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Fractions Calculator With Step by Step Solution

The online fractions calculator can add fractions, subtract fractions, multiply fractions and divide any kind of fractions with the same or different denominators and get a complete step-by-step solution.


If the fraction does not have a whole-number part, leave this field blank. If the fraction is negative, put a minus in the whole part. The (+) button allows you to insert the previous result into a fraction and perform further calculations.

Adding fractions with the same denominator

Add two fractions with the same denominators.
4  +
34
6  =
34
4 + 6  =
34
10 =
34
5
17
≈ 0,2941

Step by step solution

Add the numerators of the fractions, and leave the denominator the same.
4  +
34
6  =
34
4 + 6  =
34
10
34
Simplify the fraction.
10
34

4  +
34
6  =
34
4 + 6  =
34
10 =
34
5
17

Adding fractions with different denominators

Add two fractions with different denominators
7  +
15
9  =
14
7 ∙ 14  +
210
9 ∙ 15  =
210
98  +
210
135  =
210
98 + 135  =
210
233 =
210
1 23
210
≈ 1,1095

Step by step solution

Let's make the denominator for
7  
15
and
9  
14
the same. In order for the fractions to have a common denominator, we calculate the least common multiple (LCM) of the denominators of the first and second fractions.
LCM( 15 ; 14 ) = 210

Divide the LCM 210 by the denominator of the first fraction and the denominator of the second fraction.
210 : 15 = 14
210 : 14 = 15

Now we write the LCM( 15 ; 14 ), into the denominator of each fraction, and multiply the numerator of each fraction by the result of dividing the LCM by the corresponding denominator.
7  +
15
9  =
14
7 ∙ 14  +
210
9 ∙ 15  =
210
98  +
210
135  
210
Add the numerators of the fractions, and leave the denominator the same.
7  +
15
9  =
14
7 ∙ 14  +
210
9 ∙ 15  =
210
98  +
210
135  =
210
98 + 135  =
210
233
210
Simplify the fraction.
233
210

7  +
15
9  =
14
7 ∙ 14  +
210
9 ∙ 15  =
210
98  +
210
135  =
210
98 + 135  =
210
233 =
210
1 23
210

Adding mixed fractions with different denominators

Add two mixed fractions with different denominators.
7 3  +
8
4 9  =
12
59  +
8
57  =
12
59 ∙ 3  +
24
57 ∙ 2  =
24
177  +
24
114  =
24
177 + 114  =
24
291 =
24
97 =
8
12 1
8
= 12,125

Step by step solution

Convert mixed fractions
7 3  
8
and
4 9  
12
into improper fractions. To do this, for each fraction, we will leave the denominator the same, and write the sum in the numerator, where the first term is the product of the denominator and the whole-number part, and the second is the numerator.
7 3  +
8
4 9  =
12
(8∙7) + 3  +
8
(12∙4) + 9  =
12
59  +
8
57  
12
Let's make the denominator for
59  
8
and
57  
12
the same. In order for the fractions to have a common denominator, we calculate the least common multiple (LCM) of the denominators of the first and second fractions.
LCM( 8 ; 12 ) = 24

Divide the LCM 24 by the denominator of the first fraction and the denominator of the second fraction.
24 : 8 = 3
24 : 12 = 2

Now we write the LCM( 8 ; 12 ), into the denominator of each fraction, and multiply the numerator of each fraction by the result of dividing the LCM by the corresponding denominator.
7 3  +
8
4 9  =
12
59  +
8
57  =
12
59 ∙ 3  +
24
57 ∙ 2  =
24
177  +
24
114  
24
Add the numerators of the fractions, and leave the denominator the same.
7 3  +
8
4 9  =
12
59  +
8
57  =
12
59 ∙ 3  +
24
57 ∙ 2  =
24
177  +
24
114  =
24
177 + 114  =
24
291
24
Simplify the fraction.
291
24

7 3  +
8
4 9  =
12
59  +
8
57  =
12
59 ∙ 3  +
24
57 ∙ 2  =
24
177  +
24
114  =
24
177 + 114  =
24
291 =
24
97 =
8
12 1
8

Subtracting fractions with the same denominator

Subtract two fractions with the same denominator.
6  -
8
2  =
8
6 - 2  =
8
4 =
8
1
2
= 0,5

Step by step solution

Subtract the numerator of the second fraction from the numerator of the first fraction, and leave the denominator the same.
6  -
8
2  =
8
6 - 2  =
8
4
8
Simplify the fraction.
4
8

