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Chapter 2: Problem 52

Simplify. \((9+12) \div(3+4)\)

Short Answer

Expert verified
The simplified result is 3.

Step by step solution

01

Simplify the Numerator

First, simplify the expression inside the parentheses in the numerator. Here, you need to add the numbers together: \[ 9 + 12 = 21 \]
02

Simplify the Denominator

Next, simplify the expression inside the parentheses in the denominator. Add these numbers together: \[ 3 + 4 = 7 \]
03

Divide the Simplified Numerator by the Simplified Denominator

Finally, divide the simplified numerator by the simplified denominator to find the result: \[ 21 \div 7 = 3 \]

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Key Concepts

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

simplifying expressions
Simplifying expressions means making a math problem easier to solve. It involves combining like terms and reducing the problem step-by-step until you get a simple answer. For example, in the problem \((9+12) \div (3+4)\), we simplify both the numerator and the denominator. Simplifying helps us see the solution more clearly. Working through the simplification step-by-step ensures we don鈥檛 make mistakes along the way.
numerator and denominator
In any fraction or division problem, the numerator is the top number and the denominator is the bottom number. For instance, in \( \frac{9+12}{3+4} \), \((9+12)\) is the numerator and \((3+4)\) is the denominator. Knowing this is important because we first simplify the numerator and the denominator separately. Once simplified, we divide the numerator by the denominator to get the final result. This helps us break down complex problems into smaller, manageable parts.
basic arithmetic operations
Basic arithmetic operations include addition, subtraction, multiplication, and division. These operations are the foundation of math. In our exercise, we mainly used addition and division. First, we added the numbers in the parentheses: \(9+12=21\) and \(3+4=7\). Then, we used division to find the final answer: \(21\div\7 = 3\). Mastering these basic operations is essential because they are used in nearly every math problem.
division
Division is one of the four basic math operations. It involves splitting a number into equal parts. The division equation \((21\div 7)\) means you are dividing 21 into 7 equal parts. The answer is how many parts you get in each group, which is 3 in this case. When dealing with division in fractions, simplify both parts (numerator and denominator) before dividing. This makes the calculation straightforward and ensures accuracy.

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Most popular questions from this chapter

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