How to Find Y Intercept with 2 Points

How to Find Y Intercept with 2 Points

How to Find Y Intercept with 2 Points

Step-by-Step Guide: How to Find y intercept with 2 points given to you

 

Free Step-by-Step Guide: How to find y-intercept of a graph given two points.

 

Understanding how to find the y-intercept of a line given 2 points (i.e. (x,y) coordinates) that the line passes through is an incredibly important and useful algebra skill that every student can easily learn with a little practice. In fact, knowing how to find the y intercept with 2 points given is a foundational skill that will help you to develop a stronger overall understanding of linear equations on the coordinate plane.

If you are an algebra student who is struggling with this key skill or an algebra teacher looking for a simple way to explain this topic in your classroom, this free step-by-step guide to finding y intercept with 2 points given shares everything you will ever need.

In the sections ahead, we will walk through all of the steps to finding the y intercept of a line with 2 points, including a recap of some key vocabulary as well as exactly how to solve any problem that gives you 2 coordinate points and asks you to find the y-intercept of a line. After working through different practice problems, you will have gained significant practice and experience with this key algebra skill.

While we recommend that you work through each section of this guide in order (the review section covers several important foundational skills and vocabulary terms related to linear functions), you can jump to any section by using the quick-links below. Ready to get started?

How to Find Y Intercept with 2 Points: Sections:

 

Figure 01: What is the Y-Intercept?

 

Quick Review: Lines and Y-Intercepts

Before we learn how to find y intercept with 2 points, let’s do a quick review of some key algebra terms and concepts related to linear functions.

For starters, it’s important to remember that linear equations can be expressed in slope-intercept form, also known as y = mx + b form, where:

  • slope-intercept form: y = mx + b

  • m is the slope

  • b is the y-intercept

For example, a line with the equation y = ⅓x + 4 has a slope of ⅓ and a y-intercept at 4.

What exactly is a y-intercept?

The y-intercept of a line is the coordinate point where the line crosses the y-axis. The y-intercept is always written as an (x,y) coordinate where x is 0.

So, the line y = ⅓x + 4 has a y-intercept at (0,4).

The image in Figure 01 above shows three different linear functions and their y-intercepts. Do you notice a pattern?

Knowing the coordinates of the y-intercept of a line is helpful because it tells you the starting point for graphing the line, and it also helps you to write the equation of the line in slope-intercept form, y=mx+b, where m is the slope of the line and b is the y-intercept.

 

Figure 02: Review: Slope-Intercept Form (y=mx+b)

 

So, whenever you are given two coordinate points that a line passes through, you have to figure out the values of m and b in order to determine the coordinates of the y-intercepts.

With these concepts in mind, let’s go ahead and try our first example problem of how to find y intercepts with 2 points.

Make sure that you know all of the perfect squares from 1 to 144 (as shown in Figure 01 above) before moving onto the next section.

While it is relatively easy to simplify a square root of a perfect square, it is more complicated to simplify a square root of a non-perfect square, which is what we will be focusing on in the next section, where, for example, we will look at finding the perfect squares of numbers like 18, 75, and 112.

How to Find Y Intercept with 2 Points

Now we are ready to try our first example where we will learn how to find y-intercept with 2 points given, and will solve them by following these 3 simple steps:

To find the y-intercept using two points, follow these steps:

Step 1: Use the Given Coordinates to Find the Slope of the Line

Step 2: Plug One point and Slope, m, into the Slope-Intercept Form Formula (y=mx+b)

Step 3: Solve for b and determine the y-intercept

Example A: Find the y intercept of the line passing through (2,5) and (4,9)

 

Example A: Find the y intercept of the line passing through (2,5) and (4,9).

For our first example, we are given two points and we are tasked with finding the y-intercept of the line that passes through them. We can use our 3-step strategy to solve this problem as follows:

Step 1: Use the Given Coordinates to Find the Slope of the Line

For this example, we are given the following coordinate points:

  • (2,5) and (4,9)

We can use the slope formula to calculate the slope of the line that passes through these points as follows:

  • m = (y₂ - y₁) / (x₂ - x₁)

  • m = (9-5) / (4-2) = 4/2 = 2

  • m=2

So, the line has a slope of 2.

