Addition of Fractions - Examples, Exercises and Solutions

Let's focus on the fraction of the fraction.
According to the order of operations rules, we'll solve from left to right, since it only contains addition and subtraction operations:

$5+3=8$

$8-2=6$

Now we'll get the fraction:

$\frac{6}{3}$

We'll reduce the numerator and denominator by 3 and get:

$\frac{2}{1}=2$

Let's try to find the lowest common denominator between 2 and 10

To find the lowest common denominator, we need to find a number that is divisible by both 2 and 10

In this case, the common denominator is 10

Now we'll multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 5

We'll multiply the second fraction by 1

$\frac{1\times5}{2\times5}+\frac{2\times1}{10\times1}=\frac{5}{10}+\frac{2}{10}$

Now we'll combine and get:

$\frac{5+2}{10}=\frac{7}{10}$

Let's try to find the least common denominator between 2 and 10

To find the least common denominator, we need to find a number that is divisible by both 2 and 10

In this case, the common denominator is 10

Now we'll multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 5

We'll multiply the second fraction by 1

$\frac{1\times5}{2\times5}+\frac{3\times1}{10\times1}=\frac{5}{10}+\frac{3}{10}$

Now we'll combine and get:

$\frac{5+3}{10}=\frac{8}{10}$

Let's try to find the lowest common denominator between 2 and 8

To find the lowest common denominator, we need to find a number that is divisible by both 2 and 8

In this case, the common denominator is 8

Now we'll multiply each fraction by the appropriate number to reach the denominator 8

We'll multiply the first fraction by 4

We'll multiply the second fraction by 1

$\frac{1\times4}{2\times4}+\frac{3\times1}{8\times1}=\frac{4}{8}+\frac{3}{8}$

Now we'll combine and get:

$\frac{4+3}{8}=\frac{7}{8}$

Let's try to find the lowest common denominator between 3 and 9

To find the lowest common denominator, we need to find a number that is divisible by both 3 and 9

In this case, the common denominator is 9

Now we'll multiply each fraction by the appropriate number to reach the denominator 9

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

$\frac{1\times3}{3\times3}+\frac{2\times1}{9\times1}=\frac{2}{9}+\frac{2}{9}$

Now we'll combine and get:

$\frac{2+3}{9}=\frac{5}{9}$

Let's try to find the least common denominator between 3 and 6

To find the least common denominator, we need to find a number that is divisible by both 3 and 6

In this case, the common denominator is 6

Now we'll multiply each fraction by the appropriate number to reach the denominator 6

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{1\times2}{3\times2}+\frac{3\times1}{6\times1}=\frac{2}{6}+\frac{3}{6}$

Now we'll combine and get:

$\frac{2+3}{6}=\frac{5}{6}$

Let's try to find the lowest common denominator between 3 and 9

To find the lowest common denominator, we need to find a number that is divisible by both 3 and 9

In this case, the common denominator is 9

Now we'll multiply each fraction by the appropriate number to reach the denominator 9

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

$\frac{1\times3}{3\times3}+\frac{4\times1}{9\times1}=\frac{3}{9}+\frac{4}{9}$

Now we'll combine and get:

$\frac{3+4}{9}=\frac{7}{9}$

Let's try to find the lowest common denominator between 3 and 9

To find the lowest common denominator, we need to find a number that is divisible by both 3 and 9

In this case, the common denominator is 9

Now we'll multiply each fraction by the appropriate number to reach the denominator 9

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

$\frac{1\times3}{3\times3}+\frac{5\times1}{9\times1}=\frac{3}{9}+\frac{5}{9}$

Now we'll combine and get:

$\frac{3+5}{9}=\frac{8}{9}$

Let's try to find the least common denominator between 4 and 12

To find the least common denominator, we need to find a number that is divisible by both 4 and 12

In this case, the common denominator is 12

Now we'll multiply each fraction by the appropriate number to reach the denominator 12

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

$\frac{1\times3}{4\times3}+\frac{6\times1}{12\times1}=\frac{3}{12}+\frac{6}{12}$

Now we'll combine and get:

$\frac{3+6}{12}=\frac{9}{12}$

Let's try to find the least common denominator between 4 and 8

To find the least common denominator, we need to find a number that is divisible by both 4 and 8

In this case, the common denominator is 8

Now we'll multiply each fraction by the appropriate number to reach the denominator 8

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{1\times2}{4\times2}+\frac{6\times1}{8\times1}=\frac{2}{8}+\frac{6}{8}$

Now we'll combine and get:

$\frac{2+6}{8}=\frac{8}{8}=1$

Let's try to find the lowest common denominator between 5 and 15

To find the lowest common denominator, we need to find a number that is divisible by both 5 and 15

In this case, the common denominator is 15

Now we'll multiply each fraction by the appropriate number to reach the denominator 15

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

$\frac{1\times3}{5\times3}+\frac{2\times1}{15\times1}=\frac{3}{15}+\frac{2}{15}$

Now we'll combine and get:

$\frac{3+2}{15}=\frac{5}{15}$

Let's try to find the least common denominator between 5 and 10

To find the least common denominator, we need to find a number that is divisible by both 5 and 10

In this case, the common denominator is 10

Now we'll multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{1\times2}{5\times2}+\frac{6\times1}{10\times1}=\frac{2}{10}+\frac{6}{10}$

Now we'll combine and get:

$\frac{2+6}{10}=\frac{8}{10}$

Let's try to find the lowest common denominator between 3 and 6

To find the lowest common denominator, we need to find a number that is divisible by both 3 and 6

In this case, the common denominator is 6

Now we'll multiply each fraction by the appropriate number to reach the denominator 6

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{2\times2}{3\times2}+\frac{1\times1}{6\times1}=\frac{4}{6}+\frac{1}{6}$

Now we'll combine and get:

$\frac{4+1}{6}=\frac{5}{6}$

Let's try to find the lowest common denominator between 4 and 2

To find the lowest common denominator, we need to find a number that is divisible by both 4 and 2

In this case, the common denominator is 4

Now we'll multiply each fraction by the appropriate number to reach the denominator 4

We'll multiply the first fraction by 1

We'll multiply the second fraction by 2

$\frac{2\times1}{4\times1}+\frac{1\times2}{2\times2}=\frac{2}{4}+\frac{2}{4}$

Now we'll combine and get:

$\frac{2+2}{4}=\frac{4}{4}=1$

Let's try to find the lowest common denominator between 4 and 8

To find the lowest common denominator, we need to find a number that is divisible by both 4 and 8

In this case, the common denominator is 8

Now we'll multiply each fraction by the appropriate number to reach the denominator 8

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{2\times2}{4\times2}+\frac{1\times1}{8\times1}=\frac{4}{8}+\frac{1}{8}$

Now we'll combine and get:

$\frac{4+1}{8}=\frac{5}{8}$