Examples with solutions for All Operations in Fractions: The common denominator is smaller than the product of the denominators

Exercise #1

14+78= \frac{1}{4}+\frac{7}{8}=

Video Solution

Step-by-Step Solution

To find the sum 14+78 \frac{1}{4} + \frac{7}{8} , follow these steps:

  • Step 1: Identify the least common denominator (LCD) of the fractions. The denominators 4 and 8 have an LCD of 8.
  • Step 2: Convert 14 \frac{1}{4} to an equivalent fraction with a denominator of 8. Multiply both the numerator and the denominator by 2: 14=1×24×2=28 \frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8} .
  • Step 3: The second fraction, 78 \frac{7}{8} , already has the correct denominator. Therefore, it remains 78 \frac{7}{8} .
  • Step 4: Add the numerators of the two fractions: 28+78=2+78=98 \frac{2}{8} + \frac{7}{8} = \frac{2+7}{8} = \frac{9}{8} .

Therefore, the sum of 14 \frac{1}{4} and 78 \frac{7}{8} is 98 \frac{9}{8} .

Answer

98 \frac{9}{8}

Exercise #2

46+18= \frac{4}{6}+\frac{1}{8}=

Video Solution

Step-by-Step Solution

To solve the addition of the fractions 46+18 \frac{4}{6} + \frac{1}{8} , we will first find the least common denominator.

  • The denominators of the fractions are 6 and 8. To add these fractions, we need a common denominator.
  • Calculate the least common multiple (LCM) of 6 and 8:
    • Prime factorization of 6: 6=2×3 6 = 2 \times 3 .
    • Prime factorization of 8: 8=23 8 = 2^3 .
    • The LCM will take the highest power of each prime that appears in these factorizations: 23×3=24 2^3 \times 3 = 24 .
  • Convert each fraction to an equivalent fraction with 24 as the denominator:
    • Convert 46 \frac{4}{6} : Multiply both the numerator and denominator by 4 (since 246=4 \frac{24}{6} = 4 ): 4×46×4=1624\frac{4 \times 4}{6 \times 4} = \frac{16}{24}.
    • Convert 18 \frac{1}{8} : Multiply both the numerator and denominator by 3 (since 248=3 \frac{24}{8} = 3 ): 1×38×3=324\frac{1 \times 3}{8 \times 3} = \frac{3}{24}.
  • Now, add these two fractions:
    • 1624+324=16+324=1924\frac{16}{24} + \frac{3}{24} = \frac{16 + 3}{24} = \frac{19}{24}.

Thus, the sum of the fractions 46 \frac{4}{6} and 18 \frac{1}{8} is 1924\frac{19}{24}.

The correct choice from the available options is 1924\frac{19}{24}.

Therefore, the solution to the problem is 1924 \frac{19}{24} .

Answer

1924 \frac{19}{24}

Exercise #3

Solve the following exercise:

34+16=? \frac{3}{4}+\frac{1}{6}=\text{?}

Video Solution

Step-by-Step Solution

To solve the addition of these two fractions, we'll proceed as follows:

  • Step 1: Determine the least common denominator (LCD) of the fractions.
    The denominators are 4 and 6, and the smallest number that is a multiple of both is 12. Thus, the LCD is 12.
  • Step 2: Convert each fraction to an equivalent fraction with the denominator 12.
    - For 34 \frac{3}{4} , multiply both numerator and denominator by 3: 3×34×3=912 \frac{3 \times 3}{4 \times 3} = \frac{9}{12} .
    - For 16 \frac{1}{6} , multiply both numerator and denominator by 2: 1×26×2=212 \frac{1 \times 2}{6 \times 2} = \frac{2}{12} .
  • Step 3: Add the converted fractions.
    912+212=9+212=1112 \frac{9}{12} + \frac{2}{12} = \frac{9 + 2}{12} = \frac{11}{12} .

Therefore, the solution to the problem is 1112\frac{11}{12}.

Answer

1112 \frac{11}{12}

Exercise #4

Solve the following exercise:

24+26=? \frac{2}{4}+\frac{2}{6}=\text{?}

Video Solution

Step-by-Step Solution

To solve the fraction addition problem 24+26\frac{2}{4} + \frac{2}{6}, follow these steps:

  • Step 1: Identify the least common denominator (LCD) of the fractions. The denominators are 4 and 6. The factors of 4 are 2 and 2, and the factors of 6 are 2 and 3. The LCD is the smallest number that both denominators divide into, which is 12.

