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Welcome to our Subtracting Fractions Worksheets page. We have a range of worksheets designed to help students learn to subtract fractions with both like and unlike denominators.
Our sheets range in difficulty from easier supported sheets with like denominators to harder sheets with different denominators and improper fractions.
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Here you will find support pages and our subtracting fraction calculator to help you to learn about how to subtract fractions.
For those of you who like to see some algebra, here is the simple formula for subtracting two fractions:
Formula for subtracting two fractions
\[{a \over b} - {c \over d} = {ad - bc \over bd} \]
Here you will find a selection of Fraction worksheets designed to help your child practice how to subtract fractions.
The sheets are carefully graded so that the easiest sheets come first, and the most difficult sheet is the last one.
Next to each sheet is a description of the math skills involved.
Using these sheets will help your child to:
These skills and worksheets are aimed at 3rd through to 7th grade.
The easiest sheets with like denominators are suitable for 3rd graders (sheet 1)
The hardest sheets with subtracting improper fractions with different denominators are more suitable for 7th graders.
If you are looking to subtract fractions which have the same denominator, take a look at our sheets below.
Like Denominators
Sheet 1: the easiest sheet, no simplifying or converting needed.
Sheet 2: like denominators; simplifying needed.
Sheet 3: like denominators; simplifying and/or converting to a mixed number.
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This quick quiz tests your knowledge and skill at subtracting fractions with like denominators.
Sheet 1: easy to convert denominators with one denominator a multiple of the other; no simplifying or converting needed
Sheet 2: easy to convert denominators with one denominator a multiple of the other; simplifying needed
Sheet 3: easy to convert denominators; simplifying and/or converting to a mixed number needed
Sheet 4: harder to convert denominators; no simplifying or converting needed
Sheet 5: harder to convert denominators; simplifying needed
Sheet 6: harder to convert denominators; simplifying and/or converting needed
Sheet 1: hard to convert denominators; simplifying and/or converting needed
This quick quiz tests your knowledge and skill at subtracting a range of fractions.
Take a look at some more of our resources similar to these.
Adding and subtracting fractions works differently from adding and subtracting integers or decimals.
If the two fractions have the same denominator, then it is quite easy to add or subtract the fractions by simply adding the numerators together.
If the fractions have different denominators, then they need to be changed into equivalent fractions with the same denominator before they can be added or subtracted.
The printable learning fractions pages below contains more support, examples and practice adding and subtracting fractions.
This is a pre-requisite for knowing how to add and subtract fractions.
Our Least Common Multiple Calculator will find the lowest common multiple of 2 or more numbers.
It will tell you the best multiple to convert the denominators of the fractions you are subtracting into.
There are also some worked examples.
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Explore this compilation of subtracting fractions worksheets to sail smoothly through the steps of fraction subtraction and mixed-number subtraction! Encompassing diverse exercises ranging from subtracting unit fractions to proper or improper fractions to mixed numbers with same or different denominators to missing fractions in a subtraction equation, these pdf worksheets are a must-have for students of grade 3 through grade 6. Walk through some of these worksheets for free!
» Subtracting Fractions using Number Line
» Subtracting Like Fractions
» Subtracting Fraction from Whole Numbers
» Subtracting Unlike Fractions
» Subtracting Mixed Numbers
» Subtracting Fractions Word Problems
Subtracting Fractions using Number Lines
Establish fraction subtraction among kids using the number line diagrams in these pdf worksheets. They observe the number line models with fractional intervals, draw hops, and figure out the difference.
(54 Worksheets)
Missing Like Fractions - All Fractions
Spice up your practice session with these fraction subtraction exercises! To ensure thorough practice, all types of fractions are brought into play. Add or subtract the given fractions to find the missing ones.
Missing Variables - Like Fractions
Stretch your understanding of subtracting fractions beyond the ordinary by finding the values of variables in these subtraction equations! Add or subtract the constant terms; isolate the variable; solve for its value.
Subtracting Unit Fractions - Proper
Get used to the fact that a unit fraction is one part of a whole, and subtract two such fractions in a jiffy! Apply the cross-multiplication method or find the LCM of the denominators, and obtain the difference.
Missing Unlike Fractions - All Fractions
Subtract equations where either the minuend or the subtrahend is missing! Plug them in by performing addition or subtraction of the known fractions or mixed numbers with unlike denominators.
Missing Variables - Unlike Fractions
Relish the joy of shifting from arithmetic to variable equations involving unlike fractions and mixed numbers! Rearrange the equation to make the unknown the subject and solve. Great for 5th grade and 6th grade!
Subtracting Unit Fractions - Mixed Numbers
Recognize mixed numbers having unit fractions in their fractional parts with these subtracting fractions worksheets! Subtract the whole parts; convert the unlike fractional parts to like ones and subtract them swiftly.
