Examples with solutions for Subtraction of Fractions: One of the denominators is the common denominator

Exercise #1

Solve the following equation:

35310= \frac{3}{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 need to find a number that is divisible by both 5 and 10.

In this case, the common denominator is 10.

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

3×25×23×110×1=610310 \frac{3\times2}{5\times2}-\frac{3\times1}{10\times1}=\frac{6}{10}-\frac{3}{10}

Finally let's subtract as follows:

6310=310 \frac{6-3}{10}=\frac{3}{10}

Answer

310 \frac{3}{10}

Exercise #2

Solve the following equation:

45510= \frac{4}{5}-\frac{5}{10}=

Video Solution

Step-by-Step Solution

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

In order to identify 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

Let's proceed to multiply each fraction by the appropriate number in order to reach the denominator 10.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

4×25×25×110×1=810510 \frac{4\times2}{5\times2}-\frac{5\times1}{10\times1}=\frac{8}{10}-\frac{5}{10}

Finally let's subtract as follows:

8510=310 \frac{8-5}{10}=\frac{3}{10}

Answer

310 \frac{3}{10}

Exercise #3

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}

Exercise #4

Solve the following exercise:

2319=? \frac{2}{3}-\frac{1}{9}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem of subtracting 19\frac{1}{9} from 23\frac{2}{3}, we need a common denominator. Let's follow these steps:

  • Step 1: Identify the common denominator for the fractions 23\frac{2}{3} and 19\frac{1}{9}. Since 99 is a multiple of 33, we use 99 as the common denominator.
  • Step 2: Convert 23\frac{2}{3} to a fraction with denominator 99:
    To do this, multiply the numerator and the denominator of 23\frac{2}{3} by 33 (since 99 divided by 33 is 33):
    23=2×33×3=69\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}.
  • Step 3: Subtract 19\frac{1}{9} from 69\frac{6}{9}:
    6919=619=59\frac{6}{9} - \frac{1}{9} = \frac{6 - 1}{9} = \frac{5}{9}.

Thus, the difference between 23\frac{2}{3} and 19\frac{1}{9} is 59\frac{5}{9}.

Therefore, the correct choice from the given options is 59\boxed{\frac{5}{9}}.

Answer

59 \frac{5}{9}

Exercise #5

Solve the following exercise:

5438=? \frac{5}{4}-\frac{3}{8}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, we'll perform the following steps:

  • Step 1: Find the Least Common Denominator (LCD) between 4 4 and 8 8 .
  • Step 2: Convert both fractions to have this common denominator.
  • Step 3: Subtract the numerators, keeping the denominator the same.

Let's apply these steps starting with the first one.

Step 1: Find the Least Common Denominator
The denominators are 4 4 and 8 8 . The least common denominator is the smallest number that both denominators divide into evenly. In this case, the LCD is 8 8 because it is the smallest number that is a multiple of both 4 4 and 8 8 .

Step 2: Convert fractions to have the same denominator of 8 8
- The fraction 54 \frac{5}{4} needs to be converted to a denominator of 8 8 . To do this, multiply both the numerator and denominator by 2 2 :

54×22=108\frac{5}{4} \times \frac{2}{2} = \frac{10}{8}

- The fraction 38 \frac{3}{8} already has the denominator 8 8 , so it remains unchanged as 38 \frac{3}{8} .

Step 3: Subtract the numerators
Now that the fractions have the same denominator, subtract the numerators:

10838=1038=78\frac{10}{8} - \frac{3}{8} = \frac{10 - 3}{8} = \frac{7}{8}

Therefore, the solution to 5438 \frac{5}{4} - \frac{3}{8} is 78\frac{7}{8}.

Answer

78 \frac{7}{8}

Exercise #6

Solve the following exercise:

3438=? \frac{3}{4}-\frac{3}{8}=\text{?}

Video Solution

Step-by-Step Solution

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

  • Step 1: Convert 34 \frac{3}{4} into an equivalent fraction with a denominator of 8.
  • Step 2: Subtract the numerators of the equivalent fractions.
  • Step 3: Simplify if necessary.

Now, let's work through each step:

Step 1: Find a common denominator for the fractions 34 \frac{3}{4} and 38 \frac{3}{8} . The least common denominator is 8.

