Delving into the mathematical realm, we embark on a journey to uncover the secrets of “the sum of 3 fifteens and 4 twos.” This intriguing expression holds within it a tapestry of mathematical concepts, promising an engaging exploration of arithmetic operations, algebraic representations, and real-world applications.
Unveiling the layers of this mathematical expression, we will unravel the intricate dance of numbers, revealing the beauty and practicality that lie at its core. Join us on this mathematical odyssey as we decipher the sum of 3 fifteens and 4 twos.
Mathematical Expression
Explanation
The mathematical expression “the sum of 3 fifteens and 4 twos” represents the total value obtained by adding three numbers that are each equal to fifteen and four numbers that are each equal to two.
Numerical Representation
The numerical representation of this expression is:
15 + 15 + 15 + 2 + 2 + 2 + 2
Order of Operations
When evaluating this expression, the order of operations dictates that we first perform the additions within the parentheses (if any), then multiplication and division (from left to right), and finally addition and subtraction (from left to right).
In this case, there are no parentheses or multiplication/division operations, so we can proceed with the additions from left to right:
15 + 15 + 15 + 2 + 2 + 2 + 2 = 63
Arithmetic Operations
The expression involves two basic arithmetic operations: addition and multiplication.
Additionis the process of combining two or more numbers to get their sum. In the expression, we add three instances of the number 15 and four instances of the number 2.
Multiplicationis the process of repeatedly adding a number to itself a specified number of times. In the expression, we multiply 3 by 15 and 4 by 2.
Simplifying the Expression
To simplify the expression, we first perform the multiplication operations:
- 3 x 15 = 45
- 4 x 2 = 8
Then, we substitute the products back into the expression and perform the addition:
- 45 + 8 = 53
Therefore, the simplified expression is 53.
Numerical Result
Evaluating the expression 3 x 15 + 4 x 2, we get the numerical result:
3 x 15 + 4 x 2 = 45 + 8 = 53
The result, 53, represents the total sum of three groups of fifteen and four groups of two.
Significance and Applications
The result of the expression has practical significance in various contexts:
- Counting Objects:If we have three groups of fifteen objects and four groups of two objects, the result tells us the total number of objects, which is 53.
- Resource Allocation:In resource allocation scenarios, the result can help determine the total amount of resources needed. For example, if a school has three classes with 15 students each and four classes with 2 students each, the result would indicate the total number of students, which is 53.
- Financial Calculations:In financial contexts, the result can represent the total amount of money involved. For instance, if an individual has three accounts with $15 in each and four accounts with $2 in each, the result would give the total amount of money, which is $53.
Algebraic Representation: The Sum Of 3 Fifteens And 4 Twos
An algebraic representation is a mathematical expression that uses variables and constants to represent a problem or situation. In the case of the sum of 3 fifteens and 4 twos, the algebraic representation is:
3(15) + 4(2)
This representation simplifies the expression by grouping like terms together. The variable “n” represents the number of fifteens, and the variable “m” represents the number of twos. The expression can be rewritten as:
3n + 4m
This algebraic representation can be used to solve related problems. For example, if we want to find the sum of 5 fifteens and 6 twos, we can substitute the values of n and m into the expression:
3(5) + 4(6) = 15 + 24 = 39
Word Problem Application
The expression 3 × 15 + 4 × 2 can be used to solve a variety of word problems. One example is finding the total number of items in two different sets.
For instance, suppose you have a set of 15 apples and a set of 2 oranges. To find the total number of fruits, you can use the expression 3 × 15 + 4 × 2.
Steps Involved, The sum of 3 fifteens and 4 twos
- Identify the number of sets and the number of items in each set.
- Multiply the number of items in each set by the corresponding coefficient in the expression.
- Add the products together to find the total number of items.
In this case, you would multiply 15 by 3 and 2 by 4, then add the products together: 3 × 15 = 45 and 4 × 2 = 8. Adding these together gives you a total of 45 + 8 = 53 fruits.
Clarifying Questions
What is the numerical result of the expression “the sum of 3 fifteens and 4 twos”?
The numerical result is 66.
How can the expression be applied to solve a word problem?
The expression can be used to solve word problems involving the addition of multiple quantities. For example, if a store has 3 boxes of apples with 15 apples in each box and 4 boxes of oranges with 2 oranges in each box, the expression can be used to calculate the total number of fruits in the store.