Subtracting Unit Fractions - Mixed Review
Offering a revision of subtracting unit fractions and mixed numbers involving unit fractions, these pdf subtraction of fractions worksheets are indispensable for 3rd grade, 4th grade, and 5th grade children.
Subtracting Fractions and Mixed Numbers | Combined Review
Bestowing a comprehensive review of subtracting like fractions, unlike fractions, mixed numbers with same and different denominators this brand-new printable resource is meticulously designed to test the regrouping skills of children!
Subtracting Like Fractions Worksheets
Plunge into practice with this stock of printable subtracting like fractions worksheets to get the knack of finding the difference between fractions with like denominators!
(67 Worksheets)
Subtracting Fractions from Whole Numbers Worksheets
Rejoice in the sheer pleasure of subtracting a part from a whole with these subtracting fractions from whole numbers worksheets! Generate equivalent fractions to the whole numbers and set the ball rolling!
(16 Worksheets)
Subtracting Unlike Fractions Worksheets
Lay your hands on our subtracting unlike fractions worksheets for grade 4 and grade 5 and knock into shape your fraction subtraction skills! Subtract fractions with unlike denominators and simplify the difference.
Subtracting Mixed Numbers Worksheets
Take a whack at these subtracting mixed numbers worksheets and hone in on subtracting mixed numbers with like and unlike denominators! Subtract the whole and fractional parts individually.
(77 Worksheets)
Subtracting Fractions Word Problems Worksheets
Get a vivid picture of fraction subtraction in real life with these pdf worksheets on subtracting fractions word problems. Subtract fractions from whole numbers, like fractions, unlike fractions, and more!
(15 Worksheets)
Related Worksheets
» Fraction Addition
» Fraction Multiplication
» Fraction Division
» Fractions on a Number Line
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In today’s post, we’re going to see how to solve some of the problems that we’ve introduced in Smartick: fraction word problems. They appear during the word problems section at the end of the daily session.
We’re going to look at how to solve problems involving addition and subtraction of fractions, including mixed fractions (the ones that are made up of a whole number and a fraction).
Try and solve the fraction word problems by yourself first, before you look for the solutions and their respective explanations below.
Problem nº 1.
This is an example of a problem involving the addition of a whole number and a fraction.
The simplest way to show the number of cookies I ate is to write it as a mixed number. And the data given in the word problem gives us the result: 9 biscuits and 5 / 6 of a biscuit = 9 5 / 6 biscuits.
In this example, we have to subtract two fractions with the same denominator.
To calculate how full the gas tank is, we have to subtract both fractions. Since we are given fractions, the best way to present the solution is in the form of a fraction. Additionally, we’re dealing with two fractions with the same denominator, so we just have to subtract the numerators of both fractions to get the result. 8 / 10 – 4 / 10 = 4 / 10
This problem requires us to subtract a mixed number and a fraction.
To solve this problem, we need to subtract the number of episodes that were downloaded this morning from the total number of episodes that are now downloaded.
To do this, we need to change the mixed number into a fraction: the 5 becomes 60 / 12 (5 x 12 = 60) and we add it to the fraction 60 / 12 + 8 / 12 = 68 / 12 .
We’ve converted the mixed number 5 8 / 12 to 68 / 12 . Now we just have to subtract the number of episodes that were downloaded yesterday ( 7 / 12 ), 68 / 12 – 7 / 12 = 61 / 12 .
Hopefully, you didn’t need the explanations and were able to solve them yourself without any help!
In the following video tutorials, you can learn a bit more about fractions. And if you would like to learn more math concepts, check out Smartick’s Youtube channel !
If you would like to practice more fraction word problems like these and others, log in to Smartick and enjoy learning math.
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It is really great. It helps me a lot. Thank you
Subtracting fractions questions given here cover all types of fractions including like, unlike and mixed. These involve both numerical and word problems of subtracting fractions. Practising various questions on subtracting fractions will enhance your understanding of performing various arithmetic operations on fractions. Let’s learn how to subtract fractions using the solved problems given below.
What is the Subtraction of Fractions?
In mathematics, the subtraction of fractions involves finding the difference between two or more fractions with the same denominators or different denominators. The subtraction of fractions involves the following cases.
Also, check: Subtracting fractions
1. Subtract: 3 – (4/13)
3 – (4/13)
Here, 3 is a whole number and 4/13 is a fraction.
= (39 – 4)/13
Therefore, 3 – (4/13) = 35/13
2. Evaluate the following:
(i) (9/14) – (5/14)
(ii) (7/10) – (3/10)
Here, the denominators are the same, i.e., they are like fractions.
