Fractions and Decimals - Shortcuts & Tricks for Placement Tests, Job Interviews & Exams

Introduction

This tutorial covers essential shortcuts and tricks for working with fractions and decimals, particularly useful for placement tests, job interviews, and various entrance exams. Mastering these concepts can significantly enhance your quantitative aptitude and help you tackle numerical problems efficiently.

Step 1: Converting Decimals to Fractions

To convert a decimal into a fraction, follow these steps:

1. Identify the decimal you want to convert. For example, take 0.3523.
2. Count the number of decimal places. Here, 0.3523 has four decimal places.
3. Write the decimal as a fraction using the place value as the denominator:
   • 0.3523 = 3523/10000
4. Simplify the fraction if possible by finding the greatest common divisor (GCD).

Practical Tip

Use a calculator to simplify if the numbers are large.

Step 2: Adding Decimals

When adding decimals, align the numbers by their decimal points. For example, to calculate:

5.55 + 5 + 5.5 + 5.555 + 5.05 + 5.00:

1. Align the numbers:

     5.550
     5.000
     5.500
     5.555
     5.050
   + 5.000
   ---------
   

2. Add each column starting from the right.

Common Pitfall

Ensure all numbers have the same number of decimal places for accurate addition.

Step 3: Performing Decimal Operations

For calculations like 0.15268 + 0.45804:

1. Align the decimals.
2. Add as you would with whole numbers, keeping the decimal point in its place.

Example

0.15268 + 0.45804 = 0.61072

Step 4: Approximate Values

When dealing with large numbers or complex calculations, estimating can save time. For example, to estimate 8459 + 11.98 - 23.99:

1. Round each number to the nearest whole number:
   • 8459 ≈ 8460
   • 11.98 ≈ 12
   • 23.99 ≈ 24
2. Perform the addition and subtraction:
   • 8460 + 12 - 24 = 8448

Real-World Application

This method is particularly useful in exams where time is limited.

Step 5: Working with Mixed Fractions

If a fraction's denominator decreases by 80% and the numerator increases by 300%, you can solve for the original fraction as follows:

1. Let the original fraction be x/y.
2. The new fraction becomes (3x)/(0.2y) = 2/9.
3. Cross-multiply to solve for x and y.

Tip

Setting up equations can help clarify relationships between numbers.

Step 6: Comparing Fractions

To determine which of several fractions is the largest, convert them to a common denominator or decimal form. This simplifies comparison.

Conclusion

By mastering these tricks and shortcuts for fractions and decimals, you can improve your quantitative skills significantly. Practice these techniques using sample problems to enhance your speed and accuracy. For further learning, explore additional resources or practice tests related to quantitative aptitude.