Examples with solutions for Addition and Subtraction of Mixed Numbers: Addition and subtraction from a whole

Exercise #1

6+523= 6+5\frac{2}{3}=

Video Solution

Step-by-Step Solution

To solve the problem 6+523 6 + 5\frac{2}{3} , we will follow these steps:

  • Step 1: Identify the whole numbers: 66 and 55.
  • Step 2: Add the whole numbers: 6+5=116 + 5 = 11.
  • Step 3: Recognize the fractional part: 23\frac{2}{3}.
  • Step 4: Combine the whole number result with the fractional part: 11+2311 + \frac{2}{3}.

Resultantly, when adding these components, the complete sum is 112311\frac{2}{3}.

Therefore, the solution to the problem is 1123 11\frac{2}{3} .

Answer

1123 11\frac{2}{3}

Exercise #2

7+213= 7+2\frac{1}{3}=

Video Solution

Step-by-Step Solution

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

  • Step 1: Separate the mixed number into whole and fractional parts.
  • Step 2: Add the whole numbers separately from the fractional part.
  • Step 3: Combine the results for the final sum.

Now, let's work through each step:

Step 1: The mixed number 2132\frac{1}{3} consists of the whole number 2 and the fraction 13\frac{1}{3}.

Step 2: Add the whole numbers: 7+2=97 + 2 = 9.

Step 3: Since the fraction 13\frac{1}{3} has no other fractional parts to add, we simply keep it as is and attach it to the 9.

Therefore, the overall sum is 9139\frac{1}{3}.

After comparing our solution to the possible answer choices, the correct choice is 9139\frac{1}{3}.

Answer

913 9\frac{1}{3}

Exercise #3

2+337= 2+3\frac{3}{7}=

Video Solution

Step-by-Step Solution

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

  • Step 1: Identify the whole and fractional parts of the mixed number.
  • Step 2: Add the whole numbers together.
  • Step 3: Combine the result with the fractional part.

Now, let's work through each step:
Step 1: The mixed number 337 3\frac{3}{7} consists of the whole number 3 and the fraction 37 \frac{3}{7} .
Step 2: Add the whole numbers: 3+2=5 3 + 2 = 5 .
Step 3: The final result combines the sum of the whole numbers with the original fraction: 5+37=537 5 + \frac{3}{7} = 5\frac{3}{7} .

Therefore, the solution to the problem is 537 5\frac{3}{7} .

Answer

537 5\frac{3}{7}

Exercise #4

1+212= 1+2\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve the problem 1+2121 + 2\frac{1}{2}, follow these steps:

  • Step 1: Identify the numbers to add: 11 is a whole number, and 2122\frac{1}{2} is a mixed number consisting of the whole part 22 and the fractional part 12\frac{1}{2}.
  • Step 2: Add the whole numbers: 1+2=31 + 2 = 3.
  • Step 3: Keep the fractional part from the mixed number unchanged: 12\frac{1}{2}.
  • Step 4: Combine the result of the whole numbers' addition with the fractional part: 3+12=3123 + \frac{1}{2} = 3\frac{1}{2}.

Therefore, the solution to the problem 1+2121 + 2\frac{1}{2} is 312 3\frac{1}{2} .

Answer

312 3\frac{1}{2}

Exercise #5

134= 1-\frac{3}{4}=

Video Solution

Step-by-Step Solution

To solve the problem of 134 1 - \frac{3}{4} , we need to follow these steps:

  • Step 1: Express the whole number 1 as a fraction with the same denominator as 34 \frac{3}{4} .
  • Step 2: Perform the subtraction with the common denominators.
  • Step 3: Simplify the resulting fraction, if necessary.

Let's work through each step:
Step 1: Convert the whole number 1 into a fraction with a denominator of 4. Therefore, 1 1 can be written as 44 \frac{4}{4} .
Step 2: Now subtract 34 \frac{3}{4} from 44 \frac{4}{4} . The formula for subtracting fractions is:

abcb=acb \frac{a}{b} - \frac{c}{b} = \frac{a-c}{b}

Using the numbers we have:

4434=434=14 \frac{4}{4} - \frac{3}{4} = \frac{4-3}{4} = \frac{1}{4}

Step 3: The resulting fraction 14 \frac{1}{4} is already in its simplest form.

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

Answer

14 \frac{1}{4}

Exercise #6

212= 2-\frac{1}{2}=

Video Solution

Step-by-Step Solution

To solve the problem of subtracting 12\frac{1}{2} from the whole number 22, we proceed as follows:

First, understand that the whole number 22 can be considered as a fraction with a denominator of 2. This means that 22 is equivalent to 42\frac{4}{2}. This step is crucial to ensure both numbers have a common denominator, facilitating the subtraction of fractions.

Now, subtract the fraction 12\frac{1}{2} from 42\frac{4}{2}:

4212=412=32 \frac{4}{2} - \frac{1}{2} = \frac{4-1}{2} = \frac{3}{2}

The fraction 32\frac{3}{2} is improper because the numerator is larger than the denominator. Thus, we convert this into a mixed number, which is a combination of a whole number and a proper fraction. The mixed number form of 32\frac{3}{2} is 1121\frac{1}{2} because 22 fits into 33 once with a remainder of 11.

