Examples with solutions for Addition and Subtraction of Decimal Fractions: Graphical representation - addition with regrouping

Exercise #1

0.5+0.5= 0.5+0.5=

+=

Video Solution

Step-by-Step Solution

To solve this problem, we will add the decimal numbers 0.5 and 0.5 together. The process involves:

  • Step 1: Align the decimal points of both numbers, which results in:

0.5
+ 0.5

  • Step 2: Start adding from the rightmost digit (tenths position in this case). The digits in the tenths position are both 5. Adding them gives 5 + 5 = 10. Because this is in the tenths position, write 0 in the tenths column, and carry over 1 to the units column.
  • Step 3: Proceed to the units column. The digits are 0 in the top row and 0 in the bottom row, while you have a carryover of 1. Therefore, 1 (carry) + 0 + 0 = 1.

Therefore, the sum of 0.5 + 0.5 is precisely 1 1 .

Given that this was a multiple-choice question, the correct answer is choice 2: 1.

Answer

1

Exercise #2

0.7+0.4= 0.7+0.4=

+=

Video Solution

Step-by-Step Solution

To solve this problem, we will add the two decimal fractions 0.7 0.7 and 0.4 0.4 .

Let's break down the process:

  • Step 1: Align the numbers by their decimal points:
    +0.7 \phantom{+}0.7
    +0.4 +0.4
  • Step 2: Add the numbers column by column starting from the rightmost place (tenths place):
    7+4=11 7 + 4 = 11
  • Step 3: Write down the 1 in the tenths place and carry over 1 to the units place. There is no whole number component in this addition, so simply add the carry to 00 which is 1+0=1 1 + 0 = 1 .
  • Step 4: Combine the results to find the total: 1.1 1.1 .

Thus, the sum of 0.7 0.7 and 0.4 0.4 is 1.1 \mathbf{1.1} .

The correct choice is 1: 1.1.

Answer

1.1

Exercise #3

0.6+0.7= 0.6+0.7=

+=

Video Solution

Step-by-Step Solution

To solve the problem 0.6+0.7 0.6 + 0.7 , we'll perform simple addition of decimal numbers:

  • Step 1: Align the numbers by their decimal points:
         0.6
    +  0.7
  • Step 2: Add the numbers column by column, starting from the rightmost digit:

0.6 can be thought of as 0.60 if we want to align them neatly:
       0.60
+     0.70
---------------

  • Add the hundredths (rightmost) digit: 0 + 0 = 0
  • Add the tenths digit: 6 + 7 = 13. Since this sum is greater than 9, we write down 3 and carry over 1 to the ones column.
  • Add the digits in the ones column: 0 + 0 = 0, then add the carried over 1 to get 1.

The result of the addition 0.6+0.7 0.6 + 0.7 is 1.3 1.3 . This matches our expectations from the arithmetic process.

Therefore, the solution to the problem is 1.3 1.3 .

Answer

1.3

Exercise #4

0.5+0.9= 0.5+0.9=

+=

Video Solution

Step-by-Step Solution

To solve the problem of adding 0.50.5 and 0.90.9, we follow these steps:

  • Step 1: Write the numbers vertically and align the decimal points:
  • 0.5+0.9 \begin{array}{c} 0.5 \\ +0.9 \\ \hline \end{array}

  • Step 2: Add the numbers starting from the rightmost digit:
  • The digit after the decimal in 0.50.5 is 55, and in 0.90.9 it is 99.
    Adding these, 5+9=145 + 9 = 14. Write down 44 and carry over 11.

  • Step 3: Add the numbers before the decimal point with the carryover:
  • Since 0.50.5 has 00 and 0.90.9 has 00 before the decimal, add these along with the carryover. 0+0+1=1 0 + 0 + 1 = 1

Thus, when we perform the addition, we find the result is 1.41.4.

Therefore, the solution to the problem is 1.41.4.

Answer

1.4

Exercise #5

0.7+0.8= 0.7+0.8=

+=

Video Solution

Step-by-Step Solution

To solve the problem, let's add the decimals 0.7 and 0.8:

  • Step 1: Align the numbers by their decimal points:
    • 0.70.7
    • +0.8+0.8
  • Step 2: Add the digits from right to left:
    • Tenths place: 7+8=157 + 8 = 15

The result of 7+87 + 8 gives 1515. Since we are in the tenths column, the value is 1.5 (carrying the 1 over to the units place). Thus, the sum is 1.51.5.

Therefore, the solution to the problem is 1.5 \boxed{1.5} .

Answer

1.5

Exercise #6

0.9+0.8= 0.9+0.8=

+=

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 furthest right decimal place.
  • Step 3: Handle any carryover if necessary.

Let's apply these steps to our problem:

Step 1: We align 0.90.9 and 0.80.8 so that their decimal points are in a column:
0.9+0.8 \begin{array}{c} 0.9 \\ +0.8 \\ \hline \end{array}

Step 2: Add the numbers starting from the rightmost digit (tenths place):
- In the tenths place, 9+8=179 + 8 = 17. This results in 77 in the tenths place and carry 11 to the units place.

Step 3: Handle the carryover:
- In the units place, we consider any carry. Adding the carry 11 from the tenths place gives us 1+(0+0)=11 + (0 + 0) = 1.

So, the final result after addition is:
1.7 \begin{array}{c} 1.7 \\ \end{array}

Therefore, the sum of 0.90.9 and 0.80.8 is 1.7\boxed{1.7}.

Answer

1.7

Exercise #7

0.6+0.6= 0.6+0.6=

+=

Video Solution

Step-by-Step Solution

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

  • Step 1: Align the numbers by their decimal points.
    Write 0.60.6 directly under 0.60.6:
  • 0.6+0.6 \begin{array}{c} 0.6 \\ +0.6 \end{array}
  • Step 2: Add the tenths places. 6+6=126 + 6 = 12. Write down 22 in the tenths place and carry over 11 to the units place.
  • Step 3: Add the units place with the carry-over. 0+0+1=10 + 0 + 1 = 1. Write down 11 in the whole number place.

Thus, when we add 0.60.6 and 0.60.6, we obtain:

1.2 1.2

Therefore, the solution to the problem is 1.21.2.

Answer

1.2

Exercise #8

0.6+0.5= \text{0.6+0}.5=

+=

Step-by-Step Solution

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

  • Step 1: Align the numbers 0.60.6 and 0.50.5 by their decimal points.
  • Step 2: Add the numbers as you would do with whole numbers.
  • Step 3: Place the decimal point in the sum directly under the decimal points of the addends.

Now, let's work through each step:
Step 1: Write the numbers aligned by the decimal point:
     0.6
+ 0.5
Step 2: Add the digits: - Start from the right: 6+5=116 + 5 = 11. Place a 11 in the tenths column and carry over 11.
Step 3: Add the whole number part considering any carry: - 0+0+10 + 0 + 1 (from the carry) = 11.

The sum of 0.60.6 and 0.50.5 gives 1.11.1.

Therefore, the solution to the problem is 1.11.1.

Answer

1.1

Exercise #9

0.8+0.4= 0.8+0.4=

+=

Video Solution

Answer

1.2

Exercise #10

0.7+0.7= 0.7+0.7=

+=

Video Solution

Answer

1.4