Question

Find each sum or difference without using a calculator. \(194.5+73.94\)

Short answer

268.44

Step-by-step solution

Align the Numbers

Write the numbers one below the other, aligning the decimal points. This ensures each digit is in the correct place value.194.5+ 73.94

Add Zeroes

Add a zero to the end of the number with fewer decimal places to make the decimal places equal.194.50+ 73.94

Add the Hundredths Place

Add the digits in the hundredths place. Since there is no hundredth digit in 194.50, consider it as 0. 0 + 4 = 4

Add the Tenths Place

Add the digits in the tenths place.5 + 9 = 14, write down 4 and carry over 1

Add the Units Place

Add the units place digits and include any carry over.4 + 3 + 1 = 8

Add the Tens Place

Add the digits in the tens place.9 + 7 = 16, write down 6 and carry over 1

Add the Hundreds Place

Finally, add the hundreds place with the carry over.1 + 0 + 1 = 2

Write the Sum

Combine all the digits you have calculated to get the final result.194.50 + 73.94 = 268.44

Key concepts

Aligning Decimal Points

When working with decimal numbers, it’s crucial to align the decimal points. This ensures that each digit is in its proper column, making addition simpler and more accurate. For instance, if you are adding 194.5 and 73.94, line up the decimal points directly under each other:
194.5
+ 73.94
.
Notice that the digits are now aligned according to place value, where the decimal point stays in a straight line. This helps prevent mistakes, such as adding tenths with hundredths.

By aligning the decimal points:

• You keep the columns straight
• Ensure accurate addition
• Avoid calculation errors

Next, we need to equalize the number of decimal places before adding.

Adding Decimal Numbers

Once you've aligned the decimal points, you need to ensure each number has the same amount of digits after the decimal. In our example:
194.5
+ 73.94

We add a zero to 194.5 to make it 194.50. This small change makes it easier to add digit by digit:
194.50
+ 73.94

Now start simple additions from the rightmost digit (hundredths place). Add 0 and 4, which equals 4. Next, add the tenths place digits, 5 and 9. Since it sums to 14, write down 4 and carry over 1. Then go to the units place, sum 4 + 3, plus the carried over 1, giving 8.

• Step-by-step addition reduces mistakes
• Helps track place value
• Carrying over manages larger sums

Let’s discuss carrying over in detail next.

Carrying Over in Addition

Carrying over happens when a column’s sum exceeds 9. In decimal addition, treat it the same as in whole numbers. With our previous digit sum:
5 + 9 = 14
Write down the 4 and carry over 1. Then:
4 + 3 + 1 (carried over) = 8

For the next column sums that are 10 or more, you write down the rightmost digit and add the left number to the following column. For example, tens place sums:
9 + 7 = 16
Write down 6 and carry over 1 to the hundreds place. Finally, add carried-over 1 from the hundreds place:
1 + 0 + 1 = 2.

Carrying over is:

• Essential for accurate addition
• Keeps track of larger sums
• Vital for maintaining place value

Understanding these steps simplifies decimal addition and helps achieve accurate results!