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Chapter 15: Problem 3

Tell whether each statement is true or false. \(5+6=14\)

Short Answer

Expert verified
False

Step by step solution

01

Understand the Equation

The equation given is \(5 + 6 = 14\). This is an addition problem with the numbers 5 and 6 on the left side of the equation and the number 14 on the right side of the equation.
02

Calculate the Left Side

Add the numbers on the left side of the equation: \(5 + 6 = 11\). This is a simple addition operation.
03

Compare Both Sides

Compare the sum calculated from the left side \(11\) with the value on the right side of the equation \(14\).
04

Make the Conclusion

Since \(11\) is not equal to \(14\), the statement \(5 + 6 = 14\) is false.

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Key Concepts

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

Addition
Addition is one of the most basic operations in arithmetic, involving combining two or more numbers to get a sum. It is often represented by the plus sign "+". In the equation \( 5 + 6 = 14 \), addition occurs on the left side, where the numbers 5 and 6 are added together.
When performing addition:
  • Identify the addends (the numbers being added), 5 and 6 in this case.
  • Calculate the sum by finding the total amount. Here, \(5 + 6 = 11\).
  • The result here, 11, is what we refer to as the sum.
Understanding addition helps in solving many mathematical problems and is a foundational skill for more advanced mathematics.
Equation Solving
Solving an equation involves finding the value of unknown numbers or verifying if an equation is true or false. In our given exercise, the equation is \( 5 + 6 = 14 \). Though there are no unknowns to solve for, we need to verify the truth of the equation.
To solve an equation like this:
  • Understand each part of the equation clearly鈥攈ere, two sides are compared.
  • Perform the necessary operations, adding 5 and 6 to ensure you are correct.
  • Compare the computed sum to the number on the other side of the equation to verify correctness.
If both sides equal the same number, the equation is true. If not, as in this case (11 does not equal 14), the equation is false.
Mathematical Comparison
Comparison in mathematics is crucial, especially in assessing the truthfulness of statements. From our equation \(5 + 6 = 14\), understanding how to compare both sides shows why precise calculations matter.
In comparing:
  • First, calculate the sum of the left side.
  • Then, examine the right side value.
  • Assess the equality of the two results.
If both sides of the equation do not match, it signals a discrepancy, as seen in \(11 eq 14\). This indicates a false statement. Comparisons like these are fundamental in verifying mathematical expressions, ensuring you draw correct conclusions from your calculations.

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