Problem 19 Add. $$ \begin{array}{r} 7... [FREE SOLUTION]

91影视

Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 1: Problem 19

Add. $$ \begin{array}{r} 77,543 \\ +\quad 23,767 \\ \hline \end{array} $$

Short Answer

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Step by step solution

Add the Units Place

Start by adding the numbers in the units place (the rightmost digit). Add 3 and 7, which equals 10. Write down 0 and carry over the 1 to the next place value.

Add the Tens Place

Now add the digits in the tens place along with the carryover. Add 4, 6, and the carryover 1 to get a total of 11. Write down 1 and carry over the 1 to the hundreds place.

Add the Hundreds Place

Move to the hundreds place. Add 5, 7, and the carryover 1, which gives 13. Write down 3 and carry over the 1 to the thousands place.

Add the Thousands Place

Next, add the thousands place digits with the carryover. Add 7, 3, and the carryover 1 to get 11. Write down 1 and carry over 1 to the ten-thousands place.

Add the Ten-Thousands Place

Finally, add the digits in the ten-thousands place along with the carryover. Add 7 and 2, and the carryover 1, yielding 10. Write down the 0 and carry over the 1 to the next position, where there are no more digits, so just write down 1.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Place Value

Understanding place value is key to adding large numbers. Each digit in a number has a position, or 'place', which determines its value. For example, in the number 77,543, the digit '7' in the ten-thousands place means 70,000, while the '3' in the units place means just 3. Here's the breakdown:

77,543
Units: 3
Tens: 4
Hundreds: 5
Thousands: 7
Ten-Thousands: 7

When adding, start from the rightmost place (units) and move left, ensuring each digit is added according to its place value.

Carrying Over

Carrying over happens when the sum of digits in a column is 10 or more. For example, when adding 3 and 7 in the units place, the result is 10. This is too large for one digit, so we write down 0 and 'carry over' the 1 to the next column (tens place).

Here鈥檚 how it works step-by-step:

Add digits in the current place value.
If the sum is 10 or higher, write down the last digit and carry over the rest.
Include the carryover digit in the next column's addition.

By doing this systematically, you maintain the correct value for each place, ensuring an accurate total.

Arithmetic Steps

When performing addition, breaking it down into clear arithmetic steps makes the process simpler and more accurate. Here鈥檚 a visual guide using our example:

Step 1: Units Place

7 + 3 = 10 (write 0, carry over 1)

Step 2: Tens Place

4 + 6 + 1 = 11 (write 1, carry over 1)

Step 3: Hundreds Place

5 + 7 + 1 = 13 (write 3, carry over 1)

Step 4: Thousands Place

7 + 3 + 1 = 11 (write 1, carry over 1)

Step 5: Ten-Thousands Place

7 + 2 + 1 = 10 (write 0, but also carry over 1)

This sequence ensures each digit is accurately accounted for during the addition.

Basic Math Operations

Basic math operations like addition lay the groundwork for more complex math skills. They involve simply combining numbers to get a total sum. Here鈥檚 a quick reminder to help strengthen your foundation:

Addition involves combining numbers to find their total.
Start at the rightmost digit (units) and move left.
Use place value to keep digits aligned correctly.
Carry over extra values to the next column if needed.

By mastering basic math operations, you'll build a strong base to tackle more complicated problems in the future, ensuring success in your math journey.

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91影视

Add. $$ \begin{array}{r} 77,543 \\ +\quad 23,767 \\ \hline \end{array} $$

Short Answer

Step by step solution

Add the Units Place

Add the Tens Place

Add the Hundreds Place

Add the Thousands Place

Add the Ten-Thousands Place

Key Concepts

Place Value

Carrying Over

Arithmetic Steps

Basic Math Operations

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