Thus, (9/14) – (5/14) = (9 – 5)/14
On further simplification, we have;
(9/14) – (5/14) = 4/14 = 2/7
= (7 – 3)/10
Thus, (7/10) – (3/10) = 4/10 = ⅖
3. Compute the following.
(i) (10/12) – (⅓)
(ii) (⅔) – (5/20)
= (⅚) – (⅓)
By taking the LCM of denominators, we have;
= (5 – 2)/6
Therefore, (10/12) – (⅓) = ½
= (⅔) – (¼)
= (8 – 3)/12
Therefore, (⅔) – (5/20) = 5/12
4. Find the value of \(\begin{array}{l}14\frac{5}{9}-21\frac{7}{15}\end{array} \) .
\(\begin{array}{l}14\frac{5}{9}-21\frac{7}{15}\end{array} \)
Here, both terms are mixed fractions.
Let’s convert the mixed fractions into improper fractions.
\(\begin{array}{l}14\frac{5}{9}-21\frac{7}{15}\\=\frac{131}{9}-\frac{322}{15}\\=\frac{655-966}{45}\\=\frac{-311}{45}\\=-6\frac{41}{45} \end{array} \)
Therefore, \(\begin{array}{l}14\frac{5}{9}-21\frac{7}{15}=-6\frac{41}{45} \end{array} \)
5. Subtract 5 from 11 ⅗.
11 ⅗ – 5
Here, 11 ⅗ is a mixed fraction.
11 ⅗ = (11 × 5 + 3)/5 = 58/5
Now, 11 ⅗ – 5
= (58/5) – 5
= (58 – 25)/5
Therefore, 11 ⅗ – 5 = 33/5.
6. Find the value of (23/4) – (5/3).
(23/4) – (5/3)
By taking the LCM of denominators, we get;
= (23 × 3 – 5 × 4)/12
= (69 – 20)/12
Thus, (23/4) – (5/3) – 4 1/12.
7. Evaluate: \(\begin{array}{l}\frac{4}{3}-\left ( 1\frac{11}{12}-\frac{5}{4} \right )\end{array} \) .
\(\begin{array}{l}\frac{4}{3}-\left ( 1\frac{11}{12}-\frac{5}{4} \right )\\=\frac{4}{3}-\left ( \frac{23}{12}-\frac{5}{4} \right )\\=\frac{4}{3}-\left ( \frac{23-15}{12}\right )\\=\frac{4}{3}-\frac{8}{12}\\=\frac{4}{3}-\frac{2}{3}\\=\frac{4-2}{3}\\=\frac{2}{3}\end{array} \)
8. A father leaves his money to his four children. The first received 1/3, the second received 1/6, and the third received 2/5. How much did the remaining child receive (assume that the total money is one whole)?
Total money = 1
The amount received by the first child = 1/3
The amount received by the second child = 1/6
The amount received by the third child = 2/5
The amount received by the last child = 1 – (1/3) – (1/6) – (2/5)
= (30 – 10 – 5 – 12)/30 {since the LCM of 3, 6, and 5 is 30}
= (30 – 27)/30
Thus, the remaining child will receive 1/10th of the father’s money.
9. Vinu worked for 14/3 hours on Friday and his friend Shan worked for 25/6 hours. How many more hours than Shan did Vinu work?
Number of hours worked by Vinu = 14/3
Number of hours worked by Shan = 25/6
Difference = 14/3 – 25/6
= (28 – 25)/6
Thus, Vinu worked ½ hour, i.e., half an hour more than Shan.
10. Arnav bought some sweets that weighed 4 2/3 kg. If he gave 3 1/6 kg to his friends, what is the amount of sweets he has left?
Sweets bought by Arnav = 4 2/3 kg
Sweets given to his friends = 3 1/6 kg
Sweets left with Arnav = 4 2/3 – 3 1/6
= 14/3 – 19/6
= (28 – 19)/6
Therefore, Arnav is left with 1 1/2 kg of sweets.
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Subtraction of fractions is an arithmetic operation to find the difference between two fractions. To subtract two like fractions, we have to subtract their numerators and write the difference over the common denominator . To subtract two unlike fractions, we must first convert them into like fractions by taking the LCM of the denominators. We can also subtract a whole number and fraction by writing the whole number in fractional form, for example, $3 = \dfrac{3}{1}$. Let us learn more about subtracting fractions and fraction subtraction problems in detail in this article.
Fractions are referred to as a part of a whole. A group of fractions can be classified as like fractions and unlike fractions based on the denominator value . Like fractions are those that have the same denominator. For example, $\dfrac{3}{4}$ and $\dfrac{5}{4}$. While unlike fractions are those that have different denominators, for example, $\dfrac{2}{3}$ and $\dfrac{4}{7}$. We can find the difference between two like fractions, unlike fractions and fractions and whole numbers .
The steps for subtracting fractions are listed below:
Step 1: Identify whether the given fractions have the same denominator or different denominators.
