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Add Two Fractions with Different Denominators - Practice with Fun Math Worksheet

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Practice math problems like Add Two Fractions with Different Denominators with interactive online worksheets for 5th Graders. Splash math offers easy to understand fun math lessons aligned with common core for K-5 kids and homeschoolers.

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Example 1: Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether?

Analysis: To solve this problem, we will add two fractions with like denominators.

Solution:

Answer: Rachel rode her bike for three-fifths of a mile altogether.

Example 2: Stefanie swam four-fifths of a lap in the morning and seven-fifteenths of a lap in the evening. How much farther did Stefanie swim in the morning than in the evening?

Analysis: To solve this problem, we will subtract two fractions with unlike denominators.

Solution:

Answer: Stefanie swam one-third of a lap farther in the morning.

Example 3: It took Nick five-thirds of an hour to complete his math homework on Monday, three-fourths of an hour on Tuesday, and five-sixths of an hour on Wednesday. How many hours did he take to complete his homework altogether?

Analysis: To solve this problem, we will add three fractions with unlike denominators. Note that the first is an improper fraction.

Solution:

Answer: It took Nick three and one-fourth hours to complete his homework altogether.

Example 4: Dina added five-sixths of a bag of soil to her garden. Her neighbor Natasha added eleven-eighths bags of soil to her garden. How much more soil did Natasha add than Dina?

Analysis: To solve this problem, we will subtract two fractions with unlike denominators.

Solution:

Answer:

Example 5: At a pizza party, Diego and his friends ate three and one-fourth cheese pizzas and two and three-fourths pepperoni pizzas. How much pizza did they eat in all?

Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having like denominators.

Solution:

Answer: Diego and his friends ate six pizzas in all.

Example 6: The Cocozzelli family drove their car for five and five-sixths days to reach their vacation home, and then drove for six and one-sixth days to return home. How much longer did it take them to drive home?

Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having like denominators.

Solution:

Answer: The Cocozzelli family took one-half more days to drive home.

Example 7: A warehouse has 12 and nine-tenths meters of tape in one area of the building, and eight and three-fifths meters of tape in another part. How much tape does the warehouse have in all?

Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having unlike denominators.

Solution:

Answer: The warehouse has 21 and one-half meters of tape in all.

Example 8: An electrician has three and seven-sixteenths cm of wire. He needs only two and five-eighths cm of wire for a job. How much wire does he need to cut?

Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having unlike denominators.

Solution:

Answer: The electrician needs to cut 13 sixteenths cm of wire.

Example 9: A carpenter had a piece of wood that was 15 feet in length. If he needs only 10 and five-twelfths feet of wood, then how much wood should he cut?

Analysis: To solve this problem, we will subtract a mixed number from a whole number.

Solution:

Answer: The carpenter needs to cut four and seven-twelfths feet of wood.

Summary: In this lesson we learned how to solve word problems involving addition and subtraction of fractions and mixed numbers. We used the following skills to solve these problems:

1. Add fractions with like denominators.

2. Subtract fractions with like denominators.

3. Find the LCD.

4. Add fractions with unlike denominators.

5. Subtract fractions with unlike denominators.

6. Add mixed numbers with like denominators.

7. Subtract mixed numbers with like denominators.

8. Add mixed numbers with unlike denominators.

9. Subtract mixed numbers with unlike denominators.

Exercises

Directions: Subtract the mixed numbers in each exercise below. Be sure to simplify your result, if necessary. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.
Note: To write the fraction three-fourths, enter 3/4 into the form. To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.

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solving word problems by adding and subtracting fractions and mixed numbers

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Solving Word Problems by Adding and Subtracting Fractions and Mixed Numbers

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Example 1: Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether? Analysis: To solve this problem, we will add two fractions with like denominators. Solution: Answer: Rachel rode her bike for three-fifths of a mile altogether.

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Interactive Math Lesson | Adding and Subtracting Fractions with Unlike Denominators

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I Know It is an elementary math practice website. Try out this fifth grade level math lesson for adding and subtracting fractions with unlike denominators practice with your class today!

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Add & Subtract Unlike Denominators: StudyJams! Math | Scholastic.com

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Fractions with unlike denominators are difficult to work with. In this activity, students will find common denominators that will make solving problems easier.

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Butterfly Fractions: an Easily Remembered Strategy for Adding and Subtracting Fractions Using Cross Multiplication

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Butterfly Fractions: an Easily Remembered Strategy for Adding and Subtracting Fractions Using Cross Multiplication

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click the second (numerator and denominator 5 worksheets) complete practice problems.

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Practice Fractions with Line and Circle Models

Many of the worksheets will let learners shade number lines and circles to illustrate fraction concepts. The circle and number line images on the following worksheets were made with the Fraction Designer pages that can be found on this web site.

