Examples with solutions for Common Denominators: One of the denominators is the common denominator

Exercise #1

Solve the following equation:

14+58= \frac{1}{4}+\frac{5}{8}=

Video Solution

Step-by-Step Solution

We must first identify the lowest common denominator between 4 and 8.

In order to determine 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.

We will then proceed to 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+5×18×1=28+58 \frac{1\times2}{4\times2}+\frac{5\times1}{8\times1}=\frac{2}{8}+\frac{5}{8}

Finally we'll combine and obtain the following:

2+58=78 \frac{2+5}{8}=\frac{7}{8}

Answer

78 \frac{7}{8}

Exercise #2

Solve the following equation:

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

Video Solution

Step-by-Step Solution

Let's first identify the lowest common denominator between 4 and 2.

In order to identify 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

We will then proceed to multiply each fraction by the appropriate number in order 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}

Finally we will combine and obtain the following:

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

Answer

1 1

Exercise #3

Solve the following equation:

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

Video Solution

Step-by-Step Solution

Let's first identify the lowest common denominator between 2 and 8.

In order to determine the lowest common denominator, we need to first find a number that is divisible by both 2 and 8.

In this case, the common denominator is 8.

We'll then proceed to multiply each fraction by the appropriate number in order 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}

Finally we'll combine and obtain the following:

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

Answer

78 \frac{7}{8}

Exercise #4

Solve the following equation:

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

Video Solution

Step-by-Step Solution

We must first identify the lowest common denominator between 3 and 9.

In order to determine 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.

We will then proceed to 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}

Finally we'll combine and obtain the following:

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

Answer

79 \frac{7}{9}

Exercise #5

Solve the following equation:

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

Video Solution

Step-by-Step Solution

Let's begin by identifying the lowest common denominator between 3 and 6.

In order to determine 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.

Let's proceed to multiply each fraction by the appropriate number in order 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}

Finally we'll combine and obtain the following result:

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

Answer

56 \frac{5}{6}

Exercise #6

Solve the following equation:

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

Video Solution

Step-by-Step Solution

We must first identify the lowest common denominator between 4 and 8

In order to determine 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.

We will proceed to 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}

Finally we'll combine and obtain the following:

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

Answer

58 \frac{5}{8}

Exercise #7

Solve the following equation:

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

Video Solution

Step-by-Step Solution

We must first identify the lowest common denominator between 5 and 10.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 5 and 10.

In this case, the common denominator is 10.

We will proceed to 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}

Finally we'll combine and obtain the following:

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

Answer

810 \frac{8}{10}

Exercise #8

Solve the following equation:

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

Video Solution

Step-by-Step Solution

We must first identify the lowest common denominator between 3 and 6.

In order to determine 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.

We'll then proceed to 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}

Finally we'll combine and obtain the following:

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

Answer

56 \frac{5}{6}

Exercise #9

Solve the following equation:

34+18= \frac{3}{4}+\frac{1}{8}=

Video Solution

Step-by-Step Solution

We must first identify the lowest common denominator between 4 and 8.

In order to determine 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.

We'll then proceed to 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

3×24×2+1×18×1=68+18 \frac{3\times2}{4\times2}+\frac{1\times1}{8\times1}=\frac{6}{8}+\frac{1}{8}

Finally we'll combine and obtain the following:

6+18=78 \frac{6+1}{8}=\frac{7}{8}

Answer

78 \frac{7}{8}

Exercise #10

Solve the following equation:

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

Video Solution

Step-by-Step Solution

We must first identify the lowest common denominator between 4 and 12.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 4 and 12.

In this case, the common denominator is 12.

We will then proceed to 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}

Finally we'll combine and obtain the following:

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

Answer

912 \frac{9}{12}

Exercise #11

Solve the following equation:

26+412= \frac{2}{6}+\frac{4}{12}=

Video Solution

Step-by-Step Solution

We must first identify the lowest common denominator between 6 and 12.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 6 and 12.

In this case, the common denominator is 12.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 12.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

2×26×2+4×112×1=412+412 \frac{2\times2}{6\times2}+\frac{4\times1}{12\times1}=\frac{4}{12}+\frac{4}{12}

Finally we'll combine and obtain the following:

4+412=812 \frac{4+4}{12}=\frac{8}{12}

Answer

812 \frac{8}{12}

Exercise #12

Solve the following equation:

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

Video Solution

Step-by-Step Solution

We must first identify the lowest common denominator between 3 and 9.

In order to determine 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.

We will then proceed to 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}

Finally we'll combine and obtain the following:

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

Answer

59 \frac{5}{9}

Exercise #13

Solve the following exercise:

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 #14

Solve the following exercise:

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

Solve the following exercise:

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 #16

Solve the following exercise:

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 #17

Solve the following exercise:

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 #18

Solve the following exercise:

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 #19

Solve the following exercise:

14+48= \frac{1}{4}+\frac{4}{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

1×24×2+4×18×1=28+48 \frac{1\times2}{4\times2}+\frac{4\times1}{8\times1}=\frac{2}{8}+\frac{4}{8}

Now we'll combine and get:

2+48=68 \frac{2+4}{8}=\frac{6}{8}

Answer

68 \frac{6}{8}

Exercise #20

Solve the following equation:

45310= \frac{4}{5}-\frac{3}{10}=

Video Solution

Step-by-Step Solution

Let's begin by identifying the lowest common denominator between 5 and 10.

In order to determine the lowest common denominator, we must find a number that is divisible by both 5 and 10.

In this case, the common denominator is 10.

Now let's proceed to 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

4×25×23×110×1=810310 \frac{4\times2}{5\times2}-\frac{3\times1}{10\times1}=\frac{8}{10}-\frac{3}{10}

Finally let's subtract as follows:

8310=510 \frac{8-3}{10}=\frac{5}{10}

Answer

510 \frac{5}{10}