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Chapter 1: Problem 89

In the following exercises, add. $$64 + 78$$

Short Answer

Expert verified
142

Step by step solution

01

Setup the Addition

Write down the numbers vertically, aligning the digits by place value.\[ \begin{array}{c@{}c@{}c} & 6 & 4 \ + & 7 & 8 \ \hline derline{} \end{array} \]
02

Add the Units Place

Add the digits in the units place: \(4 + 8 = 12\). Write down 2 in the units place and carry over 1 to the tens place.
03

Add the Tens Place

Add the digits in the tens place along with the carry over: \(6 + 7 + 1 = 14\). Write down 4 in the tens place and carry over 1 to the next place value, though there are no more digits left.
04

Combine the Result

Combine the digits from each place value to get the final answer: \(142\).

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Key Concepts

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

Adding Numbers
Adding numbers is one of the most fundamental skills in mathematics. It involves combining two or more numbers to find their total. When adding numbers, it is crucial to align them correctly: the digits must be positioned according to their place value (ones, tens, hundreds, etc.). For example, if you are adding 64 and 78, write them one below the other as follows:

64
+ 78

Now, you can add the digits column by column, starting from the right.
Place Value
Place value is a key concept in understanding and performing addition. It helps you know the value of each digit in a number based on its position. In the number 64, the digit 6 is in the tens place, meaning it stands for 60, and the digit 4 is in the units place, meaning it stands for 4. Similarly, in the number 78, the digit 7 is in the tens place (70) and the digit 8 is in the units place (8).

When adding, always align the digits according to their place values. For example, in the exercise above, ensure that:
  • The tens place digits (6 and 7) are aligned vertically.
  • The units place digits (4 and 8) are aligned vertically as well.
This alignment helps ensure the addition process is accurate.
Carrying Digits
Carrying digits is a critical step in addition, especially when adding numbers results in a sum greater than 9 in any column. For instance, in the original exercise:
  • Add the units place digits: 4 + 8 = 12. Write down 2 in the units place and carry over 1 to the tens place.
  • Next, add the digits in the tens place along with the carried over 1: 6 + 7 + 1 = 14. Write down 4 in the tens place and carry over 1 to the next place value.
Although there are no digits left in the next place value in this exercise, carrying over ensures accuracy in addition.

Always remember to:
  • Write down only the rightmost digit of the sum in the current column.
  • Carry over any other digits to the next left column.
By following these steps, accurate results in addition can be achieved every time.

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Most popular questions from this chapter

Translate each phrase to math notation and then simplify. The quotient of 63 and 21

Find the place value of the given digits. \(472,981\) (a) 8 (b) 4 (c) 1 (d) 7 (e) 2

Find the place value of the given digits. \(12,403,295\) (a) 4 (b) 0 (c) 1 (d) 9 (e) 2

In the following exercises, multiply. $$23\cdot 10$$

Translate and simplify. The quotient of 64 and 16
See all solutions

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