Problem 40 - Prealgebra

Question

Divide the decimals. \(\frac{4.959}{8.7}\)

Step-by-Step Solution

Answer

The result of dividing \(\frac{4.959}{8.7}\) is 0.57.

Step 1: Convert the Decimals to Whole Numbers

To simplify the division, we multiply the numerator and the denominator by 10 to remove the decimals. This changes the fraction from \(\frac{4.959}{8.7}\) to \(\frac{49.59}{87}\).

Step 2: Perform Long Division

Divide 49.59 by 87 using long division. We find that 87 goes into 495 five times (5 x 87 = 435), leaving a remainder of 60. Then, bring down the 9, making it 609. 87 goes into 609 exactly seven times (7 x 87 = 609), leaving no remainder.

Step 3: Write the Result

After the division, we find that 49.59 divided by 87 is 0.57. Therefore, \(\frac{4.959}{8.7} = 0.57\).

Key Concepts

Long Division

Long division is a method used for dividing large numbers and decimals without a calculator. It's like teaching a recipe—if you follow the steps, you'll succeed. You break down the division process into smaller, manageable pieces. Here’s how it works:

• Divide: You start by dividing the outside number (divisor) into the first part of the inside number (dividend). If it doesn’t fit, you add more digits to the dividend until it can.
• Multiply: Once divided, you multiply the divisor by the number obtained in the previous step. Write this result under the dividend.
• Subtract: Then subtract the result from the dividend. This helps you measure how close you are to dividing evenly.
• Bring Down: Finally, bring down the next number from the dividend and repeat the process until there are no more numbers to bring down.

New lines are crucial in deciphering each step—missing them might lead to division blunders. Long division demands focus and systematic precision, which can significantly ease the process.

Converting Decimals

Converting decimals is essential when you want to simplify operations like division. Decimal numbers can become cumbersome; converting them into whole numbers often makes calculations straightforward. In the exercise, we multiply both the numerator and the denominator by 10. Why do we do this? It's because multiplying by a power of 10 effectively shifts the decimal point to the right.

• For instance, converting 4.959 to 49.59 involves moving the decimal one place to the right.
• This same rule applies to the 87, aiming to line up a fair equation.

This move simplifies your division task. The more decimals you convert, the easier the division. Remember this trick next time you face decimals in division; it’s like simplifying the road before driving.

Numerator and Denominator

The terms numerator and denominator are fundamental in the world of fractions. - **Numerator:** The top part of a fraction, indicating how many parts you have. - **Denominator:** The bottom part, showing into how many parts the whole is divided. In our exercise, the fraction turned from 4.959 (numerator) over 8.7 (denominator) to 49.59 over 87. Multiplying the numerator and the denominator by the same number (10) does not alter the value of the fraction, it just changes the form. These concepts allow you to manipulate and solve fraction problems easily. Knowing the role of each part will assist with dividing evenly and converting fractions into decimals. The interplay between the two can unlock many math puzzles, making life easier with complex problems.