Examples with solutions for Addition of Fractions: Finding a Common Denominator by Multiplying the Denominators

Exercise #1

14+19= \frac{1}{4}+\frac{1}{9}=

Video Solution

Step-by-Step Solution

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

1×94×9+1×49×4=936+436 \frac{1\times9}{4\times9}+\frac{1\times4}{9\times4}=\frac{9}{36}+\frac{4}{36}

Now we'll combine and get:

9+436=1336 \frac{9+4}{36}=\frac{13}{36}

Answer

1336 \frac{13}{36}

Exercise #2

17+13= \frac{1}{7}+\frac{1}{3}=

Video Solution

Step-by-Step Solution

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

1×37×3+1×73×7=321+721 \frac{1\times3}{7\times3}+\frac{1\times7}{3\times7}=\frac{3}{21}+\frac{7}{21}

Now we'll combine and get:

3+721=1021 \frac{3+7}{21}=\frac{10}{21}

Answer

1021 \frac{10}{21}

Exercise #3

25+16= \frac{2}{5}+\frac{1}{6}=

Video Solution

Step-by-Step Solution

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

2×65×6+1×56×5=1230+530 \frac{2\times6}{5\times6}+\frac{1\times5}{6\times5}=\frac{12}{30}+\frac{5}{30}

Now we'll combine and get:

12+530=1730 \frac{12+5}{30}=\frac{17}{30}

Answer

1730 \frac{17}{30}

Exercise #4

38+23= \frac{3}{8}+\frac{2}{3}=

Video Solution

Step-by-Step Solution

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

3×38×3+2×83×8=924+1624 \frac{3\times3}{8\times3}+\frac{2\times8}{3\times8}=\frac{9}{24}+\frac{16}{24}

Now we'll combine and get:

9+1624=2524 \frac{9+16}{24}=\frac{25}{24}

Answer

2524 \frac{25}{24}

Exercise #5

12+29= \frac{1}{2}+\frac{2}{9}=

Video Solution

Step-by-Step Solution

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

1×92×9+2×29×2=918+418 \frac{1\times9}{2\times9}+\frac{2\times2}{9\times2}=\frac{9}{18}+\frac{4}{18}

Now we'll combine and get:

9+418=1318 \frac{9+4}{18}=\frac{13}{18}

Answer

1318 \frac{13}{18}

Exercise #6

210+13= \frac{2}{10}+\frac{1}{3}=

Video Solution

Step-by-Step Solution

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

2×310×3+1×103×10=630+1030 \frac{2\times3}{10\times3}+\frac{1\times10}{3\times10}=\frac{6}{30}+\frac{10}{30}

Now we'll combine and get:

6+1030=1630 \frac{6+10}{30}=\frac{16}{30}

Answer

1630 \frac{16}{30}

Exercise #7

15+13= \frac{1}{5}+\frac{1}{3}=

Video Solution

Step-by-Step Solution

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

1×35×3+1×53×5=315+515 \frac{1\times3}{5\times3}+\frac{1\times5}{3\times5}=\frac{3}{15}+\frac{5}{15}

Now we'll combine and get:

3+515=815 \frac{3+5}{15}=\frac{8}{15}

Answer

815 \frac{8}{15}

Exercise #8

25+36= \frac{2}{5}+\frac{3}{6}=

Video Solution

Step-by-Step Solution

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

2×65×6+3×56×5=1230+1530 \frac{2\times6}{5\times6}+\frac{3\times5}{6\times5}=\frac{12}{30}+\frac{15}{30}

Now we'll combine and get:

12+1530=2730 \frac{12+15}{30}=\frac{27}{30}

Answer

2730 \frac{27}{30}

Exercise #9

28+23= \frac{2}{8}+\frac{2}{3}=

Video Solution

Step-by-Step Solution

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

2×38×3+2×83×8=624+1624 \frac{2\times3}{8\times3}+\frac{2\times8}{3\times8}=\frac{6}{24}+\frac{16}{24}

Now we'll combine and get:

6+1624=2224 \frac{6+16}{24}=\frac{22}{24}

Answer

2224 \frac{22}{24}

Exercise #10

14+26= \frac{1}{4}+\frac{2}{6}=

Video Solution

Step-by-Step Solution

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

1×34×3+2×26×2=312+412 \frac{1\times3}{4\times3}+\frac{2\times2}{6\times2}=\frac{3}{12}+\frac{4}{12}

Now we'll combine and get:

3+412=712 \frac{3+4}{12}=\frac{7}{12}

Answer

712 \frac{7}{12}

Exercise #11

25+13= \frac{2}{5}+\frac{1}{3}=

Video Solution

Step-by-Step Solution

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

2×35×3+1×53×5=615+515 \frac{2\times3}{5\times3}+\frac{1\times5}{3\times5}=\frac{6}{15}+\frac{5}{15}

Now we'll combine and get:

6+515=1115 \frac{6+5}{15}=\frac{11}{15}

Answer

1115 \frac{11}{15}

Exercise #12

25+14= \frac{2}{5}+\frac{1}{4}=

Video Solution

Step-by-Step Solution

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

2×45×4+1×54×5=820+520 \frac{2\times4}{5\times4}+\frac{1\times5}{4\times5}=\frac{8}{20}+\frac{5}{20}

Now we'll combine and get:

8+520=1320 \frac{8+5}{20}=\frac{13}{20}

Answer

1320 \frac{13}{20}

Exercise #13

25+13= \frac{2}{5}+\frac{1}{3}=

Video Solution

Step-by-Step Solution

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

2×35×3+1×53×5=615+515 \frac{2\times3}{5\times3}+\frac{1\times5}{3\times5}=\frac{6}{15}+\frac{5}{15}

Now we'll combine and get:

6+515=1115 \frac{6+5}{15}=\frac{11}{15}

Answer

1115 \frac{11}{15}

Exercise #14

49+12= \frac{4}{9}+\frac{1}{2}=

Video Solution

Answer

1718 \frac{17}{18}

Exercise #15

35+27= \frac{3}{5}+\frac{2}{7}=

Video Solution

Answer

3135 \frac{31}{35}

Exercise #16

45+13= \frac{4}{5}+\frac{1}{3}=

Video Solution

Answer

1715 \frac{17}{15}

Exercise #17

13+14= \frac{1}{3}+\frac{1}{4}=

Video Solution

Answer

712 \frac{7}{12}

Exercise #18

29+12= \frac{2}{9}+\frac{1}{2}=

Video Solution

Answer

1318 \frac{13}{18}

Exercise #19

38+19= \frac{3}{8}+\frac{1}{9}=

Video Solution

Answer

3572 \frac{35}{72}

Exercise #20

17+18= \frac{1}{7}+\frac{1}{8}=

Video Solution

Answer

1556 \frac{15}{56}