Examples with solutions for All Operations in Fractions: Finding a Common Denominator by Multiplying the Denominators

Exercise #1

Solve the following exercise:

1315=? \frac{1}{3}-\frac{1}{5}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem 1315 \frac{1}{3} - \frac{1}{5} , we follow these steps:

First, we need to find a common denominator for the fractions 13\frac{1}{3} and 15\frac{1}{5}. The denominators are 3 and 5, and their least common multiple (LCM) is 15.

We will convert each fraction to an equivalent fraction with the denominator 15:

  • To convert 13\frac{1}{3} to a fraction with denominator 15, multiply both the numerator and the denominator by 5: 13=1×53×5=515 \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
  • To convert 15\frac{1}{5} to a fraction with denominator 15, multiply both the numerator and the denominator by 3: 15=1×35×3=315 \frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}

Now that both fractions have the same denominator, we can subtract the numerators:

515315=5315=215 \frac{5}{15} - \frac{3}{15} = \frac{5 - 3}{15} = \frac{2}{15}

Therefore, the solution to the problem is 215\frac{2}{15}.

Answer

215 \frac{2}{15}

Exercise #2

Solve the following exercise:

2413=? \frac{2}{4}-\frac{1}{3}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Find the common denominator for the fractions 24\frac{2}{4} and 13\frac{1}{3}.
  • Step 2: Convert each fraction to have the common denominator.
  • Step 3: Perform the subtraction and simplify if necessary.

Now, let's work through these steps:

Step 1: The denominators are 44 and 33. The common denominator is the product 4×3=124 \times 3 = 12.

Step 2: Convert each fraction:
24=2×34×3=612\frac{2}{4} = \frac{2 \times 3}{4 \times 3} = \frac{6}{12}
13=1×43×4=412\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}

Step 3: Subtract the fractions with a common denominator:
612412=6412=212\frac{6}{12} - \frac{4}{12} = \frac{6 - 4}{12} = \frac{2}{12}

Finally, simplify 212\frac{2}{12}. The greatest common divisor of 2 and 12 is 2, so:
212=2÷212÷2=16\frac{2}{12} = \frac{2 \div 2}{12 \div 2} = \frac{1}{6}

Therefore, the solution to the problem is 16\frac{1}{6}.

Answer

16 \frac{1}{6}

Exercise #3

Solve the following exercise:

3512=? \frac{3}{5}-\frac{1}{2}=\text{?}

Video Solution

Step-by-Step Solution

To solve the subtraction of fractions 3512 \frac{3}{5} - \frac{1}{2} , we will follow these steps:

  • Step 1: Find the least common multiple (LCM) of the denominators 5 and 2. The LCM of 5 and 2 is 10.
  • Step 2: Convert each fraction to have a denominator of 10.
  • Step 3: Subtract the converted fractions.
  • Step 4: Simplify the result if necessary.

Now, let's work through each step in detail:

Step 1: The LCM of 5 and 2 is 10, since 10 is the smallest number that both 5 and 2 divide into evenly.

Step 2: Convert each fraction to have a denominator of 10.

For 35\frac{3}{5}:
Multiply numerator and denominator by 2 to get 3×25×2=610\frac{3 \times 2}{5 \times 2} = \frac{6}{10}.

For 12\frac{1}{2}:
Multiply numerator and denominator by 5 to get 1×52×5=510\frac{1 \times 5}{2 \times 5} = \frac{5}{10}.

Step 3: Subtract the fractions:

610510=6510=110\frac{6}{10} - \frac{5}{10} = \frac{6 - 5}{10} = \frac{1}{10}.

Step 4: There is no further simplification needed for 110\frac{1}{10} as it is already in its simplest form.

Therefore, the solution to the problem is 110\frac{1}{10}.

The correct answer, choice (4), is 110\frac{1}{10}.

Answer

110 \frac{1}{10}

Exercise #4

Solve the following exercise:

3514=? \frac{3}{5}-\frac{1}{4}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem of subtracting 14 \frac{1}{4} from 35 \frac{3}{5} , we need a common denominator.

