Examples with solutions for Subtraction of Fractions: Fractions with common denominators

Exercise #1

Solve the following exercise:

6545=? \frac{6}{5}-\frac{4}{5}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, we'll proceed as follows:

  • Step 1: Identify the common denominator, which is already present as 5.
  • Step 2: Subtract the numerators: 646 - 4.
  • Step 3: Write the result over the common denominator.

Now, let's work through these steps:
Step 1: The denominators are the same, so we maintain the denominator of 5.
Step 2: Subtract the numerators: 64=26 - 4 = 2.
Step 3: Place the result above the common denominator: 25\frac{2}{5}.

Therefore, the solution to the problem is 25\frac{2}{5}.

Answer

25 \frac{2}{5}

Exercise #2

Solve the following exercise:

5737=? \frac{5}{7}-\frac{3}{7}=\text{?}

Video Solution

Step-by-Step Solution

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

  • Step 1: Identify the given fractions, 57\frac{5}{7} and 37\frac{3}{7}, which have a common denominator of 7.
  • Step 2: Subtract the numerators, because the denominators are the same: 535 - 3.
  • Step 3: Write the result over the common denominator: 537=27\frac{5-3}{7} = \frac{2}{7}.

Now, let's work through each step:

Step 1: We recognize that both fractions have the same denominator, 7.

Step 2: We focus on subtracting the numerators: 53=25 - 3 = 2.

Step 3: We keep the denominator the same: 27\frac{2}{7}.

Therefore, the solution to the problem is 27\frac{2}{7}.

Answer

27 \frac{2}{7}

Exercise #3

Solve the following exercise:

5323=? \frac{5}{3}-\frac{2}{3}=\text{?}

Video Solution

Step-by-Step Solution

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

  • Step 1: Recognize that both fractions have the same denominator, which allows direct subtraction of the numerators.
  • Step 2: Subtract the numerator of the second fraction (22) from the numerator of the first fraction (55).
  • Step 3: Place the result over the common denominator.

Now, let's work through each step:
Step 1: We have 5323\frac{5}{3} - \frac{2}{3}. Both denominators are 3.
Step 2: Subtract the numerators: 52=35 - 2 = 3.
Step 3: The resulting fraction is 33\frac{3}{3}.

Finally, simplify 33=1\frac{3}{3} = 1.

Therefore, the solution to the problem is 1.

Answer

1

Exercise #4

Solve the following exercise:

8565=? \frac{8}{5}-\frac{6}{5}=\text{?}

Video Solution

Step-by-Step Solution

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

  • Step 1: Subtract the numerators.
  • Step 2: Keep the common denominator.
  • Step 3: Simplify the result if possible.

Now, let's work through each step:
Step 1: The numerators are 8 and 6. Subtract them: 86=2 8 - 6 = 2 .
Step 2: The common denominator is 5, so the fraction becomes 25 \frac{2}{5} .
Step 3: Since 25 \frac{2}{5} is already in its simplest form, no further simplification is necessary.

Therefore, the solution to the problem is 25 \frac{2}{5} .

Answer

25 \frac{2}{5}

Exercise #5

Solve the following exercise:

3414=? \frac{3}{4}-\frac{1}{4}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, we will use the following steps:

  • Step 1: Since both fractions, 34\frac{3}{4} and 14\frac{1}{4}, have the common denominator of 4, we can subtract them directly by subtracting their numerators.
  • Step 2: Subtract the numerators: 31=23 - 1 = 2.
  • Step 3: Place the result over the common denominator: 24\frac{2}{4}.
  • Step 4: Simplify the fraction if possible. In this case, we can simplify 24\frac{2}{4} by dividing both numerator and denominator by their greatest common divisor, which is 2.
  • Step 5: Performing the simplification results in 12\frac{1}{2}.

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

Answer

12 \frac{1}{2}

Exercise #6

Solve the following exercise:

6838=? \frac{6}{8}-\frac{3}{8}=\text{?}

Video Solution

Step-by-Step Solution

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

  • Step 1: Identify the given fractions and note their common denominator.
  • Step 2: Subtract the numerators.
  • Step 3: Write down the resulting fraction and simplify if needed.
  • Step 4: Determine which of the choices matches our result.