Step 2: Plug One point and Slope, m, into the Slope-Intercept Form Formula (y=mx+b)

Now that we know that m=2, we can start to build the equation of this line in y=mx+b form as follows:

  • y = 2x + b

For the second step, we have to select one of the two (x,y) coordinates that was given to us, plug it into the slope-intercept form equation, and solve for b as follows:

  • Let’s choose the point (2,5), where x=2 and y=5

  • y = 2x + b

  • 5 = 2 (2) + b

  • 5 = 4 + b

  • 1 = b → b = 1

We have now solved for b, and we can conclude that b=1.

Step 3: Solve for b and determine the y-intercept

Now that we know that b=1, we can write the y intercept as a coordinate point and finish the problem.

Remember that the y-intercept of a line is always written as an (x,y) coordinate where x is 0.

Final Answer: The line has an equation of y=2x + 1 and the y-intercept is at (0,1)

Figure 02 shows the step-by-step process for solving this first problem, and Figure 03 shows the graph of y=2x+1 (notice how the line passes through the two given points (2,5) and (4,9) as well as the y-intercept at (0,1).

Figure 02: How to Find Y Intercept with 2 Points (Step-by-Step)

Figure 03: The graph of y=2x+1

Now that we have solved our first how to find y intercept with 2 points problem, let’s apply what we have learned to another example.

Example B: Find y intercept with 2 points given: (-1,4) and (3,0)

 

Example B: Find the y intercept of the line passing through (-1,4) and (3,0).

Let’s go ahead and solve this next problem using the same steps as the previous example.

Step 1: Use the Given Coordinates to Find the Slope of the Line

For Example B, we know that the line passes through the points:

  • (-1,4) and (3,0)

Let’s plug these points into the slope formula to figure out the slope (m) of the line as follows:

  • m = (y₂ - y₁) / (x₂ - x₁)

  • m = (0-4) / (3-(-1)) = 4/4 = -1

  • m=-1

This line has a slope of —1.

Step 2: Plug One point and Slope, m, into the Slope-Intercept Form Formula (y=mx+b)

Now we can write the equation of the line in slope-intercept form where m=-1 as follows:

  • y = -1x + b

  • y= -x + b

Now, let’s take one of the two given points and plug it into the slope-intercept form equation to solve for b as follows:

  • Let’s choose the point (3,0), where x=3 and y=0

  • y = -x + b

  • 0 = -(3) + b

  • 0 = -3 + b

  • 3 = b → b = 3

Therefore, we know that the y-intercept (b) is equal to 3.

Step 3: Solve for b and determine the y-intercept

Finally, we can take our result from Step 2 (b=3) and use it to write the y-intercept in coordinate form.

Final Answer: The line has an equation of y=-x + 3 and the y-intercept is at (0,3)

The entire process for solving this problem is shown in Figure 04 below, and the corresponding graph is shown in Figure 05.

Figure 04: How to find y-intercept with 2 points

Figure 05: The graph of y=-x+3.

 
 

More Free Math Resources:

Free Fraction to Decimal Chart (Printable PDF)

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Free Fraction to Decimal Chart (Printable PDF)

Image: Mashup Math

Free Fraction to Decimal Chart

Are you in need of a quick reference chart for converting between fractions and decimals? Whether you are a student learning how to convert between fractions and decimals, or someone who could use a handy reference for everyday use, the free fraction to decimal chart shared on this page is the perfect tool for you.

Having a fraction to decimal conversion chart is incredibly useful for making fast and one hundred percent accurate conversions between decimals and fractions. Our free fraction to decimal chart includes 64 common fractions and their decimal equivalents. In terms of measurement, our fractions to decimals chart includes conversions for all common fractional measurement units starting at 1/64.

In the next section, you will find a link to download your free Fraction to Decimal Chart as a PDF file. Some great ways to use our free fractions to decimals chart include:

  • Saving the PDF file on your phone to reference conversions wherever you go.

  • Print the chart and have it laminated for repeated use (you can keep it in your notebook, tool box, etc.)

  • Email the PDF chart to yourself and keep it in your inbox as an accessible conversion guide.

Do you want to learn how to convert between fractions and decimals without a chart? Check out our free step-by-step lesson on converting between decimals and fractions in 3 easy steps!