First, find the least common denominator (LCD) of 5 and 4, which is 20. This is done by multiplying the denominators: 5×4=20 5 \times 4 = 20 .

Next, convert each fraction to an equivalent fraction with the denominator of 20:

  • For 35 \frac{3}{5} : Multiply both numerator and denominator by 4 to get 3×45×4=1220 \frac{3 \times 4}{5 \times 4} = \frac{12}{20} .
  • For 14 \frac{1}{4} : Multiply both numerator and denominator by 5 to get 1×54×5=520 \frac{1 \times 5}{4 \times 5} = \frac{5}{20} .

Now perform the subtraction with these equivalent fractions:

1220520=12520=720 \frac{12}{20} - \frac{5}{20} = \frac{12 - 5}{20} = \frac{7}{20}

The resulting fraction, 720 \frac{7}{20} , is already in its simplest form.

Therefore, the solution to the subtraction 3514 \frac{3}{5} - \frac{1}{4} is 720 \frac{7}{20} .

Checking against the multiple-choice answers, the correct choice is the first one: 720 \frac{7}{20} .

Answer

720 \frac{7}{20}

Exercise #5

Solve the following exercise:

3513=? \frac{3}{5}-\frac{1}{3}=\text{?}

Video Solution

Step-by-Step Solution

To solve the subtraction of fractions 3513 \frac{3}{5} - \frac{1}{3} , follow these steps:

  • Step 1: Find the Least Common Denominator (LCD)
    The denominators are 5 and 3. The least common multiple of 5 and 3 is 15. Thus, the common denominator will be 15.
  • Step 2: Convert fractions to have the same denominator
    For 35 \frac{3}{5} , multiply both the numerator and the denominator by 3 to get:
    35=3×35×3=915\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}.
    For 13 \frac{1}{3} , multiply both the numerator and the denominator by 5 to get:
    13=1×53×5=515\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}.
  • Step 3: Subtract the numerators
    Now subtract the equivalent fractions:
    915515=9515=415\frac{9}{15} - \frac{5}{15} = \frac{9 - 5}{15} = \frac{4}{15}.
  • Step 4: Simplify the fraction
    The fraction 415\frac{4}{15} is already in its simplest form.

Thus, the solution to the problem is 415\frac{4}{15}.

Answer

415 \frac{4}{15}

Exercise #6

Solve the following exercise:

1219=? \frac{1}{2}-\frac{1}{9}=\text{?}

Video Solution

Step-by-Step Solution

To solve 1219\frac{1}{2} - \frac{1}{9}, follow these steps:

Step 1: Find the least common multiple (LCM) of the denominators 2 and 9.
The multiples of 2 are 2,4,6,8,10,12,14,16,18,2, 4, 6, 8, 10, 12, 14, 16, 18, \ldots
The multiples of 9 are 9,18,27,9, 18, 27, \ldots
The smallest common multiple is 18. Thus, the LCM of 2 and 9 is 18.

Step 2: Convert each fraction to an equivalent fraction with the common denominator 18.
For 12\frac{1}{2}, the equivalent fraction with 18 as the denominator is calculated by finding the factor needed:
12=1×92×9=918 \frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18} .
For 19\frac{1}{9}, the equivalent fraction with 18 as the denominator is:
19=1×29×2=218 \frac{1}{9} = \frac{1 \times 2}{9 \times 2} = \frac{2}{18} .

Step 3: Perform the subtraction of these equivalent fractions.
918218=9218=718 \frac{9}{18} - \frac{2}{18} = \frac{9 - 2}{18} = \frac{7}{18} .

Therefore, the solution to the problem is 718\boxed{\frac{7}{18}}.

Answer

718 \frac{7}{18}

Exercise #7

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

Video Solution

Step-by-Step Solution

To solve the problem of adding 49\frac{4}{9} and 12\frac{1}{2}, we'll proceed step-by-step:

  • Step 1: Determine a common denominator.
  • Step 2: Convert each fraction to an equivalent fraction with this common denominator.
  • Step 3: Add the numerators of these converted fractions.
  • Step 4: Simplify the resulting fraction if necessary.