Convert 34 \frac{3}{4} to an equivalent fraction with a denominator of 8:

34=3×24×2=68 \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}

Step 2: Subtract 38 \frac{3}{8} from 68 \frac{6}{8} :

6838=638=38 \frac{6}{8} - \frac{3}{8} = \frac{6 - 3}{8} = \frac{3}{8}

Step 3: There is no need to simplify further as the fraction 38 \frac{3}{8} is already in its simplest form.

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

Answer

38 \frac{3}{8}

Exercise #7

Solve the following exercise:

1228=? \frac{1}{2}-\frac{2}{8}=\text{?}

Video Solution

Step-by-Step Solution

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

  • Step 1: Find a common denominator for both fractions.
  • Step 2: Convert the fractions to have the same denominator.
  • Step 3: Perform the subtraction with the converted fractions.
  • Step 4: Simplify the result, if needed.

Now, let's work through each step:
Step 1: The problem gives us the fractions 12\frac{1}{2} and 28\frac{2}{8}. The denominator 22 can be converted to 88 (the denominator of the second fraction) by multiplying by 4.
Step 2: Convert 12\frac{1}{2} to 48\frac{4}{8}, since 1×42×4=48\frac{1 \times 4}{2 \times 4} = \frac{4}{8}. Now both fractions have a denominator of 8.
Step 3: Perform the subtraction: 4828=428=28\frac{4}{8} - \frac{2}{8} = \frac{4 - 2}{8} = \frac{2}{8}.
Step 4: Simplify 28\frac{2}{8} by dividing both numerator and denominator by 2: 2÷28÷2=14\frac{2 \div 2}{8 \div 2} = \frac{1}{4}.

Therefore, the solution to the problem is 14 \frac{1}{4} .

Answer

14 \frac{1}{4}

Exercise #8

Solve the following exercise:

1214=? \frac{1}{2}-\frac{1}{4}=\text{?}

Video Solution

Step-by-Step Solution

To solve the subtraction 1214 \frac{1}{2} - \frac{1}{4} , follow these steps:

  • Step 1: Identify a common denominator. Here, the least common denominator of 2 and 4 is 4.
  • Step 2: Convert 12 \frac{1}{2} to a fraction with denominator 4. This involves multiplying both the numerator and denominator by 2: 12=24 \frac{1}{2} = \frac{2}{4} .
  • Step 3: 14 \frac{1}{4} already has the denominator of 4, so we don't need any adjustment there.
  • Step 4: Subtract the numerators: 21=1 2 - 1 = 1 .
  • Step 5: Write the result over the common denominator: 14 \frac{1}{4} .

Therefore, the solution to 1214 \frac{1}{2} - \frac{1}{4} is 14 \frac{1}{4} .

Answer

14 \frac{1}{4}

Exercise #9

Solve the following exercise:

1418=? \frac{1}{4}-\frac{1}{8}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem 1418 \frac{1}{4} - \frac{1}{8} , we need to subtract these two fractions:

Step 1: Determine the common denominator.
The denominators are 4 and 8. The least common multiple of 4 and 8 is 8.

Step 2: Convert each fraction to an equivalent fraction with the common denominator of 8.
- Convert 14 \frac{1}{4} to 1×24×2=28\frac{1 \times 2}{4 \times 2} = \frac{2}{8}
- The fraction 18 \frac{1}{8} already has the denominator 8.

Step 3: Subtract the numerators.
Subtract 18 \frac{1}{8} from 28 \frac{2}{8} :
2818=218=18 \frac{2}{8} - \frac{1}{8} = \frac{2 - 1}{8} = \frac{1}{8}

The resulting fraction is already in its simplest form.

Therefore, the solution to the problem is 18 \frac{1}{8} .

Answer

18 \frac{1}{8}

Exercise #10

Solve the following exercise:

12210=? \frac{1}{2}-\frac{2}{10}=\text{?}

Video Solution

Step-by-Step Solution

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

  • Step 1: Convert 12 \frac{1}{2} to a fraction with denominator 10 10 .
  • Step 2: Subtract 210 \frac{2}{10} from the converted fraction.
  • Step 3: Simplify the result, if necessary.

Let's go through each step:

Step 1: Convert 12 \frac{1}{2} into a fraction with a denominator of 10 10 .
We know that 12 \frac{1}{2} is equivalent to multiplying the numerator and the denominator by 5 5 :
12=1×52×5=510 \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}

Step 2: Subtract 210 \frac{2}{10} from 510 \frac{5}{10} .
Subtract by keeping the denominator 10 10 and subtract the numerators:
510210=5210=310 \frac{5}{10} - \frac{2}{10} = \frac{5-2}{10} = \frac{3}{10}

Step 3: Simplify the result.
The fraction 310 \frac{3}{10} is already in its simplest form.