6  -
8
2  =
8
6 - 2  =
8
4 =
8
1
2

Subtracting fractions with different denominators

Subtract two fractions with different denominators.
5  -
12
3  =
9
5 ∙ 3  -
36
3 ∙ 4  =
36
15  -
36
12  =
36
15 - 12  =
36
3 =
36
1
12
≈ 0,0833

Step by step solution

Let's make the denominator for
5  
12
and
3  
9
the same. In order for the fractions to have a common denominator, we calculate the least common multiple (LCM) of the denominators of the first and second fractions.
LCM( 12 ; 9 ) = 36

Divide the LCM 36 by the denominator of the first fraction and the denominator of the second fraction.
36 : 12 = 3
36 : 9 = 4

Now we write the LCM( 12 ; 9 ), into the denominator of each fraction, and multiply the numerator of each fraction by the result of dividing the LCM by the corresponding denominator.
5  -
12
3  =
9
5 ∙ 3  -
36
3 ∙ 4  =
36
15  -
36
12  
36
Subtract the numerator of the second fraction from the numerator of the first fraction, and leave the denominator the same.
5  -
12
3  =
9
5 ∙ 3  -
36
3 ∙ 4  =
36
15  -
36
12  =
36
15 - 12  =
36
3
36
Simplify the fraction.
3
36

5  -
12
3  =
9
5 ∙ 3  -
36
3 ∙ 4  =
36
15  -
36
12  =
36
15 - 12  =
36
3 =
36
1
12

Subtracting mixed fractions with different denominators

Subtract two mixed fractions with different denominators.
7 3  -
17
3 6  =
19
122  -
17
63  =
19
122 ∙ 19  -
323
63 ∙ 17  =
323
2318  -
323
1071  =
323
2318 - 1071  =
323
1247 =
323
3 278
323
≈ 3,8607

Step by step solution

Convert mixed fractions
7 3  
17
and
3 6  
19
into improper fractions. To do this, for each fraction, we will leave the denominator the same, and write the sum in the numerator, where the first term is the product of the denominator and the whole-number part, and the second is the numerator.
7 3  -
17
3 6  =
19
(17∙7) + 3  -
17
(19∙3) + 6  =
19
122  -
17
63  
19
Let's make the denominator for
122  
17
and
63  
19
the same. In order for the fractions to have a common denominator, we calculate the least common multiple (LCM) of the denominators of the first and second fractions.
LCM( 17 ; 19 ) = 323

Divide the LCM 323 by the denominator of the first fraction and the denominator of the second fraction.
323 : 17 = 19
323 : 19 = 17

Now we write the LCM( 17 ; 19 ), into the denominator of each fraction, and multiply the numerator of each fraction by the result of dividing the LCM by the corresponding denominator.
7 3  -
17
3 6  =
19
122  -
17
63  =
19
122 ∙ 19  -
323
63 ∙ 17  =
323
2318  -
323
1071  
323
Subtract the numerator of the second fraction from the numerator of the first fraction, and leave the denominator the same.
7 3  -
17
3 6  =
19
122  -
17
63  =
19
122 ∙ 19  -
323
63 ∙ 17  =
323
2318  -
323
1071  =
323
2318 - 1071  =
323
1247
323
Simplify the fraction.
1247
323

7 3  -
17
3 6  =
19
122  -
17
63  =
19
122 ∙ 19  -
323
63 ∙ 17  =
323
2318  -
323
1071  =
323
2318 - 1071  =
323
1247 =
323
3 278
323

Multiplication of fractions

Let's multiply two fractions.
6  ⋅
13
7  =
19
6 ⋅ 7  =
13 ⋅ 19
42
247
≈ 0,17

Step by step solution

Multiply the denominators and numerators of fractions.
6  ⋅
13
7  =
19
6 ⋅ 7  =
13 ⋅ 19
42
247

Multiplication of mixed fractions

Let's multiply two mixed fractions.
12 2  ⋅
15
5 9  =
23
182  ⋅
15
124  =
23
182 ⋅ 124  =
15 ⋅ 23
22568 =
345
65 143
345
≈ 65,4145

Step by step solution

Convert mixed fractions
12 2  
15
and
5 9  
23
into improper fractions. To do this, for each fraction, we will leave the denominator the same, and write the sum in the numerator, where the first term is the product of the denominator and the whole-number part, and the second is the numerator.
12 2  ⋅
15
5 9  =
23
(15 ⋅ 12) + 2  ⋅
15
(23 ⋅ 5) + 9  =
23
182  ⋅
15
124  
23

Multiply the denominators and numerators of fractions.
12 2  ⋅
15
5 9  =
23
182  ⋅
15
124  =
23
182 ⋅ 124  =
15 ⋅ 23
22568
345
Simplify the fraction.
22568
345