Now, let's perform these steps in detail:

Step 1: Determine the common denominator.
The denominators are 9 and 2. The least common denominator (LCD) can be found by multiplying these because they have no common factors other than 1:
LCD=9×2=18 \text{LCD} = 9 \times 2 = 18 .

Step 2: Convert each fraction to have the common denominator of 18.

  • Convert 49\frac{4}{9}: 49=4×29×2=818 \frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18}
  • Convert 12\frac{1}{2}: 12=1×92×9=918 \frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18}

Step 3: Add the numerators of the converted fractions:
818+918=8+918=1718 \frac{8}{18} + \frac{9}{18} = \frac{8+9}{18} = \frac{17}{18}

Step 4: Simplification (if needed):
The fraction 1718\frac{17}{18} is already in its simplest form.

Therefore, the sum of 49\frac{4}{9} and 12\frac{1}{2} is 1718 \frac{17}{18} .

Answer

1718 \frac{17}{18}

Exercise #8

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

Video Solution

Step-by-Step Solution

To solve 45+13\frac{4}{5} + \frac{1}{3}, follow these steps:

  • Step 1: Identify a common denominator for the fractions. The current denominators are 55 and 33, hence their common denominator is 1515 (since 5×3=155 \times 3 = 15).
  • Step 2: Convert each fraction to an equivalent fraction with the common denominator 1515:
    • For 45\frac{4}{5}: multiply the numerator and the denominator by 33 (since 5×3=155 \times 3 = 15).
      45=4×35×3=1215\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}.
    • For 13\frac{1}{3}: multiply the numerator and the denominator by 55 (since 3×5=153 \times 5 = 15).
      13=1×53×5=515\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}.
  • Step 3: Add the converted fractions:
    1215+515=12+515=1715\frac{12}{15} + \frac{5}{15} = \frac{12 + 5}{15} = \frac{17}{15}.

Therefore, the solution to the problem is 1715\frac{17}{15}.

Answer

1715 \frac{17}{15}

Exercise #9

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

Video Solution

Step-by-Step Solution

To solve this problem, we'll begin by finding a common denominator for the fractions 13 \frac{1}{3} and 14 \frac{1}{4} .
Step 1: Identify the denominators, which are 3 and 4. Multiply these to get a common denominator: 3×4=12 3 \times 4 = 12 .

Step 2: Convert each fraction to an equivalent fraction with the common denominator of 12.

  • To convert 13 \frac{1}{3} to a denominator of 12, multiply both the numerator and the denominator by 4: 1×43×4=412\frac{1 \times 4}{3 \times 4} = \frac{4}{12}.
  • To convert 14 \frac{1}{4} to a denominator of 12, multiply both the numerator and the denominator by 3: 1×34×3=312\frac{1 \times 3}{4 \times 3} = \frac{3}{12}.

Step 3: Add the resulting fractions: 412+312=4+312=712\frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12}.

Thus, the sum of 13 \frac{1}{3} and 14 \frac{1}{4} is 712\frac{7}{12}.

Answer

712 \frac{7}{12}

Exercise #10

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

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the common denominator.
  • Step 2: Convert each fraction to have this common denominator.
  • Step 3: Add the converted fractions.
  • Step 4: Simplify the result.

Now, let's work through each step:
Step 1: The denominators are 7 and 8. Their product is 7×8=56 7 \times 8 = 56 . So, the common denominator is 56.
Step 2: Convert 17\frac{1}{7} to have a denominator of 56 by multiplying numerator and denominator by 8: 1×87×8=856\frac{1 \times 8}{7 \times 8} = \frac{8}{56}.
Convert 18\frac{1}{8} to have a denominator of 56 by multiplying numerator and denominator by 7: 1×78×7=756\frac{1 \times 7}{8 \times 7} = \frac{7}{56}.
Step 3: Add these equivalent fractions: 856+756=8+756=1556\frac{8}{56} + \frac{7}{56} = \frac{8 + 7}{56} = \frac{15}{56}.
Step 4: The fraction 1556\frac{15}{56} is already in its simplest form.
Therefore, the solution to the problem is 1556 \frac{15}{56} .

