Addition of Fractions: Finding a Common Denominator by Multiplying the Denominators

Let's try to find the lowest common denominator between 2 and 9

To find the lowest common denominator, we need to find a number that is divisible by both 2 and 9

In this case, the common denominator is 18

Now we'll multiply each fraction by the appropriate number to reach the denominator 18

We'll multiply the first fraction by 9

We'll multiply the second fraction by 2

$\frac{1\times9}{2\times9}+\frac{2\times2}{9\times2}=\frac{9}{18}+\frac{4}{18}$

Now we'll combine and get:

$\frac{9+4}{18}=\frac{13}{18}$

Let's try to find the lowest common denominator between 4 and 9

To find the lowest common denominator, we need to find a number that is divisible by both 4 and 9

In this case, the common denominator is 36

Now we'll multiply each fraction by the appropriate number to reach the denominator 36

We'll multiply the first fraction by 9

We'll multiply the second fraction by 4

$\frac{1\times9}{4\times9}+\frac{1\times4}{9\times4}=\frac{9}{36}+\frac{4}{36}$

Now we'll combine and get:

$\frac{9+4}{36}=\frac{13}{36}$

Let's try to find the lowest common denominator between 4 and 6

To find the lowest common denominator, we need to find a number that is divisible by both 4 and 6

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 2

$\frac{1\times3}{4\times3}+\frac{2\times2}{6\times2}=\frac{3}{12}+\frac{4}{12}$

Now we'll combine and get:

$\frac{3+4}{12}=\frac{7}{12}$

Let's try to find the lowest common denominator between 5 and 3

To find the lowest common denominator, we need to find a number that is divisible by both 5 and 3

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 5

$\frac{1\times3}{5\times3}+\frac{1\times5}{3\times5}=\frac{3}{15}+\frac{5}{15}$

Now we'll combine and get:

$\frac{3+5}{15}=\frac{8}{15}$

Let's try to find the lowest common denominator between 7 and 3

To find the lowest common denominator, we need to find a number that is divisible by both 7 and 3

In this case, the common denominator is 21

Now we'll multiply each fraction by the appropriate number to reach the denominator 21

We'll multiply the first fraction by 3

We'll multiply the second fraction by 7

$\frac{1\times3}{7\times3}+\frac{1\times7}{3\times7}=\frac{3}{21}+\frac{7}{21}$

Now we'll combine and get:

$\frac{3+7}{21}=\frac{10}{21}$

Let's try to find the least common denominator between 10 and 3

To find the least common denominator, we need to find a number that is divisible by both 10 and 3

In this case, the common denominator is 30

Now we'll multiply each fraction by the appropriate number to reach the denominator 30

We'll multiply the first fraction by 3

We'll multiply the second fraction by 10

$\frac{2\times3}{10\times3}+\frac{1\times10}{3\times10}=\frac{6}{30}+\frac{10}{30}$

Now we'll combine and get:

$\frac{6+10}{30}=\frac{16}{30}$

Let's try to find the lowest common denominator between 5 and 3

To find the lowest common denominator, we need to find a number that is divisible by both 5 and 3

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 5

$\frac{2\times3}{5\times3}+\frac{1\times5}{3\times5}=\frac{6}{15}+\frac{5}{15}$

Now we'll combine and get:

$\frac{6+5}{15}=\frac{11}{15}$

Let's try to find the lowest common denominator between 5 and 6

To find the lowest common denominator, we need to find a number that is divisible by both 5 and 6

In this case, the common denominator is 30

Now we'll multiply each fraction by the appropriate number to reach the denominator 30

We'll multiply the first fraction by 6

We'll multiply the second fraction by 5

$\frac{2\times6}{5\times6}+\frac{1\times5}{6\times5}=\frac{12}{30}+\frac{5}{30}$

Now we'll combine and get:

$\frac{12+5}{30}=\frac{17}{30}$

Let's try to find the lowest common denominator between 5 and 6

To find the lowest common denominator, we need to find a number that is divisible by both 5 and 6

In this case, the common denominator is 30

Now we'll multiply each fraction by the appropriate number to reach the denominator 30

We'll multiply the first fraction by 6

We'll multiply the second fraction by 5

$\frac{2\times6}{5\times6}+\frac{3\times5}{6\times5}=\frac{12}{30}+\frac{15}{30}$

Now we'll combine and get:

$\frac{12+15}{30}=\frac{27}{30}$

Let's try to find the least common multiple (LCM) between 8 and 3

To find the least common multiple, we need to find a number that is divisible by both 8 and 3

In this case, the common multiple is 24

Now we'll multiply each fraction by the appropriate number to reach the denominator 24

We'll multiply the first fraction by 3

We'll multiply the second fraction by 8

$\frac{3\times3}{8\times3}+\frac{2\times8}{3\times8}=\frac{9}{24}+\frac{16}{24}$

Now we'll combine and get:

$\frac{9+16}{24}=\frac{25}{24}$

Let's try to find the least common denominator between 5 and 3

To find the least common denominator, we need to find a number that is divisible by both 5 and 3

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 5

$\frac{2\times3}{5\times3}+\frac{1\times5}{3\times5}=\frac{6}{15}+\frac{5}{15}$

Now we'll combine and get:

$\frac{6+5}{15}=\frac{11}{15}$

Let's try to find the lowest common denominator between 5 and 4

To find the lowest common denominator, we need to find a number that is divisible by both 5 and 4

In this case, the common denominator is 20

Now we'll multiply each fraction by the appropriate number to reach the denominator 20

We'll multiply the first fraction by 4

We'll multiply the second fraction by 5

$\frac{2\times4}{5\times4}+\frac{1\times5}{4\times5}=\frac{8}{20}+\frac{5}{20}$

Now we'll combine and get:

$\frac{8+5}{20}=\frac{13}{20}$

Let's try to find the least common multiple (LCM) between 8 and 3

To find the least common multiple, we need to find a number that is divisible by both 8 and 3

In this case, the common multiple is 24

Now we'll multiply each fraction by the appropriate number to reach the denominator 24

We'll multiply the first fraction by 3

We'll multiply the second fraction by 8

$\frac{2\times3}{8\times3}+\frac{2\times8}{3\times8}=\frac{6}{24}+\frac{16}{24}$

Now we'll combine and get:

$\frac{6+16}{24}=\frac{22}{24}$