12 2  ⋅
15
5 9  =
23
182  ⋅
15
124  =
23
182 ⋅ 124  =
15 ⋅ 23
22568 =
345
65 143
345
Let's multiply two fractions.
9 45  ⋅
15
7  =
34
180  ⋅
15
7  =
34
180 ⋅ 7  =
15 ⋅ 34
1260 =
510
42 =
17
2 8
17
≈ 2,4706

Step by step solution

Convert mixed fraction
9 45  
15
into improper. To do this, leave the denominator the same, and write the sum in the numerator, where the first term is the product of the denominator and the whole-number part, and the second is the numerator.
9 45  ⋅
15
7  =
34
(15 ⋅ 9) + 45  ⋅
15
7  =
34
180  ⋅
15
7  
34

Multiply the denominators and numerators of fractions.
9 45  ⋅
15
7  =
34
180  ⋅
15
7  =
34
180 ⋅ 7  =
15 ⋅ 34
1260
510
Simplify the fraction.
1260
510

9 45  ⋅
15
7  =
34
180  ⋅
15
7  =
34
180 ⋅ 7  =
15 ⋅ 34
1260 =
510
42 =
17
2 8
17

Division of fractions

Let's divide Fractions.
7  ∶
9
14  =
8
7  ⋅
9
8  =
14
7 ⋅ 8  =
9 ⋅ 14
56 =
126
4
9
≈ 0,4444

Step by step solution

Let's swap the numerator and denominator of the second fraction.
7  ∶
9
14  =
8
7  ⋅
9
8  
14
Multiply the denominators and numerators of fractions.
7  ∶
9
14  =
8
7  ⋅
9
8  =
14
7 ⋅ 8  =
9 ⋅ 14
56
126
Simplify the fraction.
56
126

7  ∶
9
14  =
8
7  ⋅
9
8  =
14
7 ⋅ 8  =
9 ⋅ 14
56 =
126
4
9

Division of mixed fractions

Let's divide one mixed fraction by another.
9 5  ∶
7
3 31  =
5
68  ∶
7
46  =
5
68  ⋅
7
5  =
46
68 ⋅ 5  =
7 ⋅ 46
340 =
322
170 =
161
1 9
161
≈ 1,0559

Step by step solution

Convert mixed fractions
9 5  
7
and
3 31  
5
into improper fractions. To do this, for each fraction, we will leave the denominator the same, and write the sum in the numerator, where the first term is the product of the denominator and the whole-number part, and the second is the numerator.
9 5  ∶
7
3 31  =
5
(7 ⋅ 9) + 5  ∶
7
(5 ⋅ 3) + 31  =
5
68  ∶
7
46  
5

Let's swap the numerator and denominator of the second fraction.
9 5  ∶
7
3 31  =
5
68  ∶
7
46  =
5
68  ⋅
7
5  
46
Multiply the denominators and numerators of fractions.
9 5  ∶
7
3 31  =
5
68  ∶
7
46  =
5
68  ⋅
7
5  =
46
68 ⋅ 5  =
7 ⋅ 46
340
322
Simplify the fraction.
340
322

9 5  ∶
7
3 31  =
5
68  ∶
7
46  =
5
68  ⋅
7
5  =
46
68 ⋅ 5  =
7 ⋅ 46
340 =
322
170 =
161
1 9
161
Let's divide Fractions.
10 3  ∶
14
7  =
9
143  ∶
14
7  =
9
143  ⋅
14
9  =
7
143 ⋅ 9  =
14 ⋅ 7
1287 =
98
13 13
98
≈ 13,1327

Step by step solution

Convert mixed fraction
10 3  
14
into improper. To do this, leave the denominator the same, and write the sum in the numerator, where the first term is the product of the denominator and the whole-number part, and the second is the numerator.
10 3  ∶
14
7  =
9
(14 ⋅ 10) + 3  ∶
14
7  =
9
143  ∶
14
7  
9

Let's swap the numerator and denominator of the second fraction.
10 3  ∶
14
7  =
9
143  ∶
14
7  =
9
143  ⋅
14
9  
7
Multiply the denominators and numerators of fractions.
10 3  ∶
14
7  =
9
143  ∶
14
7  =
9
143  ⋅
14
9  =
7
143 ⋅ 9  =
14 ⋅ 7
1287
98
Simplify the fraction.
1287
98

10 3  ∶
14
7  =
9
143  ∶
14
7  =
9
143  ⋅
14
9  =
7
143 ⋅ 9  =
14 ⋅ 7
1287 =
98
13 13
98
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