets are appropriate for 3rd Grade, 4th Grade, and 5th Grade. Addition Word Problems Worksheets Using 2 Digits with 2 Addends These addition word problems worksheets will produce 2 digits problems with two addends, with ten problems per worksheet.

Addition Word Problems Worksheets Using 1 Digit with 3 Addends These addition word problems worksheets will produce 1 digit problems with three addends, with ten problems per worksheet. Addition Word Problems Worksheets Using 2 Digits with 3 Addends These addition word problems worksheets will produce 2 digits problems with three addends, with ten problems per worksheet. Addition Word Problems Worksheets 2 Digits Missing Addends These addition word problems worksheet will produce 2 digits problems with missing addends, with ten problems per worksheet.

You may select between regrouping and non-regrouping type of problems. Subtraction Word Problems Worksheets Using 1 Digit These subtraction word problems worksheets will produce 1 digit problems, with ten problems per worksheet. Subtraction Word Problems Worksheets Using 2 Digits These subtraction word problems worksheets will produce 2 digits problems, with ten problems per worksheet.

Addition and Subtraction Word Problems Worksheets Using 1 Digit These addition and subtraction word problems worksheets will produce 1 digit problems, with ten problems per worksheet.

Addition and Subtraction Word Problems Worksheets Using 2 Digits These addition and subtraction word problems worksheets will produce 2 digits problems, with ten problems per worksheet. Addition and Subtraction Word Problems Worksheets 2 Digits With No Regrouping These addition and subtraction word problems worksheets will produce 2 digits problems with no regrouping and ten problems per worksheet.

Addition and Subtraction Word Problems Worksheets Using 3 Digits These addition and subtraction word problems worksheets will produce 3 digits problems, with ten problems per worksheet. Multi-Step Problems Addition and Subtraction These multi-step addition and subtraction word problems worksheets will produce 10 problems per worksheet.

Multiplication Word Problems Worksheets Using 1 Digit These multiplication word problems worksheets will produce 1 digit problems, with ten problems per worksheet. Multiplication Word Problems Worksheets Using Dozens These multiplication word problems worksheets will produce problems using dozens, with ten problems per worksheet.

Multiplication Word Problems Worksheets Using 2 Digits These multiplication word problems worksheets will produce 2 digits problems, with ten problems per worksheet.Enter expression, e. Enter a set of expressions, e.

Enter equation to solve, e. Enter equation to graph, e. Number of equations to solve: 2 3 4 5 6 7 8 9 Sample Problem Equ. Enter inequality to solve, e. Enter inequality to graph, e. Number of inequalities to solve: 2 3 4 5 6 7 8 9 Sample Problem Ineq. Please use this form if you would like to have this math solver on your website, free of charge. Expression Equation Inequality Contact us. Solve Graph System. Math solver on your site. I have a set of math problems that I need to answer and I am hopelessly lost.

Kindly let me know if you are good in absolute values or if there is a good site which can assist me. I was in a similar situation sometime back, when my friend advised that I should try Algebrator. Algebrator has a really easy to use GUI but it can help you crack the most difficult of the problems that you might face in math at school.

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rational expression word problems

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I wish to know more about this fabulous product. Please let me know. They also claim to provide an unrestricted money back guarantee, so you have nothing to lose. Try this and Good Luck! Back to top. Rational Expressions. Graphs of Rational Functions. Solve Two-Step Equations. Solving a Quadratic Equation.

Systems of Linear Equations Introduction. Equations and Inequalities.Math is about translating English into funny symbols. Not laugh-out-loud funny, usually, but some of them should at least bring a wry smile to your face.

What English statements translate into polynomials and rational expressions? Polynomials often appear in problems where one quantity depends on another. In other words, the quantities are clingy. Janna has finished weaving a blanket. She made the length of the blanket 1 foot greater than twice its width, because otherwise her toes get cold.

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If the area covered by the blanket is 28 square feet, how long is the blanket? Whenever it makes sense to do so, draw a picture. You can draw a picture when it doesn't make sense to do so, but it's rare that a doodle of Mickey Mouse will help you solve a word problem, unless you're asked to find the circumference of his ears. We need a variable somewhere. We'll use a variable for the width since the problem discusses the length in relation to the width.

That means the area covered by this blanket is:. To solve this equation, we need to rearrange the terms so that we have a polynomial set equal to Do these solutions make sense? That won't cover even one of Janna's toes. The blanket must be 3. Wait, we hope you wrote that down in pencil.