Step 2: In the case of like fractions, subtract the numerators and write their difference over the common denominator. For example, $\dfrac{5}{7} - \dfrac{2}{7} = \dfrac{5 - 2}{7} = \dfrac{3}{7}$.
On the other hand, unlike fractions, find the LCM of the denominators.
Step 3: Multiply the numerator and denominator of each fraction with a whole number to get the LCM in the denominator. It is done to convert unlike fractions to like fractions.
Step 4: Subtract their numerators and write the difference over the common denominator.
This is how we subtract two fractions.
Fractions with the same denominator can be easily subtracted. To subtract fractions with the same denominators, follow the given steps:
Subtract the numerator.
Write the common denominator as the denominator of the resulting fraction.
Now, reduce the result to the lowest fraction, if possible.
Example: $\dfrac{4}{5}-\dfrac{2}{5}=\dfrac{2}{5}$
Two fractions with different or unequal denominators can be subtracted by following these steps:
First, take the LCM of the denominators.
We convert the given fractions to like fractions with the denominator as the LCM.
Now, subtract the numerators and write their difference over the common denominator.
Simplify, if needed.
Just like you have subtracted two fractions, you can also subtract fractions from whole numbers and vice-versa. Any integer can be written in fractional form by writing 1 as the denominator. For example, 7 can be written as $\dfrac{7}{1}$. Therefore, to subtract fractions and whole numbers, write them in the fractional form first. Then you can easily find the difference using the same rules for subtracting two unequal fractions. Consider the following example of subtracting a fraction from an integer: $2 - \dfrac{1}{4}$
Convert the integer, 2 to fractional form, i.e. $\dfrac{2}{1}$
Now, to subtract $\dfrac{2}{1} - \dfrac{1}{4}$, the least common multiple of 1 and 4 is 4. Multiply the numerator and denominator of $\dfrac{2}{1}$ by 4 to get 4 in the denominator.
$\dfrac{2}{1} - \dfrac{1}{4}$
= $\dfrac{2 \times 4}{1 \times 4} - \dfrac{1}{4}$
= $\dfrac{8}{4} - \dfrac{1}{4}$
= $\dfrac{7}{4}$
Thus, the subtraction of an integer and fraction, $2 - \dfrac{1}{4} = \dfrac{7}{4}$.
Q 1. Jack jumped $4 \dfrac{1}{7}$ m in the long jump competition. Shane jumped $3 \dfrac{2}{9}$ m. Who jumped longer, and how many meters?
Ans: Jack jumped $=4 \dfrac{1}{7} \mathrm{~m}=\dfrac{29}{7} \mathrm{~m}=\dfrac{261}{63} \mathrm{~m}$
Shane jumped $=3 \dfrac{2}{9} \mathrm{~m}=\dfrac{29}{9} \mathrm{~m}=\dfrac{203}{63} \mathrm{~m}$
Because $261>203$, Jack jumped more.
$\text { Difference }=\dfrac{261}{63} \mathrm{~m}-\dfrac{203}{63} \mathrm{~m}$
$=\dfrac{261-203}{63} \mathrm{~m}$
$=\dfrac{58}{63} \mathrm{~m}$
Therefore, Jack jumped $\dfrac{58}{63} \mathrm{~m}$ more than Shane.
Q 2. Mary gave $\dfrac{1}{8}$ part of her money to Shelly. What fraction of money is left with her?
Ans: Money given to Shelly $=\dfrac{1}{8}$
Remaining money $=1-\dfrac{1}{8}$
$=\dfrac{1}{1}-\dfrac{1}{8}$
$=\dfrac{8}{8}-\dfrac{1}{8}$
$=\dfrac{7}{8}$
Thus, the fraction of money left is $=\dfrac{7}{8}$.
Q 1. Sharon spent $4 \dfrac{3}{7}$ hours studying maths and playing tennis. How long did she study if she played tennis for $2 \dfrac{1}{4}$ hours?
Ans: $\dfrac{61}{28}$
Q 2. Rex had some money. He spent $\dfrac{1}{6}$ of it on Monday, $\dfrac{3}{8}$ on Thursday, and $\dfrac{1}{4}$ on Wednesday. What part of the money is still left with him?
Ans: $\dfrac{5}{24}$.
Q 3. Ron used $3 \dfrac{1}{4}$ litres of paint from a tin of $5 \dfrac{1}{2}$, to colour the walls of his room. What fraction of paint is still left in the tin?
Ans: $\dfrac{9}{4}$ litres.
In this article, we have learned about fractions. Then we learned about the different rules of how to solve subtracting fractions word problems having like as well as unlike denominators with the help of an example. We became aware of solving, unlike denominators, by taking the help of LCM of the denominators, then multiplying with the numerator and calculating the difference. We also did numerous word problems on fraction subtraction. Kindly solve the given unsolved problems for practice.
