Examples with solutions for Addition and Subtraction of Mixed Numbers: Fractions with common denominators

Exercise #1

213123= 2\frac{1}{3}-1\frac{2}{3}=

Video Solution

Step-by-Step Solution

To solve the problem 2131232\frac{1}{3} - 1\frac{2}{3}, we'll perform the following steps:

  • Step 1: Subtract the integer parts: 21=12 - 1 = 1.
  • Step 2: Subtract the fractional parts: 1323\frac{1}{3} - \frac{2}{3}.

To calculate 1323\frac{1}{3} - \frac{2}{3}:

Since the fractions have a common denominator, subtract only the numerators:
12=11 - 2 = -1.
Therefore, 1323=13\frac{1}{3} - \frac{2}{3} = -\frac{1}{3}.

Now combine the results:

The subtraction results in 1131 - \frac{1}{3}.

To simplify, note 1=331 = \frac{3}{3}.

Thus, 113=3313=231 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{2}{3}.

Therefore, the solution to 2131232\frac{1}{3} - 1\frac{2}{3} is 23\frac{2}{3}.

Answer

23 \frac{2}{3}

Exercise #2

525+215= 5\frac{2}{5}+2\frac{1}{5}=

Video Solution

Step-by-Step Solution

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

  • Step 1: Add the whole number parts.
  • Step 2: Add the fractional parts.
  • Step 3: Combine results and simplify if necessary.

Now, let's work through each step:
Step 1: The mixed numbers are 5255\frac{2}{5} and 2152\frac{1}{5}. First, add the whole number parts: 5+2=75 + 2 = 7.
Step 2: Next, add the fractional parts: 25+15=35\frac{2}{5} + \frac{1}{5} = \frac{3}{5}. Since the denominators are the same, just add the numerators.
Step 3: Combine these sums to form the mixed number: 7+35=7357 + \frac{3}{5} = 7\frac{3}{5}.

Therefore, the solution to the problem is 735 7\frac{3}{5} .

Answer

735 7\frac{3}{5}

Exercise #3

101212= 10\frac{1}{2}-\frac{1}{2}=

Video Solution

Step-by-Step Solution

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

  • Step 1: Identify the parts of the mixed number 1012 10\frac{1}{2} . It consists of the whole number 10 10 and the fraction 12 \frac{1}{2} .

  • Step 2: We'll subtract 12 \frac{1}{2} (the fraction we are given to subtract) from the fraction part of the mixed number:

1212=0 \frac{1}{2} - \frac{1}{2} = 0

Step 3: After performing the subtraction, the fractional part becomes 0 0 .

Step 4: This leaves us with the whole part of the mixed number on its own, which is 10 10 .

Therefore, the solution to the problem is 10 10 .

Answer

10 10

Exercise #4

626+126= 6\frac{2}{6}+1\frac{2}{6}=

Video Solution

Step-by-Step Solution

To solve this problem, we will add the mixed numbers 626 6\frac{2}{6} and 126 1\frac{2}{6} by following these steps:

  • Step 1: Add the integer parts: 6+1=7 6 + 1 = 7 .
  • Step 2: Add the fractional parts: 26+26=46\frac{2}{6} + \frac{2}{6} = \frac{4}{6}.
  • Step 3: Combine the results to express the sum: 7+46 7 + \frac{4}{6} .

Now, let's work through each step:
Step 1: Adding the whole numbers, we get 7 7 .
Step 2: Since both fractions have a common denominator of 6, we add the numerators: 2+2=4 2 + 2 = 4 , thus giving us the fraction 46\frac{4}{6}.
Step 3: The combined sum of the whole number and the fraction is 746 7\frac{4}{6} .

Hence, the solution to the problem is 746 7\frac{4}{6} .

Answer

746 7\frac{4}{6}

Exercise #5

225+225= 2\frac{2}{5}+2\frac{2}{5}=

Video Solution

Step-by-Step Solution

To solve the problem 225+225 2\frac{2}{5} + 2\frac{2}{5} , follow these steps:

  • Step 1: Add the whole numbers together. We have 2+2=42 + 2 = 4.
  • Step 2: Add the fractional parts together. Since both fractions have the same denominator, simply add the numerators: 25+25=45\frac{2}{5} + \frac{2}{5} = \frac{4}{5}.
  • Step 3: Combine the results from Step 1 and Step 2. The sum of the whole numbers and fraction parts is 4+45=4454 + \frac{4}{5} = 4\frac{4}{5}.

Thus, the sum of 225 2\frac{2}{5} and 225 2\frac{2}{5} is 445\mathbf{4\frac{4}{5}}.

The answer corresponds to choice 4.

