Problem 33 - Prealgebra

Question

Divide the decimals. \(\frac{1.248}{0.52}\)

Step-by-Step Solution

Answer

1.248 divided by 0.52 equals 2.4.

Step 1: Understand the Problem

We need to divide the decimal 1.248 by 0.52. To do this effectively, we need to convert the divisor to a whole number by moving the decimal point.

Step 2: Eliminate the Decimal from Divisor

To eliminate the decimal from the divisor 0.52, we move the decimal point two places to the right in both the divisor and the dividend. This transforms the operation into dividing 124.8 by 52.

Step 3: Perform the Division

Now, divide 124.8 by 52. Start by dividing the integer part. 52 into 124 goes twice (as 52 x 2 = 104), and subtract 104 from 124 to get 20. Bring down the 8 to make it 208.

Step 4: Continue Division

Next, divide 208 by 52. Multiply 52 by 4 to get 208 (as 52 x 4 = 208). Subtract 208 from 208 to get 0. Therefore, the division is complete.

Step 5: Write the Result

After performing the division, the result is 2.4. Thus, \[ rac{1.248}{0.52} = 2.4 \]

Key Concepts

Dividing Decimals

Dividing decimals may seem challenging at first, but with practice, it becomes intuitive. In this process, the goal is often to simplify the calculation by converting the division problem into one involving whole numbers. This involves shifting the decimal places so that the divisor becomes a whole number.

• Identify the divisor and the dividend in your problem.
• To make the divisor a whole number, count how many decimal places it has.
• Shift the decimal point in both the divisor and dividend to the right by the same number of places.

By following these steps, you convert a complex-looking division problem into one that is easier to solve using traditional division methods.

Converting Decimals

Converting decimals effectively is a key skill in mastering decimal division. This involves re-positioning the decimal point to simplify division calculations.

• Look at the divisor: how many decimal places does it have?
• Move the decimal point to the right to convert the divisor into a whole number. If the divisor is 0.52, moving the decimal two places to the right turns it into 52.
• Apply the same shift to the dividend. For 1.248, moving the decimal two places results in 124.8.

Converting decimals in this way allows simplest application of the long division, enhancing both efficiency and accuracy of computation.

Long Division

Long division is a traditional method of dividing two numbers, which can apply equally to decimals once they're converted to whole numbers. Here’s how to efficiently perform long division:

• Divide the first part of the dividend by the whole divisor: For example, divide 124 by 52.
• Find the maximum number that fits: 52 fits into 124 two times. Multiply 2 by 52 to get 104.
• Subtract this product from the first part of the dividend and bring down the next digit.
• Continue the process with the new number formed after bringing down the digit: Here, bring down the 8 to convert the 20 to 208.
• Again, divide, subtract, and repeat: 208 divided by 52 is 4.
• Repeat until you have no more digits to bring down.

Ultimately, this method helps us achieve an accurate answer, ensuring completeness in calculations. Whether dealing with simple numbers or decimals, mastering long division will equip you to handle even the most complex mathematical challenges.