Lesson 10.4: Using the On-Screen Calculator Wisely

Introduction

In this lesson, we will explore how to effectively use the on-screen calculator provided during the GRE General test. Many students rely heavily on calculators, often leading to time loss and inefficiency. However, knowing when to utilize the calculator, how to leverage mental math, and when to apply estimation can greatly enhance your performance in the quantitative section. By the end of this lesson, you will:

• Understand the capabilities and limitations of the on-screen calculator.
• Make informed decisions about whether to use mental math, estimation, or the calculator depending on the problem at hand.
• Recognize the risks associated with over-reliance on the calculator and avoid common pitfalls.
• Use the on-screen calculator for appropriate computations efficiently.
• Opt for faster methods such as mental math or estimation when they are more applicable.

Understanding the On-Screen Calculator

The on-screen calculator is a tool designed to assist you with various calculations during the GRE test. Familiarizing yourself with its functions can save you time and allow you to focus on solving problems.

What the On-Screen Calculator Can Do

The on-screen calculator can:

• Perform basic arithmetic operations: addition, subtraction, multiplication, and division.
• Handle decimal numbers.
• Execute square root calculations and exponentiation (raising numbers to a power).

Example:

Calculate $5 \times 6.3 + \sqrt{49}$ using the calculator.

1. Input $5 \times 6.3$ and press enter: $31.5$
2. Calculate $\sqrt{49}$: press $7$ (since $\sqrt{49} = 7$).
3. Add the results: $31.5 + 7 = 38.5$

What the On-Screen Calculator Cannot Do

The limitations of the on-screen calculator include:

• It cannot perform operations with fractions in a direct manner, such as simplifying $\frac{1}{2} + \frac{1}{3}$. Instead, you must convert fractions to decimals.
• It does not possess the capability for complex mathematical operations involving variables or symbolic algebra.
• It cannot store or reference previous calculations, which necessitates re-entering numbers for sequential calculations.

Example:

To compute $\frac{1}{2} + \frac{1}{3}$:

1. Convert fractions: $\frac{1}{2} = 0.5$ and $\frac{1}{3} \approx 0.333$.
2. Add $0.5 + 0.333 = 0.833$ using your calculator.

Deciding Between Mental Math, Estimation, and the Calculator

One of the fundamental skills you need to master is choosing the right approach for each problem. The strategy you choose can significantly affect accuracy and time management.

When to Use Mental Math

Mental math is often the fastest way to solve simple problems, especially when they require calculations that can be handled without a calculator.

Example:

Estimate $12 \times 19$:

1. Break $19$ down: $12 \times 20 - 12 = 240 - 12 = 228$.
2. A quick mental check shows it's close to $228$ and easy to compute in your head.

When to Estimate

Estimation is useful when precision is less critical, but you still want an approximate answer quickly without relying on a calculator.

Example:

Estimate the total cost of buying $47$ items at $3.50$ each:

1. Round $47$ to $50$ and $3.50$ to $4$.
2. Calculate $50 \times 4 = 200$.
3. You can confidently guess the total will be near $200$ without the exact number.

When to Use the Calculator

Utilize the on-screen calculator for calculations that involve:

• Large numbers or complex operations (e.g. large multiplications, finding square roots).
• Difficult fractions that are cumbersome to handle mentally.

Example:

Calculate $1234 \times 56$ using a calculator when the numbers are unwieldy. The calculator gives $69104$ immediately without manual errors or lengthy steps.

Avoiding Time Loss from Over-Reliance on the Calculator

Over-reliance on the on-screen calculator can lead to time waste, especially if you're struggling with complex calculations or attempting to enter unwieldy fractions.

Recognizing Over-Reliance

• If you find yourself getting stuck on problems requiring the calculator, consider if simpler methods could yield answers.
• Check the time spent calculating versus reading and understanding the question.

Example:

Instead of using the calculator to find $72\div 8$, recognize that it’s simple mental math that equals $9$.

Tips for Efficient Calculator Use

• Familiarize yourself with the calculator's features prior to the test to avoid wasting time.
• Practice using the on-screen calculator efficiently during practice tests to build familiarity and speed.
• Limit calculator use to problems that require it, choosing mental math or estimation for quicker work.

Conclusion

By understanding the capabilities and limitations of the on-screen calculator, along with adopting a balanced approach to mental math and estimation, you can enhance your performance on the GRE quantitative section. Remember that your goal should be to minimize reliance on the calculator and to find solutions using the most efficient method available for each problem.

Study Notes

• The on-screen calculator can perform basic operations but cannot simplify fractions directly.
• Mental math is advantageous for simple calculations and estimates.
• Estimation is useful for rough calculations where exact numbers are not required.
• Use the calculator for complex or large number operations.
• Avoid over-reliance on the calculator to save time.
• Familiarize with the calculator's functionality before the exam.