Examples with solutions for Addition and Subtraction of Decimal Fractions: Simple addition

Exercise #1

0.1+0.1= 0.1+0.1=

Video Solution

Step-by-Step Solution

To solve this problem, we will follow these steps:

  • Step 1: Align the decimal points of the numbers to be added.
  • Step 2: Add the numbers directly using their place values.
  • Step 3: Write down the sum.

Now, let's perform each step in detail:

Step 1: Align the decimal points of 0.10.1 and 0.10.1.

Step 2: Add the tenths place values. Since both digits in the tenths place are 11, we add them together:

1+1=21 + 1 = 2

Step 3: Write down the sum with the decimal point aligned:

The sum is 0.20.2.

Therefore, the solution to the problem is 0.20.2.

Answer

0.2

Exercise #2

0.2+0.1= 0.2+0.1=

Video Solution

Step-by-Step Solution

To solve this problem, we need to add the decimal numbers 0.20.2 and 0.10.1.

Here are the steps to perform the addition:

  • Step 1: Align the numbers by their decimal points:
        0.20.2
    + 0.10.1
  • Step 2: Start adding from the rightmost digit to the left:
    • The tenths column contains 2 tenths (from 0.20.2) and 1 tenth (from 0.10.1), and adding these gives 3 tenths. There is no carryover since the result is below 10 tenths.
    • The single whole number place doesn't have digits to sum aside from the carry, which in this case, is zero.
  • Step 3: The sum of 0.2+0.10.2 + 0.1 is 0.30.3.

Therefore, the solution to the problem is 0.30.3.

Answer

0.3

Exercise #3

0.4+0.4= 0.4+0.4=

Video Solution

Step-by-Step Solution

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

  • Step 1: Align the decimal points vertically in the numbers to be added.
  • Step 2: Add the numbers as if they were whole numbers, placing the decimal correctly in the sum.

Let's perform the addition:

Step 1: Align the numbers 0.4 0.4 and 0.4 0.4 : +0.4+0.4\begin{array}{c} \phantom{+}0.4 \\ + 0.4 \\ \hline \end{array}

Step 2: Add 4 4 and 4 4 in the tenths place, which gives us 8 8 . The decimal point remains in the same position, resulting in 0.8 0.8 .

Therefore, the sum of 0.4+0.4 0.4 + 0.4 is 0.8 0.8 .

Answer

0.8

Exercise #4

0.5+0.3= 0.5+0.3=

Video Solution

Step-by-Step Solution

To solve this problem, follow these steps:

  • Step 1: Align the numbers vertically by their decimal point. Write 0.50.5 and 0.30.3 ensuring the decimal points are aligned.
  • Step 2: Perform the addition:
          0.5
    +    0.3
    —---------
  • Step 3: Add the numbers starting from the right (tenths place):
    - Add 0.5+0.3=0.80.5 + 0.3 = 0.8.

Therefore, the sum of 0.50.5 and 0.30.3 is 0.80.8.

Answer

0.8

Exercise #5

5.1+2.3= \text{5}.1+2.3=

Video Solution

Step-by-Step Solution

To solve this problem, let's follow these steps for decimal addition:

  • Step 1: Align the decimals of the numbers vertically, so that both 5.1 5.1 and 2.3 2.3 have their decimal points in the same position:


   5.1
+  2.3
---------

  • Step 2: Start adding from the rightmost column (the tenths position). Add the tenths: 1+3=41 + 3 = 4.
  • Step 3: Move to the left to add the units: 5+2=75 + 2 = 7.

Put these sums together, and we have:


   5.1
+  2.3
---------
   7.4

Therefore, the sum of 5.15.1 and 2.32.3 is 7.47.4. This matches choice 3 \text{3} .

Thus, the correct answer is 7.4 7.4 .

Answer

7.4

Exercise #6

6.2+2.4= 6.2+2.4=

Video Solution

Step-by-Step Solution

To solve this problem, we follow these steps:

  • Step 1: Write down the numbers vertically, aligning the decimal points.
  • Step 2: Add each column of digits, starting from the rightmost column (the tenths place).
  • Step 3: If any column adds to a number equal to or greater than 10, carry over to the next left column.