1. What are the rules for adding fractions?
The basic rule of adding fractions is to first ensure whether the denominators are the same. If the denominators are different, first convert them to equal fractions by taking LCM and then solve the fractions by the usual addition.
2. How to add Improper Fractions?
Improper fractions are added in the same way as proper fractions. Some steps are given below:
If the fractions are the same, add the numerator keeping the same denominator.
To add different fractions, take the lowest common multiple of the denominators, convert them to equivalent fractions, and then add them as equal fractions.
When the addition is complete, and the answer is an improper fraction, convert the fraction to a mixed one and write it in its simplest form.
3. Why are addition and subtraction important?
Addition and subtraction play a very important role in our daily life activities, which involve counting, such as billing at the store, buying groceries, travelling, the speed of a vehicle, checking weight, and so on. It helps us understand situational-based problems. Hence, addition and subtraction are important in our life.
What is addition and subtraction of fractions, methods of addition and subtraction of fractions, addition and subtraction of mixed numbers, solved examples on addition and subtraction of fractions, practice problems on addition and subtraction of fractions, frequently asked questions on addition and subtraction of fractions.
Addition and subtraction of fractions are the fundamental operations on fractions that can be studied easily using two cases:
A fraction represents parts of a whole. For example, the fraction 37 represents 3 parts out of 7 equal parts of a whole. Here, 3 is the numerator and it represents the number of parts taken. 7 is the denominator and it represents the total number of parts of the whole.
Adding and subtracting fractions is simple and straightforward when it comes to like fractions. In the case of unlike fractions, we first need to make the denominators the same. Let’s take a closer look at both these cases.
Before adding and subtracting fractions, we first need to make sure that the fractions have the same denominators.
When the denominators are the same, we simply add the numerators and keep the denominator as it is. To add or subtract unlike fractions, we first need to learn how to make the denominators alike. Let’s learn how to add fractions and how to subtract fractions in both cases.
More Worksheets
The rules for adding fractions with the same denominator are really simple and straightforward.
Let’s learn with the help of examples and visual bar models.
Addition of Like Fractions
Here are the steps to add fractions with the same denominator:
Step 1: Add the numerators of the given fractions.
Step 2: Keep the denominator the same.
Step 3: Simplify.
$\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$ …$c \neq 0$
Example 1: Find $\frac{1}{4} + \frac{2}{4}$ .
$\frac{1}{4} + \frac{2}{4} = \frac{1 + 2}{4} = \frac{3}{4}$
We can visualize this addition using a bar model:
Example 2: $\frac{1}{8} + \frac{3}{8} = \frac{1 + 3}{8} = \frac{4}{8} = \frac{1}{2}$
Subtraction of Like Fractions
Here are the steps to subtract fractions with the same denominator:
Step 1: Subtract the numerators of the given fractions.
Step 3: Simplify.
$\frac{a}{c}\;-\;\frac{b}{c} = \frac{a \;-\; b}{c}$ …$c \neq 0$
Example 1: Find $\frac{4}{6} \;-\; \frac{1}{6}$.
$\frac{4}{6}\;-\;\frac{1}{6} = \frac{4-1}{6} = \frac{3}{6} = \frac{1}{2}$
Addition and subtraction of fractions with unlike denominators can be a little bit tricky since the denominators are not the same. So, we need to first convert the unlike fractions into like fractions. Let’s look at a few ways to do this!
Addition of Unlike Fractions
We can make the denominators the same by finding the LCM of the two denominators. Once we calculate the LCM, we multiply both the numerator and the denominator with an appropriate number so that we get the LCM value in the denominator.
Example: $\frac{3}{5} + \frac{3}{2}$
Step 1: Find the LCM (Least Common Multiple) of the two denominators.
The LCM of 5 and 2 is 10.
Step 2: Convert both the fractions into like fractions by making the denominators same.
$\frac{3 \times 2}{5 \times 2} = \frac{6}{10}$
$\frac{3 \times 5}{2 \times 5} = \frac{15}{10}$
Step 3: Add the numerators. The denominator stays the same.
$\frac{6}{10} + \frac{15}{10} = \frac{21}{10}$
Step 4: Convert the resultant fraction to its simplest form if the GCF of the numerator and denominator is not 1.
In this case, GCF (21,10) $= 1$
The fraction $\frac{21}{10}$ is already in its simplest form.
Thus, $\frac{3}{5} + \frac{3}{2} = \frac{21}{10}$
Subtraction of Unlike Fractions
Let’s learn how to subtract fractions when denominators are not the same. To subtract unlike fractions, we use the LCM method. The process is similar to what we discussed in the previous example.
Example: $\frac{5}{6} \;-\; \frac{2}{9}$
Step 1: Find the LCM of the two denominators.
LCM of 6 and $9 = 18$
Step 2: Convert both the fractions into like fractions by making the denominators same.