These worksheets are pdf documents that may be reproduced for your own use and for your student's use.

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Practice Fractions with Line and Circle Models Many of the worksheets will let learners shade number lines and circles to illustrate fraction concepts. The circle and number line images on the following worksheets were made with the Fraction Designer pages that can be found on this web site.

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Add fractions with unlike denominators by creating area models

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In this lesson you will learn how to add fractions with unlike denominators by creating area models.

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part 1: create your own notes from the following page: (Click the pizza) videos, examples, songs all easy ways to learn.

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A fraction like says we have 3 out of the 4 parts the whole is divided into.

To add fractions there are Three Simple Steps:

Step 1: Make sure the bottom numbers (the denominators) are the same

Step 2: Add the top numbers (the numerators), put that answer over the denominator

Step 3: Simplify the fraction (if possible)

Example:

Step 1. The bottom numbers (the denominators) are already the same. Go straight to step 2.

Step 2. Add the top numbers and put the answer over the same denominator:

Step 3. Simplify the fraction:

In picture form it looks like this:

Example:

Step 1: The bottom numbers are different. See how the slices are different sizes?

We need to make them the same before we can continue, because we can't add them like that.

The number "6" is twice as big as "3", so to make the bottom numbers the same we can multiply the top and bottom of the first fraction by 2, like this:

× 2

× 2

Important: you multiply both top and bottom by the same amount,
to keep the value of the fraction the same

Now the fractions have the same bottom number ("6"), and our question looks like this:

The bottom numbers are now the same, so we can go to step 2.

Step 2: Add the top numbers and put them over the same denominator:

In picture form it looks like this:

Step 3: Simplify the fraction:

In picture form the whole answer looks like this:

With Pen and Paper

And here is how to do it with a pen and paper (press the play button):

A Rhyme To Help You Remember
♫ "If adding or subtracting is your aim,
The bottom numbers must be the same!
♫ "Change the bottom using multiply or divide,
But the same to the top must be applied,
♫ "And don't forget to simplify,
Before its time to say good bye"
Example:

Again, the bottom numbers are different (the slices are different sizes)!

But let us try dividing them into smaller sizes that will each be the same:

The first fraction: by multiplying the top and bottom by 5 we ended up with :

× 5

× 5

The second fraction: by multiplying the top and bottom by 3 we ended up with :

× 3

× 3

The bottom numbers are now the same, so we can go ahead and add the top numbers:

The result is already as simple as it can be, so that is the answer:

Making the Denominators the Same

In the previous example how did we know to cut them into ths to make the denominators the same? We simply multiplied the two denominators together (3 × 5 = 15).

Read about the two main ways to make the denominators the same here:

They both work, use which one you prefer!

Example: Cupcakes

You want to make and sell cupcakes:

A friend can supply the ingredients, if you give them ¹/₃ of sales

And a market stall costs ¹/₄ of sales

How much is that altogether?

First make the bottom numbers (the denominators) the same.

And multiply top and bottom of ¹/ ₄ by 3:

Now do the calculations:

Answer: of sales go in ingredients and market costs.

Adding Mixed Fractions

We have a special (more advanced) page on Adding Mixed Fractions.

930,931, 1399,932, 1400,933, 1401, 1402, 3564, 3565

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To add fractions there are Three Simple Steps: Step 1: Make sure the bottom numbers (the denominators) are the same, Step 2: Add the numerators, put that answer over the denominator, Step 3: Simplify the fraction (if needed)

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part 2:

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Basic Math Lesson for Kids - Adding and Subtracting Fractions

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Visually subtracting fractions with unlike denominators

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part 3:

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formula for adding and subtracting unlike denominators fractions - Google Search

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grade 5  free math games practice common core standards

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Add and Subtract Fractions with Unlike Denominators - Grade 5 - Practice with Math Games

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Solve addition and subtraction word problems with fractions with unlike denominators.

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Adding and Subtracting Fractions with Unlike Denominators

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part 4:

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Page 1 of 3

This is a bit tricky, but you'll think it's easy once you get used to it!

Let's try this:

The main rule of this game is that we can't do anything until the denominators are the same!

We need to find something called the least common denominator (LCD)... It's really just the LCM of our denominators, 2 and 3 .

The LCM of 2 and 3 is 6. So, our LCD 6.

We need to make this our new denominator...

Change the :

Change the :

Now we can do it!
Head on over to the next page to continue...

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Adding and Subtracting Fractions With Different Denominators

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Page 1 of 3 This is a bit tricky, but you'll think it's easy once you get used to it! Let's try this: The main rule of this game is that we can't do anything until the denominators are the same! We need to find something called the least common denominator (LCD)...