 

Free Fractions to Decimals Chart (Preview)

 

Fraction to Decimal Chart Download

Click Here to Download Your free Fraction to Decimal Conversion Chart PDF

When you click the link above, a PDF window will open where you can download and/or print our free decimals to fractions chart.

Decimal to Fraction Chart: Real-World Uses

Now that you have downloaded your free Fraction to Decimal Conversion Chart, here are few ideas for some awesome real-world applications of this super hand tool:

Cooking and Baking: Many recipes include fractional portions (e.g. ⅓ cup of water, ½ pound of sugar, etc.) as suggested portion sizes, while many kitchen tools (such as digital scales) use decimal measurements. To ensure that you are following any given recipe correctly and accurately, it is important to be familiar with fraction and decimal conversions. For example, knowing that ⅓ is roughly approximate to 0.333 will allow you follow recipes and use tools that incorporate fractions or decimals.

Money: Another useful application of our fraction to decimal chart is working with money. For example, if you know that the fraction ¼ is equal to the decimal 0.25, then you can easily determine and understand things like sales prices, discounts, taxes, and overall budgeting. If you want to improve your ability to work with money and make sound financial decisions, then being able to convert between fractions and decimals is a great foundational skill that will serve you for a lifetime.

Sports: Numerical statistics are a huge part of sports, and being able to accurately convert between fractions and decimals allows you to better make sense of sports-related data. For example, if a basketball team has won 6 out of 8 games (6/8 simplifies to 3/4), we can conclude that the team has a 75% winning percentage (because 3/4 equals 0.75).

 

Having a fractions to decimals chart is a handy tool for construction professionals. (Photo by Josh Olalde on Unsplash)

 

Fractions to Decimals Chart for Construction and Home Improvement Projects

Construction and Home Improvement: Any time that you have to measure the length of something, it is super important for you to be able to easily convert between fractions and decimals. In fact, most rulers are divided by segments that each represent 1/64 of an inch, and construction professionals have to be familiar with dozens of fraction to decimal conversions (which is why many of them purposely keep a fraction to decimal chart in their toolbox for quick reference.

For example, builders must know that ⅝ of an inch is the same as 0.625 inches in order to make correct measurements, create accurate scale drawings, and to ensure that their plans are build according to the design. This is why, in construction, there is a common saying: measure twice and cut once. This is because it is imperative to get your measurements correct before you make a cut (e.g. a peice of wood or metal). Why? Because, once you cut something to size, there are no do-overs. So, you absolutely have to get your measurements right before making cuts.

So, having a fractions to decimals chart on hand is a great tool that will serve you in a variety of situations inside and outside of the classroom. By having a quick and reliable reference guide at your disposal, you can spend more focus and energy on whatever project you are working on (baking, buying, building, etc.), and less time on making mathematical calculations and conversions between fractions and decimals.

Read More Posts About Math Education:

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How to Simplify a Square Root in 3 Easy Steps

How to Simplify a Square Root in 3 Easy Steps

How to Simplify a Square Root

Step-by-Step Guide: How to Simplify a Square Root in 3 Steps

 

Free Step-by-Step Guide: Ready to learn how to simplify a square root?

 

Simplifying square roots is a useful and important math skill that every student can learn with enough practice. By learning a simple 3-step process for simplifying square roots, you can learn to quickly and correctly simplify any square root (whether it is a perfect square or not), and that is exactly what we will be doing in this free guide.

The sections below will teach you exactly how to simplify a square root using a simple step-by-step method. Together, we will recap some key concepts and vocabulary terms and then work through three examples of how to simplify a square root. Whether you are learning this skill for the very first time or you are an experienced student in need of a quick and comprehensive review, this page will share everything you need to know about how to simplify a square root.

This guide is organized based on the following sections:

You can use the text links above to jump to any section of this guide, or you can work through the sections in order. Let’s get started!

 

Preview: How to Simplify a Square Root in 3 Steps.

 

Quick Intro: Square Roots and Perfect Squares

Before we work through examples of how to simplify a square root, let’s quickly recap some important concepts and vocabulary terms related to this topic.

In math, square roots are the inverse (or opposite) operation of squaring a number (i.e. multiplying a number by itself). And, conversely, the square root of a number is the value that, when multiplied by itself, results in the number that you started with.