Now, let's work through each step:

Step 1: We have the fractions 68\frac{6}{8} and 38\frac{3}{8} with a common denominator of 8.

Step 2: Subtract the numerators: 63=3 6 - 3 = 3 .

Step 3: The resulting fraction is 38\frac{3}{8}. There is no need for simplification as this fraction is already in its simplest form.

Step 4: The correct choice is the one that matches 38\frac{3}{8}, which according to the list of choices, is Choice 2.

Therefore, the solution to the problem is 38\frac{3}{8}.

Answer

38 \frac{3}{8}

Exercise #7

Solve the following exercise:

710410=? \frac{7}{10}-\frac{4}{10}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, we need to subtract two fractions with the same denominator. Given the fractions 710\frac{7}{10} and 410\frac{4}{10}, we proceed as follows:

  • Step 1: Identify the numerators and the common denominator.
  • Step 2: Subtract the numerators. Here, we subtract 44 from 77, resulting in 33.
  • Step 3: Retain the common denominator, which is 1010.
  • Step 4: Express the answer as a fraction.

Putting it all together, the operation becomes: 710410=310\frac{7}{10} - \frac{4}{10} = \frac{3}{10}.

Since the fraction 310\frac{3}{10} is already in its simplest form, no further simplification is needed.

Therefore, the solution to the problem is 310 \frac{3}{10} .

Answer

310 \frac{3}{10}

Exercise #8

Solve the following exercise:

4535=? \frac{4}{5}-\frac{3}{5}=\text{?}

Video Solution

Step-by-Step Solution

To solve the subtraction of fractions problem 4535 \frac{4}{5} - \frac{3}{5} , we will follow these steps:

  • Step 1: Identify that both fractions share the same denominator, 5.
  • Step 2: Subtract the numerators: 43=1 4 - 3 = 1 .
  • Step 3: Place the result from Step 2 over the common denominator: 15\frac{1}{5}.

Now, let's work through each step:
Step 1: We observe that 45\frac{4}{5} and 35\frac{3}{5} have the same denominator of 5.
Step 2: Subtract the numerators: 43=1 4 - 3 = 1 .
Step 3: Write the result from Step 2 over the common denominator: 15\frac{1}{5}.

Therefore, the solution to the problem 4535 \frac{4}{5} - \frac{3}{5} is 15 \frac{1}{5} .

Answer

15 \frac{1}{5}

Exercise #9

Solve the following exercise:

712512=? \frac{7}{12}-\frac{5}{12}=\text{?}

Video Solution

Step-by-Step Solution

The problem requires us to subtract the fraction 512\frac{5}{12} from 712\frac{7}{12}. Since both fractions have the same denominator, we can directly subtract their numerators while keeping the denominator constant:

The calculation is as follows:

  • Subtract the numerators: 75=27 - 5 = 2.
  • Keep the denominator the same: 12.
  • Thus, 712512=212\frac{7}{12} - \frac{5}{12} = \frac{2}{12}. Simplifying 212\frac{2}{12} by dividing both the numerator and denominator by their greatest common divisor, which is 2, we get 16\frac{1}{6}.

After performing the simplification, the answer to the problem is 16\frac{1}{6}.

From the answer choices given, 16\frac{1}{6} corresponds to choice 2.

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

Answer

16 \frac{1}{6}

Exercise #10

Solve the following exercise:

5515=? \frac{5}{5}-\frac{1}{5}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, we can follow the simple steps of subtracting fractions with the same denominator:

  • Step 1: Identify that both fractions have the same denominator. Here, both denominators are 5.
  • Step 2: Subtract the numerators directly. The numerators are 5 and 1.
  • Step 3: Calculate the difference in the numerators: 51=4 5 - 1 = 4 .
  • Step 4: Keep the common denominator the same. Hence, the difference is 45\frac{4}{5}.

Therefore, the solution to the problem 5515 \frac{5}{5} - \frac{1}{5} is 45 \frac{4}{5} .

Answer

45 \frac{4}{5}

Exercise #11

Solve the following exercise:

2323=? \frac{2}{3}-\frac{2}{3}=\text{?}

Video Solution

Step-by-Step Solution

Let's solve the problem step-by-step:

  • Step 1: Subtract the fractions. We have 2323 \frac{2}{3} - \frac{2}{3} .
  • Step 2: Since the denominators are the same (3), subtract the numerators. Thus, 22=0 2 - 2 = 0 .
  • Step 3: The result of the fraction subtraction is 03 \frac{0}{3} .