$\frac{5 \times 3}{6 \times 3} = \frac{15}{18}$
$\frac{2 \times 2}{9 \times 2} = \frac{4}{18}$
Step 3: Subtract the numerators. The denominator stays the same.
$\frac{15}{18} \;-\; \frac{4}{18} = \frac{11}{18}$
In this case, the GCF (11,18) $= 1$
So, it is already in its simplest form.
Thus, $\frac{5}{6}\;-\; 29 = \frac{11}{18}$
A mixed number is a type of fraction that has two parts: a whole number and a proper fraction. It is also known as a mixed fraction. Any mixed number can be written in the form of an improper fraction and vice-versa.
Adding and subtracting mixed fractions is done by converting mixed numbers into improper fractions .
Addition and Subtraction of Mixed Fractions with Same Denominators
The steps of adding and subtracting mixed numbers with the same denominators are the same. The only difference is the operation.
Step 1: Convert the given mixed fractions to improper fractions.
Step 2: Add/Subtract the like fractions obtained in step 1.
Step 3: Reduce the fraction to its simplest form.
Step 4: Convert the resulting fraction into a mixed number.
Example 1: $2\frac{1}{5} + 1\frac{3}{5}$
$2\frac{1}{5} = \frac{(5 \times 2) + 1}{5} = \frac{11}{5}$
$1\frac{3}{5} = \frac{(5 \times 1) + 3}{5} = \frac{8}{5}$
Thus, $2\frac{1}{5} + 1\frac{3}{5} = \frac{11}{5} + \frac{8}{5} = \frac{19}{5}$
Converting $\frac{19}{5}$ into a mixed number, we get
$\frac{19}{5} = 3\frac{4}{5}$
Example 2: $2\frac{1}{5} + 1\frac{3}{5} = \frac{11}{5} \;-\; \frac{8}{5} = \frac{3}{5}$
Addition and Subtraction of Mixed Fractions with Unlike Denominators
Step 2: Convert both the fractions into like fractions by finding the least common denominator.
Step 3: Add the fractions. (or subtract the fractions.)
Step 4: Reduce the fraction if possible or convert back to a mixed number
Let us understand the addition of mixed numbers with unlike denominators with the help of an example.
Example 1: Find the value of $1\frac{3}{5} + 2\frac{1}{2}$.
Convert the given mixed fractions to improper fractions.
$1\frac{3}{5} = \frac{8}{5}$ and $2\frac{1}{2} = \frac{5}{2}$
Step 2: Convert both the fractions into like fractions by making the denominators the same.
Here, LCM of 5 and 2 is 10.
Thus, $\frac{8 \times 2}{5 \times 2} = \frac{16}{10}$ and $\frac{5\times 5}{2 \times 5} = \frac{25}{10}$
Step 3: Add the fractions by adding the numerators.
$\frac{16}{10} + \frac{25}{10} = \frac{41}{10}$
Step 4: Convert back into a mixed number.
Thus, $\frac{41}{10}$ will become $4\frac{1}{10}$
Therefore, $1\frac{3}{5} + 2\frac{1}{2} = 4\frac{1}{10}$
Here’s an example for subtraction. It follows the same steps.
Example 2 : $6\frac{1}{2} \;-\; 1\frac{3}{4}$
Step 1: Convert the mixed numbers into improper fractions.
$6\frac{1}{2} \;-\; 1\frac{3}{4} = \frac{13}{2} \;-\; \frac{7}{4}$
Step 2: Make the denominators equal.
LCM of 2 and 4 is 4.
$\frac{13 \times 2}{2 \times 2} = \frac{26}{4}$
Step 3: Subtract the fractions.
$\frac{26}{4} \;-\; \frac{7}{4} = \frac{19}{4}$
Step 4: Convert the fraction as a mixed number.
$\frac{19}{4} = 4\frac{3}{4}$
Thus, $6\frac{1}{2} \;-\; 1\frac{3}{4} = 4\frac{3}{4}$
In this article, we have learned about addition and subtraction of fractions (like fractions, unlike fractions, mixed fractions), methods of addition and subtraction of these fractions along with the steps. Let’s solve some examples on adding and subtracting fractions to understand the concept better.
Solution:
Here, the denominators are the same.
Thus, we add the numerators by keeping the denominators as it is.
$\frac{2}{4} + \frac{1}{4} = \frac{2 + 1}{4}$
$\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$
2. Find the sum of the fractions $\frac{3}{5}$ and $\frac{5}{2}$ by using the LCM method.
$\frac{3}{5}$ and $\frac{5}{2}$ are unlike fractions.
The LCM of 2 and 5 is 10.