Answer

1556 \frac{15}{56}

Exercise #11

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

Video Solution

Step-by-Step Solution

To solve the problem of adding 25 \frac{2}{5} and 16 \frac{1}{6} , we need to find a common denominator. We do this by multiplying the denominators: 5×6=30 5 \times 6 = 30 . This is the smallest common multiple of the two denominators and ensures that each fraction can be represented with a common base, allowing addition.

Let's convert each fraction to an equivalent fraction with the common denominator of 30:

  • Convert 25 \frac{2}{5} : Multiply both the numerator and the denominator by 6 to get 2×65×6=1230 \frac{2 \times 6}{5 \times 6} = \frac{12}{30} .

  • Convert 16 \frac{1}{6} : Multiply both the numerator and the denominator by 5 to get 1×56×5=530 \frac{1 \times 5}{6 \times 5} = \frac{5}{30} .

Now, we add these equivalent fractions:

1230+530=12+530=1730 \frac{12}{30} + \frac{5}{30} = \frac{12 + 5}{30} = \frac{17}{30} .

The resulting fraction, 1730 \frac{17}{30} , is already in its simplest form because 17 is a prime number and does not share any common factors with 30 other than 1.

Thus, the sum of 25 \frac{2}{5} and 16 \frac{1}{6} is 1730 \frac{17}{30} .

Upon reviewing the given choices, the correct and matching choice is:

Choice 2: 1730 \frac{17}{30}

Answer

1730 \frac{17}{30}

Exercise #12

14+36= \frac{1}{4}+\frac{3}{6}=

Video Solution

Step-by-Step Solution

To solve the problem of adding 14 \frac{1}{4} and 36 \frac{3}{6} , we perform the following steps:

  • Step 1: Find the least common multiple (LCM) of the denominators 44 and 66. The LCM of 44 and 66 is 1212.
  • Step 2: Convert 14 \frac{1}{4} to an equivalent fraction with a denominator of 1212.
    Multiply both the numerator and denominator of 14 \frac{1}{4} by 33 to get 312 \frac{3}{12} .
  • Step 3: Convert 36 \frac{3}{6} to an equivalent fraction with a denominator of 1212.
    Multiply both the numerator and denominator of 36 \frac{3}{6} by 22 to get 612 \frac{6}{12} .
  • Step 4: Add the equivalent fractions 312+612 \frac{3}{12} + \frac{6}{12} .
  • Step 5: Combine the numerators while keeping the common denominator: 3+612=912 \frac{3+6}{12} = \frac{9}{12} .
  • Step 6: Simplify 912 \frac{9}{12} by dividing the numerator and the denominator by their greatest common divisor, which is 33, resulting in 34 \frac{3}{4} .

Therefore, the sum of 14 \frac{1}{4} and 36 \frac{3}{6} is 34 \frac{3}{4} .

Answer

34 \frac{3}{4}

Exercise #13

13+110= \frac{1}{3}+\frac{1}{10}=

Video Solution

Step-by-Step Solution

To solve this problem, we will add the fractions 13 \frac{1}{3} and 110 \frac{1}{10} by finding a common denominator.

  • Step 1: Find a common denominator.
    Since the denominators are 3 and 10, the least common multiple (LCM) of these numbers is 30. Therefore, the common denominator will be 30.
  • Step 2: Convert each fraction to have the common denominator.
    Convert 13 \frac{1}{3} into an equivalent fraction with a denominator of 30:
    13=1×103×10=1030 \frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30} .
    Convert 110 \frac{1}{10} into an equivalent fraction with a denominator of 30:
    110=1×310×3=330 \frac{1}{10} = \frac{1 \times 3}{10 \times 3} = \frac{3}{30} .
  • Step 3: Add the equivalent fractions.
    Now that both fractions have the same denominator, add the numerators while keeping the denominator 30:
    1030+330=10+330=1330 \frac{10}{30} + \frac{3}{30} = \frac{10 + 3}{30} = \frac{13}{30} .