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

  • Step 3: For 24\frac{2}{4}:

    • Find the equivalent fraction: Multiply both the numerator and denominator by 3 (since 4 * 3 = 12).

    • The equivalent fraction is 2×34×3=612\frac{2 \times 3}{4 \times 3} = \frac{6}{12}.

  • Step 4: For 26\frac{2}{6}:

    • Find the equivalent fraction: Multiply both the numerator and denominator by 2 (since 6 * 2 = 12).

    • The equivalent fraction is 2×26×2=412\frac{2 \times 2}{6 \times 2} = \frac{4}{12}.

  • Step 5: Add the new fractions: 612+412=1012\frac{6}{12} + \frac{4}{12} = \frac{10}{12}.

Therefore, the sum of the fractions is 1012\boxed{\frac{10}{12}}.

Answer

1012 \frac{10}{12}

Exercise #5

12+16= \frac{1}{2}+\frac{1}{6}=

Video Solution

Step-by-Step Solution

To solve the problem of adding 12 \frac{1}{2} and 16 \frac{1}{6} , we need to follow these steps:

  • Step 1: Determine the least common denominator (LCD).
  • Step 2: Convert the fractions to have this common denominator.
  • Step 3: Add the fractions.
  • Step 4: Simplify the result if necessary.

Step 1: The denominators are 2 and 6. The least common multiple of 2 and 6 is 6.

Step 2: We convert each fraction:
- Convert 12 \frac{1}{2} to a denominator of 6: 12=1×32×3=36\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}.
- The fraction 16 \frac{1}{6} already has the denominator 6.

Step 3: Add the fractions with common denominators:
36+16=3+16=46. \frac{3}{6} + \frac{1}{6} = \frac{3 + 1}{6} = \frac{4}{6}.

Step 4: Simplify the fraction 46\frac{4}{6}.
The greatest common divisor of 4 and 6 is 2, so divide both the numerator and the denominator by 2:
46=4÷26÷2=23. \frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}.

Therefore, the solution to the problem is 23\frac{2}{3}.

Answer

23 \frac{2}{3}

Exercise #6

Solve the following exercise:

14+46=? \frac{1}{4}+\frac{4}{6}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem of adding 14+46 \frac{1}{4} + \frac{4}{6} , follow these steps:

  • Step 1: Find the Least Common Denominator (LCD):
    The denominators are 4 and 6. The least common multiple of 4 and 6 is 12.
  • Step 2: Convert Each Fraction:
    - Convert 14 \frac{1}{4} to a fraction with a denominator of 12:
    14=1×34×3=312 \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
    - Convert 46 \frac{4}{6} to a fraction with a denominator of 12:
    46=4×26×2=812 \frac{4}{6} = \frac{4 \times 2}{6 \times 2} = \frac{8}{12}
  • Step 3: Add the Fractions:
    Now, add the fractions: 312+812=3+812=1112 \frac{3}{12} + \frac{8}{12} = \frac{3 + 8}{12} = \frac{11}{12}
  • Step 4: Simplify the Fraction (if needed):
    The fraction 1112 \frac{11}{12} is already in its simplest form.

Therefore, the solution to the problem is 1112 \frac{11}{12} .

Answer

1112 \frac{11}{12}

Exercise #7

Solve the following exercise:

24+16=? \frac{2}{4}+\frac{1}{6}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem of adding 24 \frac{2}{4} and 16 \frac{1}{6} , follow these steps:

Step 1: Identify the least common denominator of the fractions.

The denominators of the fractions are 4 and 6. The least common multiple of 4 and 6 is 12, so 12 is our common denominator.

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

  • For 24 \frac{2}{4} : Multiply both numerator and denominator by 3 to obtain 612 \frac{6}{12} . This is because 4×3=12 4 \times 3 = 12 .

  • For 16 \frac{1}{6} : Multiply both numerator and denominator by 2 to obtain 212 \frac{2}{12} . This is because 6×2=12 {6 \times 2 = 12} .

Step 3: Add the converted fractions.

