The sum of 3 sixteens and 2 nines, a seemingly simple mathematical expression, unveils a fascinating world of algebraic operations, numerical calculations, and practical applications. Embark on a journey to explore the depths of this expression, unraveling its mathematical intricacies and uncovering its significance in real-world scenarios.
Through algebraic simplification, we will distill the expression to its core, combining like terms to reveal its underlying structure. Numerical evaluation will yield the precise value, showcasing the practical implications of the expression. Moreover, we will venture into variations and extensions, examining how modifications impact the solution and its applications.
Mathematical Expression
The mathematical expression “the sum of 3 sixteens and 2 nines” represents the mathematical operation of adding three values of sixteen and two values of nine. Numerically, this expression can be written as:
/16 + 3/16 + 3/16 + 9 + 9
The order of operations in this expression is to first perform the addition of the fractions (3/16 + 3/16 + 3/16), which results in 9/16. Then, the addition of the whole numbers (9 + 9) results in 18. Finally, the sum of these two values (9/16 + 18) is the result of the expression.
Algebraic Simplification
To simplify the expression algebraically, we can first combine the like terms (3/16 + 3/16 + 3/16 = 9/16). Then, we can add the remaining whole numbers (9 + 9 = 18). This results in the simplified form of the expression:
/16 + 18 = 289/16
Numerical Evaluation
To evaluate the simplified expression numerically, we can convert the fraction (9/16) to a decimal by dividing the numerator (9) by the denominator (16):
/16 = 0.5625
Adding this decimal to the whole number (18), we get the numerical value of the simplified expression:
5625 + 18 = 18.5625
Applications in Real-World Scenarios: The Sum Of 3 Sixteens And 2 Nines
This mathematical expression can be applied in various real-world scenarios, such as:
- Calculating the total cost of items that have different prices.
- Determining the average of a set of numbers.
- Measuring the length of a rectangular object, where the length is divided into fractional units.
- Calculating the area of a triangle, where the base and height are given in different units.
Extensions and Variations
Variations of this expression can be created by adding or removing terms. For example, we could add another term of 3/16, resulting in the expression “the sum of 4 sixteens and 2 nines.” This would change the numerical value of the expression to 19.125.
Alternatively, we could remove one of the terms of 9, resulting in the expression “the sum of 3 sixteens and 1 nine.” This would change the numerical value of the expression to 17.5625.
Visual Representation
| Mathematical Expression | Simplification Steps | Result |
|---|---|---|
| 3/16 + 3/16 + 3/16 + 9 + 9 | 3/16 + 3/16 + 3/16 = 9/169/16 + 18 = 289/16 | 289/16 |
Illustrative Examples
- If a store sells apples for $0.75 each and oranges for $1.25 each, the total cost of 3 apples and 2 oranges can be calculated using this expression: (3 – $0.75) + (2 – $1.25) = $5.50.
- To find the average of the numbers 4, 8, and 12, we can use this expression: (4 + 8 + 12) / 3 = 8.
- If a rectangular object has a length of 12 3/4 inches and a width of 6 1/2 inches, the area of the object can be calculated using this expression: (12 3/4 – 6 1/2) = 81 3/8 square inches.
Related Concepts
This mathematical expression is related to the following concepts:
- Fractions: The expression contains fractions, which represent parts of a whole.
- Decimals: The expression can be converted to a decimal form by dividing the numerator by the denominator of the fraction.
- Percentages: The expression can be used to calculate percentages by converting the fraction to a decimal and multiplying by 100.
Question & Answer Hub
What is the mathematical expression “the sum of 3 sixteens and 2 nines”?
It is a mathematical expression that represents the calculation of adding 3/16 and 2/9.
How do you simplify the expression algebraically?
Combine like terms to obtain a simplified form. In this case, there are no like terms, so the expression remains the same.
What is the numerical value of the simplified expression?
The numerical value of 3/16 + 2/9 is approximately 0.625.
Can you provide an example of a real-world scenario where this expression could be applied?
Sure, if you have 3/16 of a pizza left and your friend has 2/9 of a pizza left, the expression can be used to calculate the total amount of pizza you have together.