After calculating, we find that the sum of the fractions is 1330\frac{13}{30}.

Therefore, the correct answer to the problem is 1330 \frac{13}{30} .

Answer

1330 \frac{13}{30}

Exercise #14

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

Video Solution

Step-by-Step Solution

To solve the problem of adding 14+13 \frac{1}{4} + \frac{1}{3} , we need to find a common denominator.

  • Step 1: Determine the least common multiple (LCM) of the denominators. For 4 and 3, the LCM is 12.
  • Step 2: Convert each fraction to an equivalent fraction with the denominator of 12.
    For 14 \frac{1}{4} , multiply both numerator and denominator by 3: 1343=312 \frac{1 \cdot 3}{4 \cdot 3} = \frac{3}{12} .
    For 13 \frac{1}{3} , multiply both numerator and denominator by 4: 1434=412 \frac{1 \cdot 4}{3 \cdot 4} = \frac{4}{12} .
  • Step 3: Add the resulting fractions: 312+412=3+412=712 \frac{3}{12} + \frac{4}{12} = \frac{3 + 4}{12} = \frac{7}{12} .

Thus, the sum of 14 \frac{1}{4} and 13 \frac{1}{3} is 712 \frac{7}{12} .

Therefore, the correct solution to the problem is 712 \frac{7}{12} .

Answer

712 \frac{7}{12}

Exercise #15

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

Video Solution

Step-by-Step Solution

To solve the problem, let's follow a structured approach:

  • Step 1: Determine the least common multiple (LCM) of the denominators (5 and 4). The LCM of 5 and 4 is 20.
  • Step 2: Adjust each fraction to have the common denominator of 20.
    For 25 \frac{2}{5} , multiply both numerator and denominator by 4 to get 820 \frac{8}{20} .
    For 14 \frac{1}{4} , multiply both numerator and denominator by 5 to get 520 \frac{5}{20} .
  • Step 3: Now, add the two fractions:
    820+520=8+520=1320 \frac{8}{20} + \frac{5}{20} = \frac{8 + 5}{20} = \frac{13}{20} .
  • Step 4: Verify if the fraction needs simplification. In this case, 1320 \frac{13}{20} is already in its simplest form.

The resulting fraction after adding 25 \frac{2}{5} and 14 \frac{1}{4} is 1320 \frac{13}{20} .

Answer

1320 \frac{13}{20}

Exercise #16

Solve the following exercise:

13+24=? \frac{1}{3}+\frac{2}{4}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, let's follow these steps:

  • Step 1: Simplify the fractions if possible.
  • Step 2: Identify the common denominator.
  • Step 3: Convert each fraction to have this common denominator.
  • Step 4: Add the fractions.
  • Step 5: Simplify the result, if necessary.

Step 1: Simplify 24 \frac{2}{4} . It simplifies to 12 \frac{1}{2} .

Step 2: The denominators are now 3 and 2. Find the least common multiple of 3 and 2, which is 6.

Step 3: Convert each fraction to have the common denominator of 6:
13=1×23×2=26\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}
12=1×32×3=36\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}

Step 4: Add the fractions:
26+36=2+36=56\frac{2}{6} + \frac{3}{6} = \frac{2 + 3}{6} = \frac{5}{6}

Step 5: The fraction 56\frac{5}{6} is already in its simplest form.

Therefore, the solution to the problem is 56\frac{5}{6}.

Answer

1012 \frac{10}{12}

Exercise #17

Solve the following exercise:

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

Video Solution

Step-by-Step Solution

To solve the problem of adding the fractions 15 \frac{1}{5} and 13 \frac{1}{3} , we follow these steps:

  • Step 1: Find a common denominator for the fractions. Since the denominators are 55 and 33, the least common multiple is 1515.
  • Step 2: Convert each fraction to this common denominator:
    - For 15 \frac{1}{5} , multiply both numerator and denominator by 33 (the denominator of the other fraction), resulting in 315 \frac{3}{15} .
    - For 13 \frac{1}{3} , multiply both numerator and denominator by 55 (the denominator of the other fraction), resulting in 515 \frac{5}{15} .
  • Step 3: Add the fractions now that they have a common denominator:
    315+515=3+515=815\frac{3}{15} + \frac{5}{15} = \frac{3+5}{15} = \frac{8}{15}.