Let's work through the solution:
Step 1: Align the numbers vertically:
    6.2
+ 2.4
--------
Step 2: Add the digits in the tenths column: 2+4=62 + 4 = 6. Write the 6 in the tenths place below.
Step 3: Add the digits in the ones column: 6+2=86 + 2 = 8. Write the 8 in the ones place below.
Therefore, the sum of 6.26.2 and 2.42.4 is 8.68.6.

Therefore, the solution to the problem is 8.68.6, which corresponds to choice 1.

Answer

8.6

Exercise #7

2.5+3.1= 2.5+\text{3}.1=

Video Solution

Step-by-Step Solution

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

  • Step 1: Align the numbers 2.5 and 3.1 by their decimal points.
  • Step 2: Add the digits in each column starting from the rightmost digit (the tenths column in this case).

Now, let's work through each step:

Step 1: Align the numbers by decimal points:

002.5 \phantom{00}2.5
+3.1 +3.1

Step 2: Perform the addition:
- Add the tenths column: 5+1=6 5 + 1 = 6
- Add the units column: 2+3=5 2 + 3 = 5

Therefore, by aligning and adding the numbers correctly, the solution to the problem is 5.6 5.6 .

Answer

5.6

Exercise #8

4.3+6.2= 4.3+6.2=

Video Solution

Step-by-Step Solution

To solve the addition problem 4.3+6.24.3 + 6.2, follow these steps:

  • Step 1: Align the numbers by their decimal points as follows:
         4.34.3
    +6.2+\,6.2
  • Step 2: Add the digits to the right of the decimal point first:
         3+2=53 + 2 = 5
  • Step 3: Add the digits to the left of the decimal point:
         4+6=104 + 6 = 10

Now, place the decimal point in the result directly below the other decimal points:

4.3+6.2=10.54.3 + 6.2 = 10.5

Therefore, the solution to the problem is 10.510.5.

Answer

10.5

Exercise #9

10.1+2.3= \text{10}.1+2.3=

Video Solution

Step-by-Step Solution

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

  • Step 1: Align the decimal numbers so the decimal points are vertically in line. The numbers are 10.110.1 and 2.32.3.
  • Step 2: Add the numbers starting from the rightmost column (i.e., the tenths place), moving to the left.

Let's perform the addition:

10.1+2.3\begin{array}{c} 10.1 \\ + 2.3 \\ \hline \end{array}

Starting from the right, we add the digits in the tenths place: 1+3=41 + 3 = 4.

Next, add the digits in the units place: 0+2=20 + 2 = 2.

Finally, add the digit in the tens place: 1+0=11 + 0 = 1.

Therefore, the result of adding 10.1+2.310.1 + 2.3 is:

12.412.4

We can verify that this matches with the given answer choices. The correct choice is:

Option 1: 12.412.4

Answer

12.4

Exercise #10

20.4+10.4= 20.4+10.4=

Video Solution

Step-by-Step Solution

To solve this problem, we'll add the decimal numbers 20.420.4 and 10.410.4 by aligning the decimal points:

  • Step 1: Write the numbers in a column aligning their decimal points:

20.4+10.4 \begin{array}{r} 20.4 \\ +10.4 \\ \hline \end{array}

  • Step 2: Add the numbers starting from the right. First, 4+4=84 + 4 = 8.
  • Next, add the digits to the left of the decimal point: 0+0=00 + 0 = 0.
  • Finally, add the leftmost digits: 2+1=32 + 1 = 3.

Combining these, the result is 30.830.8.

Thus, the solution to the problem is 30.8 \mathbf{30.8} .

Answer

30.8

Exercise #11

Solve the following:

0.1+0.2= 0.1+0.2=

Video Solution

Step-by-Step Solution

To solve this problem, let's perform the addition of the two decimal numbers 0.1 0.1 and 0.2 0.2 step-by-step.

Step 1: Align the decimal points of the numbers.

We write the numbers as:

0.1 0.1

+0.2 +0.2

Here, the decimal points are already aligned.

Step 2: Add the numbers column by column starting from the rightmost side, which is the decimal fraction part.