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

Answer

310 \frac{3}{10}

Exercise #11

Solve the following exercise:

35615=? \frac{3}{5}-\frac{6}{15}=\text{?}

Video Solution

Step-by-Step Solution

To solve 35615 \frac{3}{5} - \frac{6}{15} , we need both fractions to have the same denominator. We observe that 15 is a multiple of 5, so it is already suitable as a common denominator.

Step 1: Convert
Convert 35 \frac{3}{5} to have a denominator of 15. Multiply both the numerator and the denominator by 3:

35×33=915 \frac{3}{5} \times \frac{3}{3} = \frac{9}{15}

Step 2: Subtract the fractions
Now, subtract 915615 \frac{9}{15} - \frac{6}{15} :

915615=9615=315 \frac{9}{15} - \frac{6}{15} = \frac{9 - 6}{15} = \frac{3}{15}

Step 3: Simplify the result
Simplify 315 \frac{3}{15} by dividing both the numerator and the denominator by 3:

315=15 \frac{3}{15} = \frac{1}{5}

Therefore, the solution to the problem is 15 \frac{1}{5} .

Answer

15 \frac{1}{5}

Exercise #12

Solve the following exercise:

56712=? \frac{5}{6}-\frac{7}{12}=\text{?}

Video Solution

Step-by-Step Solution

To solve the subtraction 56712\frac{5}{6} - \frac{7}{12}, we need a common denominator.

Step 1: Find the least common denominator (LCD) of the two fractions.
The denominators are 6 and 12. The least common multiple of 6 and 12 is 12.

Step 2: Convert 56\frac{5}{6} to an equivalent fraction with a denominator of 12.
We can multiply the numerator and the denominator by 2 to achieve this:
56=5×26×2=1012\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}.

Step 3: Now, subtract the fractions with a common denominator:
1012712=10712=312\frac{10}{12} - \frac{7}{12} = \frac{10 - 7}{12} = \frac{3}{12}.

Step 4: Simplify the result.
312\frac{3}{12} can be simplified by dividing both the numerator and the denominator by 3:
312=3÷312÷3=14\frac{3}{12} = \frac{3 \div 3}{12 \div 3} = \frac{1}{4}.

Therefore, the solution to the problem 56712\frac{5}{6} - \frac{7}{12} is 14\boxed{\frac{1}{4}}.

From the available choices, option 4, which is 14\frac{1}{4}, is the correct answer.

Answer

14 \frac{1}{4}

Exercise #13

Solve the following exercise:

34512=? \frac{3}{4}-\frac{5}{12}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem 34512 \frac{3}{4} - \frac{5}{12} , we need to subtract two fractions with different denominators. Let's follow these steps:

  • Step 1: Identify the least common denominator (LCD) of the two fractions. Here, the denominators are 4 and 12. The least common multiple of 4 and 12 is 12.
  • Step 2: Convert 34 \frac{3}{4} to an equivalent fraction with a denominator of 12. To do this, we 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}
  • Step 3: Now that both fractions have the same denominator, we can subtract the numerators:
    912512=9512=412 \frac{9}{12} - \frac{5}{12} = \frac{9 - 5}{12} = \frac{4}{12}
  • Step 4: Simplify the fraction 412 \frac{4}{12} by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
    412=4÷412÷4=13 \frac{4}{12} = \frac{4 \div 4}{12 \div 4} = \frac{1}{3}

Therefore, the solution to the problem is 13 \frac{1}{3} .

Answer

13 \frac{1}{3}

Exercise #14

Solve the following exercise:

2316=? \frac{2}{3}-\frac{1}{6}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem 2316 \frac{2}{3} - \frac{1}{6} , we follow these steps:

  • Step 1: Identify a common denominator for both fractions. Since 6 is a multiple of 3, we use 6 as the common denominator.
  • Step 2: Convert 23 \frac{2}{3} to a fraction with a denominator of 6. To do this, multiply both the numerator and the denominator by 2, giving 46 \frac{4}{6} .
  • Step 3: The fraction 16 \frac{1}{6} already has the desired denominator, so it remains 16 \frac{1}{6} .
  • Step 4: Perform the subtraction: 4616=36 \frac{4}{6} - \frac{1}{6} = \frac{3}{6} .
  • Step 5: Simplify the resulting fraction. Simplify 36 \frac{3}{6} by dividing both numerator and denominator by their greatest common divisor, which is 3, resulting in 12 \frac{1}{2} .