Answer

445 4\frac{4}{5}

Exercise #6

714324= 7\frac{1}{4}-3\frac{2}{4}=

Video Solution

Step-by-Step Solution

To solve the subtraction of the mixed numbers 714324 7\frac{1}{4} - 3\frac{2}{4} , we follow these steps:

  • Step 1: Subtract the whole numbers:
    73=4 7 - 3 = 4 .
  • Step 2: Subtract the fractions:
    1424 \frac{1}{4} - \frac{2}{4} results in 14 \frac{-1}{4} , because the numerators give 12=1 1 - 2 = -1 .
  • Step 3: Combine these results, we initially have 414 4\frac{-1}{4} . Since we can't leave a negative fraction in this form, we adjust by borrowing 1 from the whole number:
    • Convert 1 1 (borrowed from 4) into 44 \frac{4}{4} which combines with the fraction: 4414=34 \frac{4}{4} - \frac{1}{4} = \frac{3}{4} .
  • Step 4: Adjusting the whole number:
    Remove 1 from 4 to account for the adjustment: 41=3 4 - 1 = 3 .

Therefore, combining these parts, the mixed number resulting from the subtraction is 334 3\frac{3}{4} .

Thus, the final result is 334 3\frac{3}{4} .

Answer

334 3\frac{3}{4}

Exercise #7

123113= 1\frac{2}{3}-1\frac{1}{3}=

Video Solution

Step-by-Step Solution

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

  • Step 1: Decompose each mixed number into its whole and fractional parts.
  • Step 2: Subtract the whole numbers.
  • Step 3: Subtract the fractional parts having the same denominator.
  • Step 4: Combine the results to find the final answer.

Now, let's work through each step:

Step 1: Decompose the mixed numbers.
- The first mixed number is 1231\frac{2}{3}, which can be expressed as the whole number 1 and the fraction 23\frac{2}{3}.
- The second mixed number is 1131\frac{1}{3}, which can be expressed as the whole number 1 and the fraction 13\frac{1}{3}.

Step 2: Subtract the whole numbers.
- Subtract the whole numbers: 11=01 - 1 = 0.

Step 3: Subtract the fractional parts.
- Subtract the fractions: 2313=13\frac{2}{3} - \frac{1}{3} = \frac{1}{3}.

Step 4: Combine the results.
- Since the whole number result is 0, the result of the fractional subtraction 13\frac{1}{3} is the final answer.

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

Answer

13 \frac{1}{3}

Exercise #8

1323313= 13\frac{2}{3}-3\frac{1}{3}=

Video Solution

Step-by-Step Solution

To solve 132331313\frac{2}{3} - 3\frac{1}{3}, we'll follow these steps:

  • Step 1: Subtract the whole numbers: 133=1013 - 3 = 10.
  • Step 2: Subtract the fractions: 2313=13\frac{2}{3} - \frac{1}{3} = \frac{1}{3}.
  • Step 3: Combine the results: Combine the whole number and the fraction to get 101310\frac{1}{3}.

Therefore, the solution to the problem is 101310\frac{1}{3}.

Answer

1013 10\frac{1}{3}

Exercise #9

314+124= 3\frac{1}{4}+1\frac{2}{4}=

Video Solution

Step-by-Step Solution

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

  • Step 1: Extract the whole number and fraction parts from each mixed number.
  • Step 2: Add the whole numbers together.
  • Step 3: Add the fractions together using their common denominator.
  • Step 4: Combine the results, checking if any simplification is needed.

Now, let's work through each step:
Step 1: From 314 3\frac{1}{4} , the whole number is 3 3 and the fraction is 14 \frac{1}{4} . From 124 1\frac{2}{4} , the whole number is 1 1 and the fraction is 24 \frac{2}{4} .
Step 2: Add the whole numbers: 3+1=4 3 + 1 = 4 .
Step 3: Add the fractions 14+24 \frac{1}{4} + \frac{2}{4} . Since the denominators are the same, we add the numerators: 1+24=34 \frac{1+2}{4} = \frac{3}{4} .
Step 4: Combine the results from Steps 2 and 3 to get 4+34=434 4 + \frac{3}{4} = 4\frac{3}{4} .

Therefore, the solution to the problem is 434 4\frac{3}{4} , which matches choice 3.

Answer

434 4\frac{3}{4}

Exercise #10

412212= 4\frac{1}{2}-2\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve the problem 412212 4\frac{1}{2} - 2\frac{1}{2} , we need to follow these steps:

  • Step 1: Identify the components of each mixed number.
    412 4\frac{1}{2} consists of a whole number 44 and a fraction 12\frac{1}{2}.
    212 2\frac{1}{2} consists of a whole number 22 and a fraction 12\frac{1}{2}.
  • Step 2: Subtract the whole numbers.
    Subtract the whole number of the second from the first: 42=24 - 2 = 2.
  • Step 3: Subtract the fractions.
    Since both fractions are 12\frac{1}{2}, subtract them: 1212=0\frac{1}{2} - \frac{1}{2} = 0.
  • Step 4: Combine the results.
    The result from the whole numbers is 22, and the result from the fractions is 00. So, 2+0=22 + 0 = 2.

Therefore, the answer to the problem 412212 4\frac{1}{2} - 2\frac{1}{2} is 2 2 .

Answer

2 2