We need to make sure we're answering the right problem. We're supposed to give the lengthnot the width, of the blanket. Slaps forehead with palm. To find the length, we plug the width 3. The length of the blanket is:. We can easily check our answers by multiplying the width and length of the blanket, and seeing if we do end up with Be careful : When solving word problems involving polynomials or rational expressions, make sure that you only keep those solutions that make sense in the context of the word problem.

This often means throwing out one or more negative solutions. They're only bringing everybody down anyway.You are usually told how long each person takes to paint a similarly-sized house, and you are asked how long it will take the two of them to paint the house when they work together.

Many of these problems are not terribly realistic — since when can two laser printers work together on printing one report? The method of solution for "work" problems is not obvious, so don't feel bad if you're totally lost at the moment. For instance:. If the first painter can do the entire job in twelve hours and the second painter can do it in eight hours, then this here is the trick! The question then becomes, how much then can they do per hour if they work together? To find out how much they can do together per hourI make the necessary assumption that their labors are additive in other words, that they never get in each other's way in any mannerand I add together what they can do individually per hour.

So, per hour, their labors are:. But the exercise didn't ask me how much they can do per hour; it asked me how long they'll take to finish one whole job, working togets. So now I'll pick the variable " t " to stand for how long they take that is, the time they take to do the job together.

Then they can do:. This gives me an expression for their combined hourly rate. I already had a numerical expression for their combined hourly rate.

So, setting these two expressions equal, I get:. An hour has sixty minutes, so 0. They can complete the job together in 4 hours and 48 minutes. The important thing to understand about the above example is that the key was in converting how long each person took to complete the task into a rate.

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Each person took a certain number of hours to complete the task: hours to complete job:. Since the unit for completion was "hours", I converted each time to an hourly rate; that is, I restated everything in terms of how much of the entire task could be completed per hour.

To do this, I simply inverted each value for "hours to complete job":. Then, assuming that their per-hour rates were additive, I added the portion that each could do per hour, summed them, and set this equal to the "together" rate:. As you can see in the above example, "work" problems commonly create rational equations. But the equations themselves are usually pretty simple to solve.

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My first step is to list the times taken by each pipe to fill the pool, and how long the two pipes take together. In this case, I know the "together" time, but not the individual times. One of the pipes' times is expressed in terms of the other pipe's time, so I'll pick a variable to stand for one of these times.

You might wonder how to work with that " 1. If you're not sure, try doing similar computations with simpler numbers. For instance, if the faster pipe filled the pool 2 times as fast as the second pipe, then it would take one-half as long to fill the pool. If the faster pipe filled the pool 3 times as fast as the second pipe, then it would take one-third as long to fill the pool.

Following this same reasoning, since the faster pipe fills the pool 1. Since the faster pipe's time to completion is defined in terms of the second pipe's time, I'll pick a variable for the slower pipe's time, and then use this to create an expression for the faster pipe's time:.

Then I make the necessary assumption that the pipes' contributions are additive which is reasonable, in this caseadd the two pipes' contributions, and set this equal to the combined per-hour rate:. They asked me for the time of the slower pipe, so I don't need to find the time for the faster pipe. My answer is:. Note: I could have picked a variable for the faster pipe, and then defined the time for the slower pipe in terms of this variable. If you're not sure how you'd do this, then think about it in terms of nicer numbers: If someone goes twice as fast as you, then you take twice as long as he does; if he goes three times as fast as you, then you take three times as long as him.

In this case, if he goes 1.We now need to look at rational expressions. Here are some examples of rational expressions.

There is an unspoken rule when dealing with rational expressions that we now need to address. When dealing with numbers we know that division by zero is not allowed. Well the same is true for rational expressions. We rarely write these restrictions down, but we will always need to keep them in mind.

rational expression word problems

Note as well that the numerator of the second rational expression will be zero. That is okay, we just need to avoid division by zero. The first topic that we need to discuss here is reducing a rational expression to lowest terms. A rational expression has been reduced to lowest terms if all common factors from the numerator and denominator have been canceled.

We do have to be careful with canceling however. There are some common mistakes that students often make with these problems.

Recall that in order to cancel a factor it must multiply the whole numerator and the whole denominator. So, be careful with canceling. When reducing a rational expression to lowest terms the first thing that we will do is factor both the numerator and denominator as much as possible.

MULTIPLY AND DIVIDE RATIONAL NUMBERS WORD PROBLEMS WORKSHEET

That should always be the first step in these problems. Also, the factoring in this section, and all successive section for that matter, will be done without explanation. In other words, make sure that you can factor! Doing this gives. This is also all the farther that we can go. Nothing else will cancel and so we have reduced this expression to lowest terms.