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

Answer

12 \frac{1}{2}

Exercise #15

Solve the following exercise:

35510=? \frac{3}{5}-\frac{5}{10}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow a step-by-step approach:

  • Step 1: Convert both fractions to have the same denominator.
    - The original fractions are 35 \frac{3}{5} and 510 \frac{5}{10} .
    - Convert 35 \frac{3}{5} to a fraction with denominator 10. Multiply both numerator and denominator by 2:
    35×22=610 \frac{3}{5} \times \frac{2}{2} = \frac{6}{10} .

  • Step 2: Subtract the fractions now that they have a common denominator.
    - The fractions to subtract are 610510 \frac{6}{10} - \frac{5}{10} .

  • Step 3: Perform the subtraction by subtracting numerators.
    - 610510=6510=110 \frac{6}{10} - \frac{5}{10} = \frac{6-5}{10} = \frac{1}{10} .

  • Step 4: Verify if simplification is necessary.
    - The fraction 110 \frac{1}{10} is already in its simplest form.

Therefore, the solution to 35510 \frac{3}{5}-\frac{5}{10} is 110 \frac{1}{10} .

Answer

110 \frac{1}{10}

Exercise #16

Solve the following exercise:

1316=? \frac{1}{3}-\frac{1}{6}=\text{?}

Video Solution

Step-by-Step Solution

To solve this fraction subtraction problem, we need to follow these steps:

  • Step 1: Identify and adjust the fractions to have a common denominator. The given problem is 1316\frac{1}{3} - \frac{1}{6}.
  • Step 2: Find a common denominator. Since 6 is a multiple of 3, we can use 6 as the common denominator.
  • Step 3: Adjust 13\frac{1}{3} to have a denominator of 6. Multiply both the numerator and denominator of 13\frac{1}{3} by 2 to get 26\frac{2}{6}.
  • Step 4: Subtract the fractions now having the same denominator: 2616\frac{2}{6} - \frac{1}{6}.
  • Step 5: Subtract the numerators: 21=12 - 1 = 1, keeping the denominator as 6, resulting in 16\frac{1}{6}.

Therefore, the solution to 1316\frac{1}{3} - \frac{1}{6} is 16\frac{1}{6}.

Answer

16 \frac{1}{6}

Exercise #17

Solve the following exercise:

2329=? \frac{2}{3}-\frac{2}{9}=\text{?}

Video Solution

Step-by-Step Solution

To solve the subtraction of fractions 2329 \frac{2}{3} - \frac{2}{9} , we will follow a step-by-step approach:

  • Step 1: Identify the denominators of the fractions, which are 3 and 9.
  • Step 2: Find the least common denominator (LCD) of 3 and 9. Since 9 is a multiple of 3, LCD=9 \text{LCD} = 9 .
  • Step 3: Convert each fraction to an equivalent fraction with this denominator.
    • The fraction 23 \frac{2}{3} is converted to 69 \frac{6}{9} because 2×3=6 2 \times 3 = 6 and 3×3=9 3 \times 3 = 9 .
    • The fraction 29 \frac{2}{9} remains 29 \frac{2}{9} because it already has the denominator 9.
  • Step 4: Subtract the numerators: 62=4 6 - 2 = 4 .
  • Step 5: Place the result over the common denominator: 49 \frac{4}{9} .

Thus, the result of the subtraction 2329 \frac{2}{3} - \frac{2}{9} is 49 \frac{4}{9} .

Therefore, the solution to the problem is 49 \frac{4}{9} .

Answer

49 \frac{4}{9}

Exercise #18

Solve the following exercise:

5814=? \frac{5}{8}-\frac{1}{4}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem 5814\frac{5}{8} - \frac{1}{4}, we need to follow these steps:

  • Step 1: Identify a common denominator. Here, since 14\frac{1}{4} shares the denominator 4 with 8, the least common denominator (LCD) is 8.
  • Step 2: Convert 14\frac{1}{4} to have the denominator of 8 by multiplying both the numerator and denominator by 2. Thus, 14=28\frac{1}{4} = \frac{2}{8}.
  • Step 3: Perform the subtraction: 5828=38\frac{5}{8} - \frac{2}{8} = \frac{3}{8}.

Thus, the result of the subtraction 5814\frac{5}{8} - \frac{1}{4} is 38\frac{3}{8}.

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

Answer

38 \frac{3}{8}