For example, consider the square root of 16, which can be expressed using square root notation:

  • √16

We can say that √16 equals 4 because 4 times itself (i.e. 4x4 or 4²) equals 16, therefore:

  • √16 = 4 → because 4² = 16

Numbers like 16 are called perfect squares because their square roots are whole numbers, which makes them very easy to simplify.

In fact, you are likely already familiar with how to simplify many perfect squares such as:

  • √4 = 2 → because 2² = 4

  • √9 = 3 → because 3² = 9

  • √16 = 4 → because 4² = 16

  • √25 = 5 → because 5² = 25

  • √36 = 6 → because 6² = 36

  • √49 = 7 → because 7² = 49

  • √64 = 8 → because 8² = 64

  • √81 = 9 → because 9² = 81

  • √100 = 10 → because 10² = 100

Figure 01: Perfect Squares up to 144

Make sure that you know all of the perfect squares from 1 to 144 (as shown in Figure 01 above) before moving onto the next section.

While it is relatively easy to simplify a square root of a perfect square, it is more complicated to simplify a square root of a non-perfect square, which is what we will be focusing on in the next section, where, for example, we will look at finding the perfect squares of numbers like 18, 75, and 112.

How to Simplify a Square Root Examples

Now we are ready to use the following simple 3-step method for simplifying square roots to solve three practice problems:

Steps: How to Simplify a Square Root

  • Step 1: Identify two factors where one of them is a perfect square (choose the largest perfect square factor), and rewrite as a product.

  • Step 2: Split the product using two square root symbols.

  • Step 3: Simplify the perfect square and rewrite your final answer.

Example A: Simplify √18

 

Example A: Simplify √18

In our first example, we want to simplify a square root of a non-perfect square: √18.

We can simplify a square root like √18 by using our three step strategy as follows:

Step 1: Identify two factors where one of them is a perfect square.

Let’s start by listing the factors of 18:

  • Factors of 18: 1, 2, 3, 6, 9 and 18

Notice that 18 has one factor that is a perfect square: 9, and that:

  • 9 x 2 = 18

Since 9 x 2 equals 18, the two numbers that we are going to use for Step 2 are 9 and 2.

Step 2: Split the product using two square root symbols.

For the second step, we can use the factors from Step 1 to rewrite √18 as follows:

  • √18 = √(9 x 2) = √9 x √2

We can “split” the square root in this way because of the product property of square roots, which says that:

  • √(A x B) = √(A) x √(B)

(provided that A and B are non-negative numbers).

So we now have a new equivalent product that represents √18, which is…

  • √9 x √2

Step 3: Simplify the perfect square and rewrite your final answer.

For our final step, notice that one of the square roots in our new expression, √9, is a perfect square. Since we know that √9 = 3, we can rewrite √9 as 3 as follows:

  • √9 x √2 = 3 x √2

Now, all that we have to do is rewrite the result, 3 x √2, as 3√2 , and we have solved the problem!

Final Answer: √18 = 3√2

Figure 02 below shows the step-by-step process for simplifying this square root.

 

Figure 02: How to Simplify a Square Root in 3 Steps.

 

Now that you have learned how to simplify a square root, let’s gain some more experience by working through another example.

Example B: Simplify √75

 

Example B: Simplify √75

We can solve this next example by using the three steps that we used to solve the previous example.

Step 1: Identify the factors of 75 and determine the largest perfect square factor.

We can begin by listing the factors of 75:

  • Factors of 75: 1, 3, 5, 15, 25 and 75

Notice that 75 has one perfect square factor, 25, and that:

  • 25 x 3 = 75

Step 2: Split the product using two square root symbols.

Next, we can use the factors from Step 1 to rewrite √75as follows:

  • √75 = √(25 x 3) = √25 x √3

Step 3: Simplify and solve.

Finally, we can simplify √25 as 5 (since √25=5) and rewrite the expression as follows:

  • √25 x √3 = 5 x √3

We can now rewrite 5 x √3 as 5√3 and we can conclude that:

Final Answer: √75 = 5√3

The entire process for solving this problem is shown in Figure 03 below.

 

Figure 03: Multiplying fractions with whole numbers Example B solved.

 

Example C: Simplify √112

 

Example C: Simplify √112

For our final step-by-step example of how to simplify a square root, let’s take on a triple-digit number using our three-step method.

Step 1: Identify the factors of 112 and pick out the largest perfect square factor.

  • Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56 and 112

Notice 112 has two perfect square factors: 4 and 16. In cases like this, always choose the largest perfect square factor (16 in this case).

Now that we have identified our perfect square factor, we can say that:

  • w16 x 7 = 112

Step 2: Split the product using two square root symbols.

Next, we can write √112 as follows:

  • √112 = √(16 x 7) = √16 x √7

Step 3: Simplify and solve.

For the final step, we can simplify √16 as 4 and rewrite the expression as follows:

  • √16 x √7 = 4 x √7

Now we just have to rewrite 4 x √7 as 4√7 and we have solved the problem!

Final Answer: √112 = 4√7

The three-step process for solving Example C is shown in Figure 03 below

 

Figure 03: How to Simplify a Square Root in 3 Steps.

 
 
 

More Free Math Resources:

How to Multiply Fractions with Whole Numbers—Step-by-Step

How to Multiply Fractions with Whole Numbers—Step-by-Step

How to Multiply Fractions with Whole Numbers

Step-by-Step Guide: How to Multiply Fractions with Whole Numbers, Multiplying Fractions by Whole Numbers Examples

 

Free Step-by-Step Guide: How to multiply fractions with whole numbers explained.

 

Multiplying fractions with whole numbers can seem like a challenging math skill, but, with some simple strategies and an easy step-by-step method, it can be a relatively easy task that any student can master.

In this free guide, we will work through several examples of how to multiply fractions with whole numbers using a simple step-by-step process. As long as you can follow three easy steps, you will be able to confidently and accurately solve a variety of math problems where you have to multiply fractions with whole numbers.

You can work through the sections in this free guide in sequential order, or you can click on any of the quick-links below to jump to one particular section.

Quick Intro: Multiply Fractions with Whole Numbers

Before we dive into any examples of how to multiply fractions with whole numbers, let’s do a quick introductory review of what it means when we multiply fractions with whole numbers.

For example, let’s consider the example 3 x 1/4:

  • 3 is the whole number

  • 1/4 is the fraction

Whenever you multiply a fraction by a whole number, you are really just performing repeated addition (i.e. you are adding the fraction to itself a number of repeated times that is determined by the whole number).

If we think of multiplication in terms of repeated addition, we can rewrite 3 x 1/4 as follows:

  • 3 x 1/4 = 1/4 + 1/4 + 1/4

And, since 1/4 + 1/4 + 1/4 is equal to 3/4, we can conclude that:

  • 3 x 1/4 = 1/4 + 1/4 + 1/4 = 3/4

Final Answer: 3 x 1/4 = 3/4

 

Figure 01: How to Multiply Fractions with Whole Numbers Using Repeated Addition.

 

The process of multiplying fractions with whole numbers using repeated addition is shown in Figure 01.

While we will not use repeated addition to solve the examples in this guide, understanding this basic relationship between multiplication and repeated addition is the first step to easily learning how to multiply fractions with whole numbers.

Now, let’s go ahead and work through some examples of multiplying fractions with whole numbers using a simple 3-step method.

Multiplying Fractions by Whole Numbers Examples

For all of the multiplying fractions with whole numbers examples that follow, we will be using the following 3-step method for solving:

  • Step 1: Rewrite the whole number as a fraction with a denominator of 1.

  • Step 2: Multiply the numerators together and then multiply the denominators together.

  • Step 3: Simplify if possible.

 

Example A: Multiplying whole numbers with fractions.

 

Example A: Multiply 2 x 1/3

For our first example, we have to multiply the whole number 2 by the fraction ⅓, and we will do that by following our 3-step process as follows:

Step 1: Rewrite the whole number as a fraction with a denominator of 1.

First, we can rewrite the whole number, 2, as a fraction with a numerator of 1 as follows:

  • 2 → 2/1

Now we have a new multiplication problem:

  • 2 x 1/3 → 2/1 x 1/3

Step 2: Multiply the numerators together and then multiply the denominators together.

Now that we have a new expression with two fractions being multiplied by each other, we can perform multiplication by multiplying the numerators together and then multiplying the denominators together as follows:

  • 2/1 x 1/3 = (2x1) / (1x3) = 2/3

After completing Step 2, we are left with the fraction 2/3.

Step 3: Simplify if possible.

Finally, we just have to check if our result from Step 2, 2/3, can be simplified.

