Examples with solutions for Addition of Fractions: One of the denominators is the common denominator

Exercise #1

12+38= \frac{1}{2}+\frac{3}{8}=

Video Solution

Step-by-Step Solution

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

1×42×4+3×18×1=48+38 \frac{1\times4}{2\times4}+\frac{3\times1}{8\times1}=\frac{4}{8}+\frac{3}{8}

Now we'll combine and get:

4+38=78 \frac{4+3}{8}=\frac{7}{8}

Answer

78 \frac{7}{8}

Exercise #2

24+12= \frac{2}{4}+\frac{1}{2}=

Video Solution

Step-by-Step Solution

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

2×14×1+1×22×2=24+24 \frac{2\times1}{4\times1}+\frac{1\times2}{2\times2}=\frac{2}{4}+\frac{2}{4}

Now we'll combine and get:

2+24=44=1 \frac{2+2}{4}=\frac{4}{4}=1

Answer

1 1

Exercise #3

23+16= \frac{2}{3}+\frac{1}{6}=

Video Solution

Step-by-Step Solution

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

2×23×2+1×16×1=46+16 \frac{2\times2}{3\times2}+\frac{1\times1}{6\times1}=\frac{4}{6}+\frac{1}{6}

Now we'll combine and get:

4+16=56 \frac{4+1}{6}=\frac{5}{6}

Answer

56 \frac{5}{6}

Exercise #4

24+18= \frac{2}{4}+\frac{1}{8}=

Video Solution

Step-by-Step Solution

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

2×24×2+1×18×1=48+18 \frac{2\times2}{4\times2}+\frac{1\times1}{8\times1}=\frac{4}{8}+\frac{1}{8}

Now we'll combine and get:

4+18=58 \frac{4+1}{8}=\frac{5}{8}

Answer

58 \frac{5}{8}

Exercise #5

15+610= \frac{1}{5}+\frac{6}{10}=

Video Solution

Step-by-Step Solution

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

1×25×2+6×110×1=210+610 \frac{1\times2}{5\times2}+\frac{6\times1}{10\times1}=\frac{2}{10}+\frac{6}{10}

Now we'll combine and get:

2+610=810 \frac{2+6}{10}=\frac{8}{10}

Answer

810 \frac{8}{10}

Exercise #6

13+36= \frac{1}{3}+\frac{3}{6}=

Video Solution

Step-by-Step Solution

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

1×23×2+3×16×1=26+36 \frac{1\times2}{3\times2}+\frac{3\times1}{6\times1}=\frac{2}{6}+\frac{3}{6}

Now we'll combine and get:

2+36=56 \frac{2+3}{6}=\frac{5}{6}

Answer

56 \frac{5}{6}

Exercise #7

14+612= \frac{1}{4}+\frac{6}{12}=

Video Solution

Step-by-Step Solution

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

1×34×3+6×112×1=312+612 \frac{1\times3}{4\times3}+\frac{6\times1}{12\times1}=\frac{3}{12}+\frac{6}{12}

Now we'll combine and get:

3+612=912 \frac{3+6}{12}=\frac{9}{12}

Answer

912 \frac{9}{12}

Exercise #8

13+29= \frac{1}{3}+\frac{2}{9}=

Video Solution

Step-by-Step Solution

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

1×33×3+2×19×1=29+29 \frac{1\times3}{3\times3}+\frac{2\times1}{9\times1}=\frac{2}{9}+\frac{2}{9}

Now we'll combine and get:

2+39=59 \frac{2+3}{9}=\frac{5}{9}

Answer

59 \frac{5}{9}

Exercise #9

13+49= \frac{1}{3}+\frac{4}{9}=

Video Solution

Step-by-Step Solution

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

1×33×3+4×19×1=39+49 \frac{1\times3}{3\times3}+\frac{4\times1}{9\times1}=\frac{3}{9}+\frac{4}{9}

Now we'll combine and get:

3+49=79 \frac{3+4}{9}=\frac{7}{9}

Answer

79 \frac{7}{9}

Exercise #10

12+310= \frac{1}{2}+\frac{3}{10}=

Video Solution

Step-by-Step Solution

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

1×52×5+3×110×1=510+310 \frac{1\times5}{2\times5}+\frac{3\times1}{10\times1}=\frac{5}{10}+\frac{3}{10}

Now we'll combine and get:

5+310=810 \frac{5+3}{10}=\frac{8}{10}

Answer

810 \frac{8}{10}

Exercise #11

15+215= \frac{1}{5}+\frac{2}{15}=

Video Solution

Step-by-Step Solution

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

1×35×3+2×115×1=315+215 \frac{1\times3}{5\times3}+\frac{2\times1}{15\times1}=\frac{3}{15}+\frac{2}{15}

Now we'll combine and get:

3+215=515 \frac{3+2}{15}=\frac{5}{15}

Answer

515 \frac{5}{15}

Exercise #12

13+59= \frac{1}{3}+\frac{5}{9}=

Video Solution

Step-by-Step Solution

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

1×33×3+5×19×1=39+59 \frac{1\times3}{3\times3}+\frac{5\times1}{9\times1}=\frac{3}{9}+\frac{5}{9}

Now we'll combine and get:

3+59=89 \frac{3+5}{9}=\frac{8}{9}

Answer

89 \frac{8}{9}

Exercise #13

14+68= \frac{1}{4}+\frac{6}{8}=

Video Solution

Step-by-Step Solution

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

1×24×2+6×18×1=28+68 \frac{1\times2}{4\times2}+\frac{6\times1}{8\times1}=\frac{2}{8}+\frac{6}{8}

Now we'll combine and get:

2+68=88=1 \frac{2+6}{8}=\frac{8}{8}=1

Answer

1 1

Exercise #14

12+210= \frac{1}{2}+\frac{2}{10}=

Video Solution

Step-by-Step Solution

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

1×52×5+2×110×1=510+210 \frac{1\times5}{2\times5}+\frac{2\times1}{10\times1}=\frac{5}{10}+\frac{2}{10}

Now we'll combine and get:

5+210=710 \frac{5+2}{10}=\frac{7}{10}

Answer

710 \frac{7}{10}

Exercise #15

35+215= \frac{3}{5}+\frac{2}{15}=

Video Solution

Step-by-Step Solution

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

3×35×3+2×115×1=915+215 \frac{3\times3}{5\times3}+\frac{2\times1}{15\times1}=\frac{9}{15}+\frac{2}{15}

Now we'll combine and get:

9+215=1115 \frac{9+2}{15}=\frac{11}{15}

Answer

1115 \frac{11}{15}

Exercise #16

12+24= \frac{1}{2}+\frac{2}{4}=

Video Solution

Answer

1 1

Exercise #17

35+610= \frac{3}{5}+\frac{6}{10}=

Video Solution

Answer

65 \frac{6}{5}

Exercise #18

12+38= \frac{1}{2}+\frac{3}{8}=

Video Solution

Answer

78 \frac{7}{8}

Exercise #19

512+1136= \frac{5}{12}+\frac{11}{36}=

Video Solution

Answer

1318 \frac{13}{18}

Exercise #20

29+318= \frac{2}{9}+\frac{3}{18}=

Video Solution

Answer

718 \frac{7}{18}