612+212=6+212=812 \frac{6}{12} + \frac{2}{12} = \frac{6 + 2}{12} = \frac{8}{12}

Step 4: Simplify the final fraction if possible.

In this case, 812 \frac{8}{12} can be simplified by dividing numerator and denominator by their greatest common divisor, which is 4. Thus, 812 \frac{8}{12} simplifies to 23 \frac{2}{3} .

However, as per the problem's required answer, the unsimplified fraction is 812 \frac{8}{12} .

Therefore, the solution to the problem is:

812 \frac{8}{12}

Answer

812 \frac{8}{12}

Exercise #8

12+46= \frac{1}{2}+\frac{4}{6}=

Video Solution

Step-by-Step Solution

To solve the problem of adding the fractions 12\frac{1}{2} and 46\frac{4}{6}, we start by finding the least common denominator (LCD).

First, we identify the denominators: 2 and 6. The least common multiple of 2 and 6 is 6, which will be our LCD.

Next, we convert each fraction to have the denominator of 6:

  • Convert 12\frac{1}{2} to an equivalent fraction with a denominator of 6. Since 23=62 \cdot 3 = 6, multiply the numerator by 3: 1×32×3=36\frac{1 \times 3}{2 \times 3} = \frac{3}{6}.

  • The fraction 46\frac{4}{6} already has the desired common denominator.

Now that the fractions are 36\frac{3}{6} and 46\frac{4}{6}, we can add them:

36+46=3+46=76\frac{3}{6} + \frac{4}{6} = \frac{3+4}{6} = \frac{7}{6}.

The solution to the problem is 76\frac{7}{6}, which matches choice 2.

Answer

76 \frac{7}{6}

Exercise #9

34+16= \frac{3}{4}+\frac{1}{6}=

Video Solution

Step-by-Step Solution

To solve the problem of adding the fractions 34\frac{3}{4} and 16\frac{1}{6}, we need to find a common denominator.

  • Step 1: Find the LCM of the denominators:
    The denominators are 4 and 6. The LCM of 4 and 6 is 12.
  • Step 2: Convert each fraction to have the common denominator:
    - Convert 34\frac{3}{4} to an equivalent fraction with a denominator of 12. To do this, multiply both the numerator and the denominator by 3:
    34=3×34×3=912\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}.
    - Convert 16\frac{1}{6} to an equivalent fraction with a denominator of 12. Multiply both the numerator and the denominator by 2:
    16=1×26×2=212\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}.
  • Step 3: Add the fractions:
    Now that both fractions have the same denominator, add the numerators:
    912+212=1112\frac{9}{12} + \frac{2}{12} = \frac{11}{12}.
  • Step 4: Simplify if necessary:
    The fraction 1112\frac{11}{12} is already in its simplest form.

Therefore, the solution to the problem 34+16\frac{3}{4} + \frac{1}{6} is 1112\frac{11}{12}.

Answer

1112 \frac{11}{12}

Exercise #10

Solve the following exercise:

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

Video Solution

Step-by-Step Solution

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

  • Step 1: Determine the least common denominator of 4 and 6.
  • Step 2: Convert each fraction to this common denominator.
  • Step 3: Add the numerators and form the resultant fraction.
  • Step 4: Simplify the resulting fraction if necessary.

Now, let's work through each step:
Step 1: The denominators are 4 and 6. The least common multiple of 4 and 6 is 12.

Step 2: Convert each fraction to have the denominator 12.
For 14\frac{1}{4}, multiplying the numerator and denominator by 3 gives 1×34×3=312\frac{1 \times 3}{4 \times 3} = \frac{3}{12}.
For 26\frac{2}{6}, multiplying the numerator and denominator by 2 gives 2×26×2=412\frac{2 \times 2}{6 \times 2} = \frac{4}{12}.

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

Step 4: Check if 712\frac{7}{12} can be simplified. Since 7 and 12 have no common factors other than 1, it is already in its simplest form.

Therefore, the sum of 14+26\frac{1}{4} + \frac{2}{6} is 712\frac{7}{12}.

Answer

712 \frac{7}{12}

Exercise #11

14+34= \frac{1}{4}+\frac{3}{4}=

Video Solution

Step-by-Step Solution

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

  • Step 1: Identify the denominators of the fractions.
  • Step 2: Because the denominators are the same, add the numerators.
  • Step 3: Simplify the resulting fraction if necessary.