0.1 0.1 consists of 1 in the tenths place, and 0.2 0.2 consists of 2 in the tenths place. By adding these:

  • 0.1+0.2=0.3 0.1 + 0.2 = 0.3

Thus, the sum of 0.1 0.1 and 0.2 0.2 is 0.3 0.3 .

Looking at the answer choices, the correct choice is:

  • Choice 2: 0.3 0.3

Therefore, the solution to the problem is 0.3 0.3 .

Answer

0.3

Exercise #12

Solve the following:

0.4+0.3= 0.4+0.3=

Video Solution

Step-by-Step Solution

To solve the decimal addition 0.4+0.30.4 + 0.3, we will follow these steps:

  • Step 1: Line up the numbers by the decimal point.

  • Step 2: Add the decimal fractions directly as both numbers have only one digit after the decimal point.

  • Step 3: Sum the values and retain the decimal point in the same position for the result.

Let's begin the calculation:

Write the numbers aligning them by the decimal point:

0.4 0.4
+0.3 +0.3
_______
0.7 0.7

Adding the two numbers 0.40.4 and 0.30.3 gives 0.70.7.

Therefore, the solution to the problem is 0.70.7, which matches choice 1.

Answer

0.7

Exercise #13

Solve the following:

1.3+1.1= 1.3+1.1=

Video Solution

Step-by-Step Solution

To solve this problem, let's follow these steps to perform decimal addition:

  • Step 1: Align the decimal points of numbers 1.31.3 and 1.11.1.

  • Step 2: Add the numbers starting from the right, moving towards the left.

Now, let's perform the calculation:

Align the numbers:
amp;1.3+amp;1.1 \begin{aligned} &{1.}3 \\ +&1.1 \\ \hline \end{aligned}

Step 1: Add the digits in the tenths place: 3+1=43 + 1 = 4.

Step 2: Add the digits in the units place: 1+1=21 + 1 = 2.

Combine these results to find the total sum: 2.42.4.

Therefore, the solution to the problem is 2.42.4, which corresponds to choice 4.

Answer

2.4

Exercise #14

Solve the following:

10.03+5.51= 10.03+5.51=

Video Solution

Step-by-Step Solution

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

  • Step 1: Align the numbers by their decimal points.

  • Step 2: Add the numbers starting from the rightmost digit, moving left.

  • Step 3: Handle any carryovers properly.

Now, let's work through each step:

Step 1: Align the numbers:

  10.03
+    5.51

Step 2: Start adding from the rightmost digit (hundredths):
amp;10.03+amp;5.51amp;15.54 \begin{array}{c} & 10.03\\ + & \,5.51\\ \hline & 15.54\\ \end{array}

Step 3: Add the digits from right to left:
- Hundredths place: 3+1=43 + 1 = 4
- Tenths place: 0+5=50 + 5 = 5
- Whole numbers: 0+5=50 + 5 = 5, 1+0=11 + 0 = 1

Thus, the sum of 10.0310.03 and 5.515.51 is 15.54\textbf{15.54}.

After evaluating the answer choices, the correct answer is choice 3: 15.54 \textbf{15.54} .

Answer

15.54

Exercise #15

Solve the following:

11.32+10.36= 11.32+10.36=

Video Solution

Step-by-Step Solution

To solve the addition problem 11.32+10.36 11.32 + 10.36 , we follow a straightforward procedure:

  • Step 1: Align the Numbers
    Write the numbers one on top of the other, aligning by the decimal point:
    11.32+10.36 \begin{array}{c} 11.32 \\ + 10.36 \\ \hline \end{array}
  • Step 2: Add Each Column
    Start adding from the rightmost column and move left to the next columns, carrying over if necessary:
    • Add the hundredths place: 2+6=8 2 + 6 = 8
    • Add the tenths place: 3+3=6 3 + 3 = 6
    • Add the units place: 1+0=1 1 + 0 = 1
    • Add the tens place: 1+1=2 1 + 1 = 2
  • Step 3: Write the Result
    After adding all the columns, write down the result with the decimal point aligned:
    21.68 \begin{array}{c} 21.68 \\ \hline \end{array}

Therefore, the solution to the problem is 21.68 21.68 .

Answer

21.68