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Chapter 1: Problem 8

Find each of the following sums. $$5+6+7+8+9$$

Short Answer

Expert verified
The sum of 5, 6, 7, 8, and 9 is 35.

Step by step solution

01

Identify the numbers

First, list down the numbers used in the sum: 5, 6, 7, 8, and 9.
02

Perform the sum

Add the numbers together sequentially: Begin with the first two numbers: \(5 + 6 = 11\).Next, add the third number: \(11 + 7 = 18\).Then, add the fourth number: \(18 + 8 = 26\).Finally, add the last number: \(26 + 9 = 35\).
03

Verify your answer

Double-check your calculation by repeating the addition: \(5 + 6 = 11\)\(11 + 7 = 18\)\(18 + 8 = 26\)\(26 + 9 = 35\)The repeated computation confirms the sum is correct.

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Key Concepts

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

Understanding Addition
Addition is one of the four fundamental operations of arithmetic. It's essentially the process of combining two or more numbers to find their total. When you're adding numbers, you start with a base or initial number and increase it by the value of the other numbers. This process is repeated until all numbers are added, resulting in the sum.
  • Addition is commutative, meaning the order of numbers doesn't change the sum. For example, \(5 + 6\) is the same as \(6 + 5\).
  • It's also associative, which lets you group numbers for easier addition. For example, \((5 + 6) + 7\) is the same as \(5 + (6 + 7)\).
Adding a series of numbers step-by-step ensures accuracy. It also helps in understanding how numbers interact during addition.
Identifying Number Sequences
In mathematics, a number sequence is a list of numbers ordered in a specific way. Each number in the sequence is called a term. In this exercise, the numbers \(5, 6, 7, 8, 9\) form a number sequence.
  • These numbers are consecutive integers, meaning each number is exactly one greater than the previous.
  • This is a simple form of an arithmetic sequence, where the difference between terms remains constant.
Being able to recognize patterns in number sequences can simplify problems and pave the way for quick calculations. Understanding sequences is key in all branches of mathematics, from basic arithmetic to more advanced calculus.
Navigating Step-by-Step Solutions
A step-by-step solution is a logical progression whereby each part builds on the previous one consecutively. To solve the exercise of adding \(5 + 6 + 7 + 8 + 9\), following a methodical series of steps is essential.
  • List the numbers: Start by identifying all the numbers that need to be added, as laid out in the problem.
  • Add sequentially: Begin adding two numbers and then keep adding each subsequent result to the next number in the series.
  • Verify Your Work: It's vital to check your work by going through the addition again or using a calculator to ensure accuracy.
This approach reduces mistakes, promotes understanding, and enhances problem-solving skills. Detailed steps bridge the gap between basic arithmetic exercises and more complex mathematical problems that you might encounter in the future.

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Most popular questions from this chapter

Mentally give a one-digit estimate for each of the following quotients. That is, for each quotient, mentally estimate the answer using one of the digits \(1,2,3,4,5,6,7,8,\) or 9 $$673 \div 218$$

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The application problems that follow may involve more than merely division. Some may require addition, subtraction, or multiplication, whereas others may use a combination of two or more operations. Milligrams of Calcium Suppose one egg contains 25 milligrams of calcium, a piece of toast contains 40 milligrams of calcium, and a glass of milk contains 215 milligrams of calcium. How many milligrams of calcium are contained in a breakfast that consists of three eggs, two glasses of milk, and four pieces of toast?

Find a solution for each equation. $$n+6=15$$

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