Now, let's work through each step:
Step 1: Both fractions, 14 \frac{1}{4} and 34 \frac{3}{4} , have the same denominator, 4.
Step 2: Since the denominators are the same, we can add the numerators: 1+3=4 1 + 3 = 4 .
Step 3: The resulting fraction is 44 \frac{4}{4} , which simplifies to 1 1 .

Therefore, the solution to the problem is 1 1 .

Answer

1 1

Exercise #12

13+16= \frac{1}{3}+\frac{1}{6}=

Video Solution

Step-by-Step Solution

We need to find a common denominator for the fractions 13\frac{1}{3} and 16\frac{1}{6} in order to add them together.

Step 1: Identify the least common denominator (LCD).

  • The denominators are 3 and 6.
  • The least common multiple (LCM) of 3 and 6 is 6. Hence, the LCD is 6.

Step 2: Convert each fraction to an equivalent fraction with the LCD of 6.

  • 13\frac{1}{3} needs to be converted. Multiply both numerator and denominator by 2: 13=1×23×2=26\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}.
  • 16\frac{1}{6} already has the denominator as 6, so it remains 16\frac{1}{6}.

Step 3: Add the fractions.

  • Now that the denominators are the same, we can add the numerators: 26+16=2+16=36\frac{2}{6} + \frac{1}{6} = \frac{2 + 1}{6} = \frac{3}{6}.

Step 4: Simplify the result.

  • 36\frac{3}{6} can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3: 36=3÷36÷3=12\frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}.

Thus, the result of the addition of 13\frac{1}{3} and 16\frac{1}{6} is 12\frac{1}{2}.

Therefore, the solution to the problem is 12\frac{1}{2}.

Answer

12 \frac{1}{2}

Exercise #13

Solve the following exercise:

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

Video Solution

Step-by-Step Solution

The problem involves adding the fractions 13 \frac{1}{3} and 49 \frac{4}{9} .

Step 1: Identify the Least Common Denominator (LCD).

  • The denominators are 3 and 9. The least common multiple of 3 and 9 is 9. Thus, the LCD is 9.

Step 2: Convert the fractions to have the common denominator.

  • The fraction 13 \frac{1}{3} must be converted to have the denominator of 9. Multiply both the numerator and denominator by 3:
  • 13=1×33×3=39 \frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}
  • The fraction 49 \frac{4}{9} already has the denominator of 9, so it remains unchanged.

Step 3: Add the equivalent fractions.

  • Add the numerators together, keeping the denominator:
  • 39+49=3+49=79 \frac{3}{9} + \frac{4}{9} = \frac{3+4}{9} = \frac{7}{9}

Step 4: Simplify the result, if necessary.

  • The fraction 79 \frac{7}{9} is already in simplest form.

Therefore, the solution to the problem is 79 \frac{7}{9} .

Answer

79 \frac{7}{9}

Exercise #14

Solve the following exercise:

410+26=? \frac{4}{10}+\frac{2}{6}=\text{?}

Video Solution

Step-by-Step Solution

To solve for the sum of 410+26 \frac{4}{10} + \frac{2}{6} , we will proceed with the following steps:

  • Step 1: Identify the least common denominator (LCD)
  • Step 2: Convert each fraction to an equivalent fraction with this common denominator
  • Step 3: Add the numerators

Let's begin:

Step 1: Identify the least common denominator (LCD)
The denominators are 10 and 6. The least common multiple (LCM) of 10 and 6 can be found by evaluating their prime factors:
10 = 2 × 5
6 = 2 × 3
The LCM is found by taking the highest power of each prime that appears:
LCM = 2 × 3 × 5 = 30.
Thus, the common denominator is 30.

Step 2: Convert each fraction to an equivalent fraction with the common denominator of 30
For 410 \frac{4}{10} :
Multiply both the numerator and the denominator by 3 to make the denominator 30:
410=4×310×3=1230 \frac{4}{10} = \frac{4 \times 3}{10 \times 3} = \frac{12}{30} .
For 26 \frac{2}{6} :
Multiply both the numerator and the denominator by 5 to make the denominator 30:
26=2×56×5=1030 \frac{2}{6} = \frac{2 \times 5}{6 \times 5} = \frac{10}{30} .