Thus, we can write
$\frac{3}{5} + \frac{5}{2} = \frac{3 \times 2}{5 \times 2} + \frac{5 \times 5}{2 \times 5}$
$= \frac{6}{10} + \frac{25}{10}$
$= \frac{6}{10} + \frac{25}{10}$
$= \frac{31}{10}$
Thus, $\frac{3}{5} + \frac{5}{2} = \frac{31}{10}$
3. Find $\frac{4}{16} + \frac{5}{8}$.
Solution:
To add two fractions with different denominators, we first need to find the LCM of the denominators.
The LCM of 16 and 8 is 16.
$\frac{4}{16} + \frac{5}{8} = \frac{4 \times 1}{16\times 1} + \frac{5 \times 2}{8 \times 2}$
$= \frac{10}{16} + \frac{4}{16}$
$= \frac{14}{16}$
$= \frac{7}{8}$
4. From a rope $12\frac{1}{2}$ ft. long, a $7 \frac{6}{8}\;-$ ft-long piece is cut off. Find the length of the remaining rope.
Total length of the rope $= 12\frac{1}{2}$ ft.
Length of the rope that was cut off $= 7 \frac{6}{8}$ ft.
The length of the remaining rope $= 12\frac{1}{2} \;-\; 7 \frac{6}{8}$
$12\frac{1}{2} \;-\; 7 \frac{6}{8} = \frac{25}{2} \;-\; \frac{62}{8}$
$= \frac{25 \times 4}{2 \times 4} \;-\; \frac{62 \times 1}{8\times 1}$
$= \frac{100}{8} \;-\; \frac{62}{8}$
$= \frac{38}{8}$
$= \frac{19}{4}$
Converting it into a mixed fraction, $\frac{19}{4}$ becomes $4 \frac{3}{4}$.
Thus, the length of the remaining rope is $4\frac{3}{4}$ ft.
Attend this quiz & Test your knowledge.
$\frac{7}{24} + \frac{5}{16} =$, what is the least common denominator of $\frac{1}{2}$ and $\frac{1}{3}$, $\frac{3}{6} \;-\; \frac{1}{6} =$, what equation does the following figure represent.
How do we add and subtract negative fractions?
Negative fractions are simply fractions with a negative sign. The steps to add and subtract the negative fractions remain the same. We need to follow the rules for addition/subtraction with negative signs.
How can we convert an improper fraction into a mixed number?
To convert an improper fraction into a mixed number, we divide the numerator by the denominator. The denominator stays the same. The quotient represents the whole number part. The remainder represents the numerator of the mixed number.
Example: $\frac{14}{3} = 4\; \text{R}\; 2$
Quotient $= 4$
Remainder $= 2$
$\frac{14}{3} = 4\frac{2}{3}$
How do we divide two fractions?
To divide one fraction by another, we multiply the first fraction by the reciprocal of the second fraction.
$\frac{A}{B} \div \frac{C}{D} = \frac{A}{B} \times \frac{D}{C}$
For example, $\frac{1}{2} \div \frac{3}{5} = \frac{1}{2} \times \frac{5}{3} = \frac{5}{6}$
What are the rules of adding and subtracting fractions?
How do we add and subtract fractions with whole numbers?
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On this page, you can practice addition and subtraction of fractions. Each practice set will automatically include both addition and subtraction problems.
The options are:
Note: ALL answers have to be given as mixed numbers, when possible. In other words, your answer cannot be left as an improper fraction.
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Fractions - addition, fractions - subtraction, fractions - multiplication, fractions - division.
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This fraction word problem requires subtraction. The fact that the problem is asking how much more black pepper the recipe needs is an indication that 3/4 is bigger than 1/4. However, it does not hurt to check! 3/4 - 1/4 = 2/4 = 1/2. The black pepper is 1/2 of a teaspoon more than the red pepper.
There are 3 simple steps to subtract fractions. Step 1. Make sure the bottom numbers (the denominators) are the same. Step 2. Subtract the top numbers (the numerators). Put the answer over the same denominator. Step 3. Simplify the fraction (if needed). Example:
Example #1: 1/2 - 3/7. Step One: Identify whether the denominators are the same (like) or different (unlike). In this example, the fractions have unlike denominators (they are different). The first fraction's denominator is 2 and the other's is 7. Step Two: If the example involves like denominators, move onto Step Three.
Like & unlike denominators. Below are our grade 5 math word problem worksheet on adding and subtracting fractions. The problems include both like and unlike denominators, and may include more than two terms. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4. Worksheet #5 Worksheet #6.
Add bells and whistles to your fraction subtraction practice with our printables. Grade 4, grade 5, and grade 6 kids find the LCM of different denominators and obtain the difference between two mixed numbers. Download the set. Explore our subtracting fractions word problems worksheets abounding in fun realistic word problems for a high-flying ...
Problem. Subtract. 7 2 − 7 6 =. 3:36. Subtracting fractions with unlike denominators introduction. Report a problem. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for ...