At first glance it looks there is nothing that will cancel. Notice however that there is a term in the denominator that is almost the same as a term in the numerator except all the signs are the opposite. There are two forms here that cover both possibilities that we are liable to run into.

Polynomial Division and Rational Expressions

In our case however we need the first form. Notice the steps used here. Typically, when we factor out minus signs we skip all the intermediate steps and go straight to the final step. In this case the denominator is already factored for us to make our life easier. All we need to do is factor the numerator. Now we reach the point of this part of the example. Here is the rational expression reduced to lowest terms. Notice that we moved the minus sign from the denominator to the front of the rational expression in the final form.

This can always be done when we need to. Recall that the following are all equivalent. In other words, a minus sign in front of a rational expression can be moved onto the whole numerator or whole denominator if it is convenient to do that.

How Do You Solve a Word Problem with a Rational Equation?

We do have to be careful with this however. Consider the following rational expression. In order to move a minus sign to the front of a rational expression it needs to be times the whole numerator or denominator.Note that we talk about how to graph rationals using their asymptotes in the Graphing Rational Functions, including Asymptotes section.

Also, since limits exist with Rational Functions and their asymptotes, limits are discussed here in the Limits and Continuity section.

Since factoring is so important in algebra, you may want to revisit it first.

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Flip the denominator and multiply. They can be multiplied and divided like regular fractions. Here are some examples.

Solving Word Problem Involving Rational Algebraic Expression

Also, note in the last example, we are dividing rationalsso we flip the second and multiply. Remember that when you cross out factors, you can cross out from the top and bottom of the same fraction, or top and bottom from different factors that you are multiplying. You can never cross out two things on top, or two things on bottom.

When we add or subtract two or more rationals, we need to find the least common denominator LCDjust like when we add or subtract regular fractions.

If the denominators are the same, we can just add the numerators across, leaving the denominators as they are. Just like with regular fractions, we want to use the factors in the denominators in every fraction, but not repeat them across denominators.

When nothing is common, just multiply the factors. Find the common denominator on the bottom first, combine terms, and then flip and multiply to the top. Then simplify.

This means if we ever get a solution to an equation that contains rational expressions and has variables in the denominator which they probably will! Remember that with quadratics, we need to get everything to one side with 0 on the other side and either factor or use the Quadratic Formula.

The last example shows this. Check your answers to make sure no denominators are 0. In this example, we could factor. Both work! So when we solve these rational inequalities, our answers will typically be a range of numbers. Remember to start from the left.

Solving Rational Inequalities Algebraically Using a Sign Chart The easiest way to solve rational inequalities algebraically is using the sign chart methodwhich we saw here in the Quadratic Inequalities Section Method. Sign charts are easy and a lot of fun since you can pick any point in between the critical valuesand see if the whole function is positive or negative.

rational expression word problems

Then you just pick that interval or intervals by looking at the inequality. We have to have only one term on the left sideso sometimes we have to find a common denominator and combine terms. You can always use your graphing calculator to check your answers, too. Put in both sides of the inequalities and check the zeros, and make sure your ranges are correct! We now draw a sign chart. Since the roots are —4 and 1we put those on the sign chart as boundaries. Then we check each interval with random points to see the rational expression is positive or negative.

We put the signs over the interval. Rational Inequality Notes. Then we check each interval with random points to see if the rational expression factored or unfactored is positive or negative.Pari needs 4 hours to complete a work. His friend Yuvan needs 6 hours to complete the same work. How long will it take to complete if they work together? Problem 2 :. Iniya bought 50 kg of fruits consisting of apples and bananas.

She paid twice as much per kg for the apple as she did for the banana. Solution :. Let "x" be number of kgs of banana and "2x" be the number of kgs of apple. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :. We always appreciate your feedback. You can also visit the following web pages on different stuff in math. Variables and constants. Writing and evaluating expressions.

Solving linear equations using elimination method.

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Solving linear equations using substitution method. Solving linear equations using cross multiplication method. Solving one step equations. Solving quadratic equations by factoring. Solving quadratic equations by quadratic formula.

Solving quadratic equations by completing square. Nature of the roots of a quadratic equations. Sum and product of the roots of a quadratic equations. Algebraic identities. Solving absolute value equations. Solving Absolute value inequalities. Graphing absolute value equations. Combining like terms. Square root of polynomials. Remainder theorem. Synthetic division. Logarithmic problems.

Simplifying radical expression. Comparing surds. Simplifying logarithmic expressions. Negative exponents rules. Scientific notations.

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