In this case, the fraction 2/3 can not be simplified because there is no common factor between the numerator (2) and the denominator (3) other than 1.

Final Answer: 2 x 1/3 = 2/3
The complete step-by-step process for solving this first example is shown in Figure 02 below.

 

Figure 02: How to multiply fractions with whole numbers step-by-step.

 

Now that you are familiar with our 3-step method for multiplying fractions with whole numbers, let’s gain some more experience by using them to solve another example.

 

Example B: 2/3 × 34 = ?

 

Example B: Multiply 2/3 x 4

For this next example, notice how, in this case, the first term is a fraction and the second term is the whole number (this is a reverse situation compared to Example A). However, the commutative property of multiplication tells us that the order of the terms does not matter, so we can still use our 3-step process to solve this problem as follows:

Step 1: Rewrite the whole number as a fraction with a denominator of 1.

We can leave the fraction 2/3 alone and rewrite the whole number 4 as a fraction with a denominator of 1 as follows:

  • 2/3 x 4 → 2/3 x 4/1

Step 2: Multiply the numerators together and then multiply the denominators together.

Next, we can take our new expression and simply multiply the numerators together, and then the denominators together as follows:

  • 2/3 x 4/1 = (2x4) / (3x1)

  • (2x4) / (3x1) = 8/3

After completing the second step, our result is 8/3. We can now move onto the third and final step.

Step 3: Simplify if possible.

Let’s see if our result from Step 2, 8/3, can be simplified.

Since there is no common factor (other than 1) between the numerator (8) and the denominator (3), we know that the fraction 8/3 can not be simplified. However, since 8/3 is an improper fraction, we do have the option of either expressing it as 8/3 or as the mixed number 2 2/3 (in this case, we will choose to express our answer as 8/3).

Final Answer: 2/3 x 4 = 8/3
Figure 03 below illustrates our step-by-step process for solving this second example.

 

Figure 03: Multiplying fractions with whole numbers Example B solved.

 
 

5Example C: 10 × 1/5 = ?

 

Example C: Multiply 10 x 1/5

Let’s gain some more practice using our 3-step method for multiplying fractions with whole numbers.

Step 1: Rewrite the whole number as a fraction with a denominator of 1.

In this example, we have to rewrite the whole number (10) as a fraction with a denominator of 1.

  • 10 x 1/5 → 10/1 x 1/5

Step 2: Multiply the numerators together and then multiply the denominators together.

Next, let’s take our new expression, 10/1 x 1/5, and multiply the numerators and denominators together:

  • 10/1 x 1/5 = (10x1) / (1x5)

  • (10x1) / (1x5) = 10/5

Finally, let’s move onto Step 3 to see if our result (10/5) can be simplified.

Step 3: Simplify if possible.

In this case, the numerator (10) and the denominator (5) share a common factor of 5. So, we can simplify 10/5 by dividing both the numerator and denominator by 5 as follows:

  • 10 ÷ 5 = 2

  • 5 ÷ 5 = 1

After dividing, we can say that 10/5 = 2/1, and we can rewrite 2/1 as 2.

Final Answer: 10 x 1/5 = 10/5 = 2/1 = 2
The entire process of solving Example C is shown in Figure 04 below illustrates our step-by-step process for solving this second example.

 

Figure 05: Example C Solved.

 
 

Example D: 7 × 5/6 = ?

 

Example D: Multiply 7 x 5/6

Let’s work through one final example of multiplying fractions with whole numbers.

Step 1: Rewrite the whole number as a fraction with a denominator of 1.

In this case, we can rewrite the whole number (7) as a fraction as follows:

  • 7 x 5/6 → 7/1 x 5/6

Step 2: Multiply the numerators together and then multiply the denominators together.

Next, we can multiply the two fractions together as follows:

  • 7/1 x 5/6 = (7x5) / (1x6)

  • (7x5) / (1x6) = 35/6

Step 3: Simplify if possible.

Finally, we have to see if our result from Step 2 (35/6) can be simplified. Since 35 and 6 do not share any common factors besides 1, we know that it can not be simplified any further.

Final Answer: 7 x 5/6 = 35/6
Figure 06 shows how we solved this final example.

 

Figure 06: How to Multiply Fractions with Whole Numbers.