Therefore, when you add 15 \frac{1}{5} and 13 \frac{1}{3} , the solution is 815 \frac{8}{15} .

Answer

815 \frac{8}{15}

Exercise #18

Solve the following exercise:

35+14=? \frac{3}{5}+\frac{1}{4}=\text{?}

Video Solution

Step-by-Step Solution

To solve the addition of fractions 35+14 \frac{3}{5} + \frac{1}{4} , follow these steps:

  • Step 1: Find a common denominator. The denominators are 5 and 4. The least common denominator is 20, which is the product of 5 and 4.
  • Step 2: Convert each fraction to have the common denominator of 20.
    • For 35 \frac{3}{5} , multiply both the numerator and the denominator by 4: 35=3×45×4=1220 \frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20} .
    • For 14 \frac{1}{4} , multiply both the numerator and denominator by 5: 14=1×54×5=520 \frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20} .
  • Step 3: Add the equivalent fractions: 1220+520=12+520=1720 \frac{12}{20} + \frac{5}{20} = \frac{12 + 5}{20} = \frac{17}{20} .

Thus, the sum of 35 \frac{3}{5} and 14 \frac{1}{4} is 1720 \frac{17}{20} .

Answer

1720 \frac{17}{20}

Exercise #19

Solve the following exercise:

12+19=? \frac{1}{2}+\frac{1}{9}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, we will add the fractions 12 \frac{1}{2} and 19 \frac{1}{9} by finding a common denominator.

  • First, identify the denominators: 2 and 9.
  • Find a common denominator by multiplying the denominators: 2×9=18 2 \times 9 = 18 .
  • Convert each fraction to an equivalent fraction with this common denominator:
    • Convert 12 \frac{1}{2} to have a denominator of 18 by multiplying both the numerator and denominator by 9: 1×92×9=918 \frac{1 \times 9}{2 \times 9} = \frac{9}{18} .
    • Convert 19 \frac{1}{9} to have a denominator of 18 by multiplying both the numerator and denominator by 2: 1×29×2=218 \frac{1 \times 2}{9 \times 2} = \frac{2}{18} .
  • Add the converted fractions: 918+218=1118 \frac{9}{18} + \frac{2}{18} = \frac{11}{18} .
  • The fraction 1118 \frac{11}{18} is already in its simplest form.

Thus, the sum of the fractions 12 \frac{1}{2} and 19 \frac{1}{9} is 1118 \frac{11}{18} .

Answer

1118 \frac{11}{18}

Exercise #20

Solve the following exercise:

28+13=? \frac{2}{8}+\frac{1}{3}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem of adding 28\frac{2}{8} and 13\frac{1}{3}, we need to first convert these fractions to have a common denominator.

Step 1: Find the least common denominator (LCD).
- The denominators of the fractions are 88 and 33.
- The common denominator can be found by multiplying 88 and 33, which gives us 2424.

Step 2: Convert each fraction to an equivalent fraction with the common denominator of 2424.
- For 28\frac{2}{8}, multiply both the numerator and the denominator by 33:
28=2×38×3=624\frac{2}{8} = \frac{2 \times 3}{8 \times 3} = \frac{6}{24}.
- For 13\frac{1}{3}, multiply both the numerator and the denominator by 88:
13=1×83×8=824\frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24}.

Step 3: Add the resulting fractions.
- 624+824=6+824=1424\frac{6}{24} + \frac{8}{24} = \frac{6 + 8}{24} = \frac{14}{24}.

Therefore, the solution to the problem is 1424\frac{14}{24}, which simplifies our answer.

Answer

1424 \frac{14}{24}