Problem 40 - Fundamentals of Mathematics

Question

Find each value. Check each result with a calculator. \(21 \div 7 \div 3\)

Step-by-Step Solution

Answer

The final result is 1.

Step 1: Division from Left to Right

To solve the expression \(21 \div 7 \div 3\), start by dividing 21 by 7. \(21 \div 7 = 3\).

Step 2: Continue Division

Now take the result from Step 1 and divide it by 3. So, we have \(3 \div 3 = 1\).

Step 3: Check with a Calculator

To ensure the accuracy of our solution, input the expression \(21 \div 7 \div 3\) into a calculator. The calculator should also return a result of 1.

Key Concepts

Order of Operations

Understanding the order of operations is crucial when solving arithmetic expressions. It ensures that you perform calculations in the correct sequence to arrive at the right answer. A common acronym to remember the order is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Although multiplication and division are grouped together, and addition and subtraction are grouped together, you solve whichever comes first from left to right within those pairs.

In the expression \(21 \div 7 \div 3\), the order of operations dictates that we perform division operations from left to right. This means dividing 21 by 7 first, which gives us 3, and then dividing that result by 3, leading to the final result of 1. By adhering to this order, we ensure our calculations are consistent and accurate.

Arithmetic Expressions

Arithmetic expressions, like \(21 \div 7 \div 3\), consist of numbers and operators, such as addition, subtraction, multiplication, and division. Each operator indicates a specific mathematical action to be performed.

When working with these expressions, it's important to carefully identify each number and operator. In this case, the division signs are key, guiding us through the process. Starting with the number 21, we proceed by dividing it by 7, and then taking that quotient to divide by 3.

Understanding and correctly interpreting each component of an arithmetic expression is integral to solving it. This ensures that you arrive at the intended result without errors.

Calculator Verification

Using a calculator to verify your calculations can be a helpful way to ensure your answers are correct. After solving the expression \(21 \div 7 \div 3\) manually, as shown in the step-by-step solution, verifying the result with a calculator adds an extra layer of confidence.

Simply enter the expression directly as it appears: 21 divided by 7 divided by 3. The calculator should return the same result you found manually, which is 1. If it doesn't, double-check your input and revisit your manual calculation to identify any errors.

Calculator verification is not only a good practice for confirming answers but also helps you familiarise yourself with calculators, which can be invaluable during exams or complex problem-solving scenarios. Ensuring you're comfortable with both manual calculations and calculator use solidifies your arithmetic skills.