 
 
 

More Free Math Resources:

3rd Grade Word Problems—Free PDF Worksheet Library

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3rd Grade Word Problems—Free PDF Worksheet Library

3rd Grade Word Problems—Free PDF Worksheets with Answer Keys

Looking for Free Printable 3rd Grade Math Worksheets?

 

Are you looking for free and engaging 3rd grade math word problems worksheets to share with your students?

 

Whether you are a 3rd grade classroom teacher or a parent of a 3rd grade student, you could use some free and engaging word problems for 3rd grade students to help them to develop important foundational math skills. This page shares a huge collection of 3rd grade word problems that cover topics including addition, subtraction, two-step problems, elapsed time, and more.

Jump to a Topic:

Whether you’re in need of worksheets for addition or subtraction word problems, two-step word problems for 3rd grade students, telling time and elapsed time word problems, area and perimeter word problems, or even measurement word problems, the 3rd grade word problems worksheet collection below will surely have something for you.

 

All of our 3rd grade math word problems worksheets are easy to print and share in your classroom.

 

3rd Grade Word Problems: Single-Digit Addition

▶ Math Skill Focus: Simple Addition, Adding Single-Digit Numbers

The following 3rd Grade Word Problems focus on basic addition in real-world scenarios.

You can preview any of the worksheets in this collection by clicking on any of the image boxes below, and you can download the corresponding PDF file by clicking on any of the blue text links. Each PDF file will include a set of word problems for 3rd grade students followed by a complete answer key on the last page.

For example, Dotty made 2 sugar cookies and 7 chocolate chip cookies. How many cookies did she make in total?

Worksheet A

Worksheet B

Worksheet C

These 3rd grade word problems worksheets focus on the basic foundational skill of adding single-digit numbers in a real-world context. They require students to identify key information, use mathematical thinking, correctly perform simple addition, and express their answer in writing.

3rd Grade Word Problems: Double-Digit Addition

▶ Math Skill Focus: Simple Addition, Adding Double-Digit Numbers

Once your students have mastered solving single-digit word problems for 3rd grade, the next step is to work through similar problems that involve adding two-digit numbers to solve word problems related to real-world scenarios.

For example, Elly is making donuts to sell at a local bake sale. He bakes 24 chocolate donuts, 21 vanilla donuts, and 15 cinnamon donuts. How many donuts did Elly bake?

Worksheet A

Worksheet B

Worksheet C

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3rd Grade Word Problems: Single-Digit Subtraction

▶ Math Skill Focus: Simple Subtraction, Subtracting Single-Digit Numbers

The following 3rd Grade Word Problems focus on basic subtraction in real-world scenarios. Once students have mastered these types of 3rd grade math word problems, they can move onto the double-digit subtraction word problems in the next section.

For example, Ruben planted 12 flower seeds in his garden. After the first week, 3 of the seeds sprouted. After the second week, 5 more of the seeds sprouted. How may of the seeds did not sprout?

Worksheet A

Worksheet B

Worksheet C

3rd Grade Word Problems: Double-Digit Subtraction

▶ Math Skill Focus: Simple Subtraction, Subtracting Double-Digit Numbers

Once your students are comfortable with solving 3rd grade math word problems involving single-digit subtraction, they can take the next step to solving problems involving finding the difference of two-digit numbers in a word problem format.

For example, Bethany has to cleanup after a dinner party. She has to wash 28 dishes in total. She has already washed 12 of the dishes. How many dishes does she have left to wash?

Worksheet A

Worksheet B

Worksheet C

In the next section, we will share some word problems for 3rd grade that focus on mixed addition and subtraction, where students will have to extend their thinking to using the context clues from each problem to determine whether they have to perform addition or subtraction to solve each problem.

3rd Grade Word Problems: Mixed Addition and Subtraction

▶ Math Skill Focus: Mixed Addition and Subtraction, Word Problem Solving

This next set of 3rd grade math word problems require students to use their math skills to determine whether or not they have to use addition or subtraction to solve each word problem.

For example, There were 24 notebooks in a bin. Students took 11 for their backpacks. How many notebooks are left in the bin?

3rd Grade Word Problems: Two-Step Word Problems

▶ Math Skill Focus: Use addition and/or subtraction to solve two-step word problems

One of the biggest differences between 2nd grade math and 3rd grade math is that 3rd graders begin learning how to solve word problems that require multiple steps to solve.