Go through the below steps to subtract the unlike fractions. Step 1: Determine the LCM of the denominator values. Step 2: Convert the denominator to the LCM value by multiplying the numerator and denominator using the same number. Step 3: Subtract the numerators, once the fractions have the same denominator values.
To do this, multiply the numerator and the denominator of each fraction by the same number so that it results in a denominator of 24. 24. This will give you an equivalent fraction for each fraction in the problem. [Math Processing Error]8 × 37 × 3 = 2421 3 × 81 × 8 = 248. Now you can subtract the fractions.
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: Add fractions with like denominators. Subtract fractions with like denominators.
Subtracting Fractions Worksheets. Here you will find a selection of Fraction worksheets designed to help your child practice how to subtract fractions. The sheets are carefully graded so that the easiest sheets come first, and the most difficult sheet is the last one. Next to each sheet is a description of the math skills involved.
Course: 5th grade > Unit 4. Lesson 5: Adding and subtracting fractions with unlike denominators word problems. Adding fractions word problem: paint. Subtracting fractions word problem: tomatoes. Add and subtract fractions word problems. Add and subtract fractions: FAQ.
Subtracting Fractions Worksheets. Explore this compilation of subtracting fractions worksheets to sail smoothly through the steps of fraction subtraction and mixed-number subtraction! Encompassing diverse exercises ranging from subtracting unit fractions to proper or improper fractions to mixed numbers with same or different denominators to ...
To solve this problem, we need to subtract the number of episodes that were downloaded this morning from the total number of episodes that are now downloaded. To do this, we need to change the mixed number into a fraction: the 5 becomes 60 / 12 (5 x 12 = 60) and we add it to the fraction 60 / 12 + 8 / 12 = 68 / 12 .
Subtracting fractions questions given here cover all types of fractions including like, unlike and mixed.These involve both numerical and word problems of subtracting fractions. Practising various questions on subtracting fractions will enhance your understanding of performing various arithmetic operations on fractions.
Solving subtraction problems with fractions. Subtracting fractions is a lot like regular subtraction. If you can subtract whole numbers, you can subtract fractions too! Click through the slideshow to learn how to subtract fractions. Let's use our earlier example and subtract 1/4 of a tank of gas from 3/4 of a tank.
The steps for subtracting fractions are listed below: Step 1: Identify whether the given fractions have the same denominator or different denominators. Step 2: In the case of like fractions, subtract the numerators and write their difference over the common denominator. For example, $\dfrac {5} {7} - \dfrac {2} {7} = \dfrac {5 - 2} {7} = \dfrac ...
Solving for the missing fraction (Opens a modal) Practice. Add fractions with unlike denominators Get 5 of 7 questions to level up! ... Add and subtract fractions word problems Get 3 of 4 questions to level up! Quiz 3. Level up on the above skills and collect up to 240 Mastery points Start quiz. Up next for you:
Here are the steps to add fractions with the same denominator: Step 1: Add the numerators of the given fractions. Step 2: Keep the denominator the same. Step 3: Simplify. a c + b c = a + b c … c ≠ 0. Example 1: Find 1 4 + 2 4. 1 4 + 2 4 = 1 + 2 4 = 3 4. We can visualize this addition using a bar model:
On this page, you can practice addition and subtraction of fractions. Each practice set will automatically include both addition and subtraction problems. The options are: You can limit the fractions in the problems to like fractions (fractions with the same denominator), for example: 1/6 + 4/6. You can limit the script to use only proper ...
Math explained in easy language, plus puzzles, games, quizzes, videos and worksheets. For K-12 kids, teachers and parents. Fraction Worksheets ... Fractions - Subtraction. Worksheet. Example. Fractions (Same Denominator) 15 − 25. Unit Fractions. 13 − 19. Easy Proper Fractions. 38 − 27. Harder Proper Fractions. 712 − 1525.
Input proper or improper fractions, select the math sign and click Calculate. This is a fraction calculator with steps shown in the solution. If you have negative fractions insert a minus sign before the numerator. So if one of your fractions is -6/7, insert -6 in the numerator and 7 in the denominator. Sometimes math problems include the word ...
Learn how to add and subtract fractions with unlike denominators. They watch the process of finding a common denominator, then practice adding and subtracting the fractions to solve the problems. Questions Tips & Thanks
Since the fractions have a like denominator, subtract the numerators. 11 3 = 32 3. Write the answer as a mixed number. Divide 11 by 3 to get 3 with a remainder of 2. 81 3 − 42 3 = 32 3. Since addition is the inverse operation of subtraction, you can check your answer to a subtraction problem with addition.
Problem-solving Schools expand_more. What is the Problem-solving Schools initiative? ... which are problems grouped by topic. list Number and Place Value. Age. ... Try these activities which all involve addition and subtraction. list Multiplication and Division. Age. 5 to 11 Challenge level. These tasks will help you to think about ...