Step 3: Add the numerators
Now that the fractions have the same denominator, add the numerators:
1230+1030=12+1030=2230 \frac{12}{30} + \frac{10}{30} = \frac{12 + 10}{30} = \frac{22}{30} .
This fraction cannot be simplified further as 22 and 30 have no common factors besides 1.

Therefore, the sum of 410+26 \frac{4}{10} + \frac{2}{6} is 2230 \frac{22}{30} .

Answer

2230 \frac{22}{30}

Exercise #15

Solve the following exercise:

26+39=? \frac{2}{6}+\frac{3}{9}=\text{?}

Video Solution

Step-by-Step Solution

To solve the addition of fractions 26+39 \frac{2}{6} + \frac{3}{9} , we will follow these logical steps:

  • Step 1: Find a common denominator.
    The denominators are 66 and 99. The least common multiple (LCM) of these numbers is 1818.
  • Step 2: Convert each fraction to have the denominator of 1818.
    To convert 26\frac{2}{6} to a denominator of 1818, multiply both the numerator and the denominator by 33 (because 6×3=186 \times 3 = 18): 26=2×36×3=618 \frac{2}{6} = \frac{2 \times 3}{6 \times 3} = \frac{6}{18} To convert 39\frac{3}{9} to a denominator of 1818, multiply both the numerator and the denominator by 22 (because 9×2=189 \times 2 = 18): 39=3×29×2=618 \frac{3}{9} = \frac{3 \times 2}{9 \times 2} = \frac{6}{18}
  • Step 3: Add the fractions.
    Now that both fractions have the same denominator, add their numerators: 618+618=6+618=1218 \frac{6}{18} + \frac{6}{18} = \frac{6 + 6}{18} = \frac{12}{18}
  • Step 4: Simplify if possible.
    Check if 1218\frac{12}{18} can be simplified. The greatest common divisor (GCD) of 1212 and 1818 is 66, so: 1218=12÷618÷6=23 \frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3} However, since the original question focused on achieving the fraction with denominator 1818, our final non-simplified answer remains 1218\frac{12}{18}.

The final result is that the sum of the fractions is 1218\frac{12}{18}.

Answer

1218 \frac{12}{18}

Exercise #16

314+37= \frac{3}{14}+\frac{3}{7}=

Video Solution

Step-by-Step Solution

To solve the problem of adding 314+37 \frac{3}{14} + \frac{3}{7} , we need the following steps:

  • Step 1: Identify the least common denominator of 14 14 and 7 7 . Since 7 7 is a factor of 14 14 , the least common denominator is 14 14 .
  • Step 2: Rewrite the fractions with the common denominator.
    The fraction 37 \frac{3}{7} can be converted to an equivalent fraction with the denominator 14 14 :
    • Multiply the numerator and the denominator of 37 \frac{3}{7} by 2 2 (since 7×2=14 7 \times 2 = 14 ) to get 614 \frac{6}{14} .
  • Step 3: Add 314 \frac{3}{14} and 614 \frac{6}{14} now that they have the same denominator:
    314+614=3+614=914\frac{3}{14} + \frac{6}{14} = \frac{3+6}{14} = \frac{9}{14}.
  • Step 4: Simplify if necessary. The numerator and denominator here are coprime, so 914 \frac{9}{14} is already in its simplest form.

Thus, the sum of the fractions is 914 \frac{9}{14} .

Answer

914 \frac{9}{14}

Exercise #17

34+38= \frac{3}{4}+\frac{3}{8}=

Video Solution

Step-by-Step Solution

To solve the problem of adding 34 \frac{3}{4} and 38 \frac{3}{8} , let's follow a systematic approach:

  • Step 1: Identify the Common Denominator
    The denominators are 4 and 8. The least common multiple (LCM) of 4 and 8 is 8. Thus, 8 will be our common denominator.
  • Step 2: Convert Fractions to Common Denominator
    The fraction 34 \frac{3}{4} needs to be converted to an equivalent fraction with a denominator of 8. To do this, multiply both the numerator and the denominator by 2: 34=3×24×2=68 \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8} .
    The fraction 38 \frac{3}{8} already has a denominator of 8, so it remains the same: 38 \frac{3}{8} .
  • Step 3: Add the Fractions
    With a common denominator, add the numerators while keeping the denominator the same: 68+38=6+38=98 \frac{6}{8} + \frac{3}{8} = \frac{6 + 3}{8} = \frac{9}{8} .
  • Step 4: Simplify the Fraction if Necessary
    The fraction 98 \frac{9}{8} is already in its simplest form, but it is an improper fraction. If desired, it can be expressed as a mixed number: 118 1 \frac{1}{8} . However, 98 \frac{9}{8} as a fraction suffices for this problem.