For example, Joey has 10 apples. He gives 4 apples to Josh and 3 apples to Jane. How many apples does Joey have left?

Worksheet A

Worksheet B

Worksheet C

The next two sections will share word problems for 3rd grade students that focus on two auxiliary topics: elapsed time and area and perimeter of rectangles.

3rd Grade Word Problems: Elapsed Time

▶ Math Skill Focus: Solve word problems involving time, units of time (minutes, hours, etc.), and elapsed time

Outside of learning how to solve word problems involving operations, another important 3rd grade math topic is dealing with time, units of time, and elapsed time. This section shares three 3rd grade word problems worksheets related to elapsed time.

For example, Jackson started his homework at 3:15 PM. He finished at 3:50 PM. How many minutes did he spend on completing his homework?

Worksheet A

Worksheet B

Worksheet C

3rd Grade Word Problems: Area and Perimeter of Rectangles

▶ Math Skill Focus: Solve word problems involving area and perimeter of rectangles

This final section includes 3rd grade math word problems worksheets on finding the area and/or perimeter of rectangular figures in real-world scenarios.

For example, Aaron is building a small rectangular flower box that is 5 feet long and 3 feet wide. What is the area, in square feet, of Aaron’s flower box?

Note that Worksheet A focuses on area only, Worksheet focuses on perimeter only, and Worksheet C involved mixed area and perimeter 3rd grade math word problems.

Worksheet A

Worksheet B

Worksheet C

Looking for More 3rd Grade Practice Worksheets?

Be sure to visit our Free 3rd Grade Math Worksheet Library, which shares hundreds of free PDF practice worksheets for a variety of 3rd grade topics.

Helpful Hints for Solving 3rd Grade Math Word Problems

The focus of our 3rd grade word problems worksheets is to give early elementary students to apply their procedural math skills to real-world situations and scenarios. Rather than just asking students to solve a simple math operation problem (e.g. 9 + 7 = ?), these types of problems are more advanced, as they require students to apply reading comprehension and to use context clues to find answers.

Since math word problems are more advanced, many students will initially struggle with them, and it takes time and practice to get better at solving 3rd grade word problems (one-step or two-step) whether they involve addition, subtraction, multiplication, mixed operations, elapsed time, or area and perimeter.

If your 3rd grader is having a hard time with solving any of the problems on any of our 3rd grade word problems worksheets, here are a few helpful hints to improve their chances of correctly solving any given word problem:

  • Read Each Question Carefully: One of the biggest reasons why 3rd graders struggle with word problems is because they fail to read each question carefully and correctly assess exactly what the problem is asking them to do. Before students attempt to solve a math word problem, they need to read to problem, identify and keywords or important information, and identify exactly what the question is asking them to do. Many students will benefit greatly from using a marker to underline key information or by using a colored highlighter.

  • Ask Questions Before You Start: While this advice applies to solving any math problem, it is particularly useful whenever students are working on math word problems. Once you have carefully read a question and identify the important information, you should ask yourself “what is this question asking me to do?” and “what will the final answer look like?”. These two questions help students come up with a plan before they attempt to solve a problem. For example, if a question asks students to find the area of a rectangle, they should be aware that their final answer will have to be in terms of square units.

Helpful Hints for Solving 3rd Grade Word Problems: Always show your work and answer using complete sentences.

  • Show Your Work: All of our 3rd grade word problems worksheets require students to show their work. But, what does showing your work actually look like? In addition to students writing out how they performed their operations, they should also be encouraged to use additional visual aids such as drawing diagrams or using tally marks. For example, when solving an area of a rectangle word problem, it is incredibly helpful to draw a rectangle and label the length of each side before attempting to solve the problem. Or, if a question involves combining a pile of 13 apples with a pile of 9 apples, students can draw each pile and then count the total number of apples.

  • Write Your Final Answer in Sentence Form: In math, word problems typically have “word answers”, so students should get used to expressing their final answer to any word problem by using a complete sentence. While this is a general rule, it is good practice for students. For example, when solving the problem “Ethan read 32 pages on Monday and 21 pages on Tuesday. He wants to read 120 pages this week. How many more pages does he need to read? “, the final answer is not just 67, but “Ethan needs to read 67 more pages.”

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