Question

Adding integers with the same sign is similar to increasing assets or increasing debts. $$74+13$$

Short answer

Answer: The result of adding the two integers 74 and 13 is 87.

Step-by-step solution

Identifying the numbers and their signs

The given problem is to add the two integers 74 and 13. Both are positive, so we will simply add these integers together.

Breaking down the addition

Break down the addition into adding the tens place and the ones place separately: $$74+13 = (70 + 10) + (4 + 3)$$

Adding the numbers in each place

Now, add the numbers in the tens place and the ones place separately: $$(70 + 10) +(4 + 3)= 80 + 7$$

Combining the sums

Finally, combine both sums from the previous step: $$80 + 7 = 87$$ Thus, the sum of the two integers, 74 and 13, is 87.

Key concepts

Positive Integers

Positive integers represent the set of all whole numbers greater than zero and are used frequently in daily life to count, label, and measure. When you see numbers like 74 and 13, you're looking at positive integers. Unlike negative integers, which signify a deficiency or loss, positive integers indicate abundance or gain. In mathematical operations, adding two positive integers always gives a positive result.

Think of positive integers as building blocks; when combined, they stack up to form larger numbers. This concept is important to grasp as it lays the groundwork for understanding more complex mathematical principles. For example, if you have 74 apples and someone gives you 13 more, you now have a total of 87 apples. The operation you've just performed—74 + 13—is a straightforward example of adding positive integers.

Place Value Addition

Place value addition is a technique used to simplify the process of adding numbers, focusing on adding digits according to their position in the number—from the ones place to the tens place, and so on. This concept is vital in understanding how to work with large numbers effectively.

To add 74 and 13 using place value, break them down into the tens and ones. For 74: 70 (tens place) and 4 (ones place). For 13: 10 (tens place) and 3 (ones place). Adding the tens place, we get 70 + 10, which equals 80. Adding the ones place, we get 4 + 3, which equals 7. When combined, 80 + 7 results in 87. This organized approach allows you to handle each section of the number individually, making large number addition more manageable. By fully understanding place value addition, students can tackle more challenging arithmetic with confidence.

Integer Arithmetic

Integer arithmetic includes operations such as addition, subtraction, multiplication, and division with whole numbers, which can be positive, negative, or zero. Mastering integer arithmetic is a foundational skill in mathematics, as it is applied in various fields and everyday calculations.

When adding integers, as in the example of 74 + 13, it’s essential always to consider the sign of the integers involved. Since both are positive in this case, we combine their values to get a larger positive integer, 87. If one integer were negative, the operation would instead represent a combination of gain and loss, which is a different scenario entirely. Through understanding integer arithmetic, students learn to discern these differences and apply the correct operation to achieve the right solution.