Therefore, the solution to the problem is 98 \frac{9}{8} .

Answer

98 \frac{9}{8}

Exercise #18

Solve the following exercise:

38+512=? \frac{3}{8}+\frac{5}{12}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem of adding 38 \frac{3}{8} and 512 \frac{5}{12} , follow these steps:

  • Step 1: Find the least common multiple (LCM) of the denominators 8 and 12. The LCM of 8 and 12 is 24.
  • Step 2: Convert the fractions to have the common denominator 24.
    To convert 38 \frac{3}{8} to a denominator of 24:
    Multiply both the numerator and denominator by 3: 3×38×3=924 \frac{3 \times 3}{8 \times 3} = \frac{9}{24} .
  • Step 3: Convert 512 \frac{5}{12} to a denominator of 24:
    Multiply both the numerator and denominator by 2: 5×212×2=1024 \frac{5 \times 2}{12 \times 2} = \frac{10}{24} .
  • Step 4: Add the fractions 924+1024 \frac{9}{24} + \frac{10}{24} .
    Since they share the same denominator, add the numerators: 9+10=19 9 + 10 = 19 .
  • Step 5: The sum is 1924 \frac{19}{24} . There is no need to simplify further, as 19 and 24 have no common factors other than 1.

Thus, the fraction 38+512 \frac{3}{8} + \frac{5}{12} simplifies to 1924 \frac{19}{24} .

Answer

1924 \frac{19}{24}

Exercise #19

Solve the following exercise:

15+710=? \frac{1}{5}+\frac{7}{10}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem of adding the fractions 15\frac{1}{5} and 710\frac{7}{10}, we follow these steps:

  • Step 1: Identify the least common multiple (LCM) of the denominators 5 and 10, which is 10.
  • Step 2: Convert 15\frac{1}{5} to a fraction with a denominator of 10. To do this, multiply both the numerator and denominator by 2: 15=1×25×2=210 \frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}
  • Step 3: Observe that 710\frac{7}{10} already has the common denominator of 10.
  • Step 4: Add the two fractions with a common denominator: 210+710=2+710=910 \frac{2}{10} + \frac{7}{10} = \frac{2 + 7}{10} = \frac{9}{10}

The sum of 15\frac{1}{5} and 710\frac{7}{10} is thus 910\mathbf{\frac{9}{10}}.

Answer

910 \frac{9}{10}

Exercise #20

Solve the following exercise:

48+310=? \frac{4}{8}+\frac{3}{10}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem of adding the fractions 48+310\frac{4}{8} + \frac{3}{10}, we follow these steps:

  • Step 1: Determine the least common denominator (LCD) for the fractions.
  • Step 2: Convert each fraction to have the LCD.
  • Step 3: Add the numerators of these converted fractions.

Let's go through each step in detail:

Step 1: Find the least common denominator for the fractions.

The denominators are 8 and 10. The least common multiple of 8 and 10 is 40. So, the LCD is 40.

Step 2: Convert each fraction to an equivalent fraction with a denominator of 40.

For 48\frac{4}{8}: Multiply both the numerator and denominator by 5 to convert it:

4×58×5=2040\frac{4 \times 5}{8 \times 5} = \frac{20}{40}.

For 310\frac{3}{10}: Multiply both the numerator and denominator by 4 to convert it:

3×410×4=1240\frac{3 \times 4}{10 \times 4} = \frac{12}{40}.

Step 3: Add the two fractions with the common denominator:

2040+1240=20+1240=3240\frac{20}{40} + \frac{12}{40} = \frac{20 + 12}{40} = \frac{32}{40}.

Thus, the sum of the fractions is 3240\frac{32}{40}.

Therefore, the solution to the problem is 3240\frac{32}{40}.

Answer

3240 \frac{32}{40}