Observing that 03 \frac{0}{3} equals 0, we find that the subtraction results in just the number 0.

Therefore, the solution to the problem is 0.

Answer

0

Exercise #12

Solve the following exercise:

6525=? \frac{6}{5}-\frac{2}{5}=\text{?}

Video Solution

Step-by-Step Solution

Let's solve the problem by carefully following these steps:

  • Step 1: Identify the numerators and the denominator
    The fractions are 65\frac{6}{5} and 25\frac{2}{5}. Both fractions have a common denominator of 5, with numerators 6 and 2 respectively.
  • Step 2: Subtract the numerators
    Since the denominators are the same, we can directly subtract the numerators: 62=46 - 2 = 4.
  • Step 3: Retain the common denominator
    The result of the subtraction will have the same denominator, which is 5. Therefore, the resulting fraction is 45\frac{4}{5}.

Thus, after performing the subtraction, we find that:

6525=45\frac{6}{5} - \frac{2}{5} = \frac{4}{5}

Therefore, the correct answer to the problem is 45\frac{4}{5}, which matches the provided choice with ID 4.

Answer

45 \frac{4}{5}

Exercise #13

Solve the following exercise:

2414=? \frac{2}{4}-\frac{1}{4}=\text{?}

Video Solution

Step-by-Step Solution

Let's solve the problem step-by-step:

  • Step 1: Identify the numerators: We have 24\frac{2}{4} and 14\frac{1}{4}. The numerators are 2 and 1, respectively.
  • Step 2: Subtraction of numerators: Subtract the second numerator from the first: 21=12 - 1 = 1.
  • Step 3: Maintain the common denominator: The common denominator is 4, so the result of the subtraction is 14\frac{1}{4}.

The solution to the problem is that subtracting 14\frac{1}{4} from 24\frac{2}{4} gives us 14\frac{1}{4}.

Therefore, the correct answer is:

14 \frac{1}{4}

Answer

14 \frac{1}{4}

Exercise #14

Solve the following exercise:

1013513=? \frac{10}{13}-\frac{5}{13}=\text{?}

Video Solution

Step-by-Step Solution

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

  • Step 1: Identify the given fractions and ensure they have a common denominator.
  • Step 2: Subtract the numerators while keeping the denominator the same.
  • Step 3: Simplify the result if necessary.

Let's work through each step:
Step 1: The fractions given are 1013 \frac{10}{13} and 513 \frac{5}{13} , both having a denominator of 13.
Step 2: Apply the subtraction formula for fractions with common denominators: 1013513=10513=513 \frac{10}{13} - \frac{5}{13} = \frac{10 - 5}{13} = \frac{5}{13} Step 3: No further simplification is needed since 513 \frac{5}{13} is already in its simplest form.

Therefore, the solution to the problem is 513 \frac{5}{13} .

Answer

513 \frac{5}{13}

Exercise #15

Solve the following exercise:

3212=? \frac{3}{2}-\frac{1}{2}=\text{?}

Video Solution

Step-by-Step Solution

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

  • Step 1: Recognize that the fractions 32\frac{3}{2} and 12\frac{1}{2} have a common denominator.
  • Step 2: Subtract the numerators, keeping the denominator unchanged.
  • Step 3: Simplify the resulting fraction if needed.

Now, let's work through each step:

Step 1: The fractions involved are 32\frac{3}{2} and 12\frac{1}{2}, both with the denominator of 2.

Step 2: Subtract the numerators: 31=23 - 1 = 2. So, the fraction becomes 22\frac{2}{2}.

Step 3: Simplify 22\frac{2}{2}. Since 22=1\frac{2}{2} = 1, the solution is a whole number.

Therefore, the solution to the problem is 1 1 . This corresponds to choice number 2.

Answer

1 1

Exercise #16

12+85= \frac{12+8}{5}=

Video Solution

Step-by-Step Solution

Let's begin by multiplying the numerator:

12+8=20 12+8=20

We should obtain the fraction written below:

205 \frac{20}{5}

Let's now reduce the numerator and denominator by 5 and we should obtain the following result:

41=4 \frac{4}{1}=4

Answer

4 4