Therefore, the result of 212 2-\frac{1}{2} is 112\mathbf{1\frac{1}{2}}.

Answer

112 1\frac{1}{2}

Exercise #7

437= 4-\frac{3}{7}=

Video Solution

Step-by-Step Solution

To solve this problem, we will follow these steps:

  • Step 1: Convert the whole number 4 into a fraction with a denominator of 7.
  • Step 2: Subtract the fraction 37 \frac{3}{7} from the converted fraction.
  • Step 3: Simplify the resulting fraction and convert it to a mixed number if possible.

Now, let's work through each step:
Step 1: Convert the whole number 4 to a fraction with denominator 7. We multiply the numerator and denominator by 7 to get 287 \frac{28}{7} .
Step 2: Subtract the fraction 37 \frac{3}{7} from 287 \frac{28}{7} :

28737=2837=257 \frac{28}{7} - \frac{3}{7} = \frac{28-3}{7} = \frac{25}{7}

Step 3: Convert the fraction 257 \frac{25}{7} into a mixed number:

Divide 25 by 7, which gives us a quotient of 3 and a remainder of 4. Thus, the fraction 257 \frac{25}{7} is equivalent to the mixed number 347 3\frac{4}{7} .

Therefore, the solution to the problem is 347 3\frac{4}{7} .

Answer

347 3\frac{4}{7}

Exercise #8

4257= 4-2\frac{5}{7}=

Video Solution

Step-by-Step Solution

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

  • Step 1: Convert 4 to a fraction that shares a common denominator with 57\frac{5}{7}.
  • Step 2: Perform the subtraction.
  • Step 3: Simplify the result into a mixed fraction.

Now, let's work through each step:
Step 1: Convert 4 to the fraction form 287\frac{28}{7}, because 287\frac{28}{7} is equivalent to 4.

Step 2: Subtract the fractions:
28757=2857=237\frac{28}{7} - \frac{5}{7} = \frac{28 - 5}{7} = \frac{23}{7}.

Step 3: Convert 237\frac{23}{7} to a mixed fraction.
Divide 23 by 7, which goes 3 times with a remainder of 2. Hence, 237=327\frac{23}{7} = 3\frac{2}{7}.

Therefore, the solution to the problem is 3273\frac{2}{7}.

Answer

127 1\frac{2}{7}

Exercise #9

6225= 6-2\frac{2}{5}=

Video Solution

Step-by-Step Solution

To solve the problem, we need to subtract the mixed number 225 2\frac{2}{5} from 6. We will handle the subtraction in steps:

  • Step 1: Break the mixed fraction 225 2\frac{2}{5} into its whole and fractional parts: the whole number is 2, and the fractional part is 25\frac{2}{5}.
  • Step 2: Subtract the whole numbers: 62=4 6 - 2 = 4.
  • Step 3: Now, we need to subtract the fractional part from 4: 425 4 - \frac{2}{5} .
  • Step 4: Convert 4 to a fraction with the same denominator as 25\frac{2}{5}.
    This means writing 4 as 205\frac{20}{5} (since 4=2054 = \frac{20}{5}).
  • Step 5: Perform the subtraction: 20525=185\frac{20}{5} - \frac{2}{5} = \frac{18}{5}.
  • Step 6: Convert 185\frac{18}{5} back to a mixed number.
    Divide 18 by 5: 18 divided by 5 is 3 with a remainder of 3. This gives the mixed number 3353\frac{3}{5}.

Therefore, the final result of 62256 - 2\frac{2}{5} is 335\mathbf{3\frac{3}{5}}.

Answer

335 3\frac{3}{5}

Exercise #10

5213= 5-2\frac{1}{3}=

Video Solution

Step-by-Step Solution

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

  • Step 1: Convert the mixed number 2132\frac{1}{3} to an improper fraction.
  • Step 2: Subtract the improper fraction from the whole number 5.
  • Step 3: Convert the resulting improper fraction back to a mixed number.

Now, let's work through each step:

Step 1: Convert the mixed number to an improper fraction. For 2132\frac{1}{3}, multiply the whole number 2 by the denominator 3 and add the numerator 1: (2×3)+1=7(2 \times 3) + 1 = 7. Thus, 2132\frac{1}{3} is 73\frac{7}{3}.

Step 2: Subtract 73\frac{7}{3} from 5. First, convert 5 to a fraction with the same denominator: 5=1535 = \frac{15}{3}. Subtract: 15373=83\frac{15}{3} - \frac{7}{3} = \frac{8}{3}.

Step 3: Convert 83\frac{8}{3} back to a mixed number. Divide 8 by 3: 8 divided by 3 is 2 with a remainder of 2, so 83=223\frac{8}{3} = 2\frac{2}{3}.

Therefore, the solution to the problem is 2232\frac{2}{3}.

Answer

223 2\frac{2}{3}