Problem 51 - Prealgebra

Question

Perform the indicated operations. \(80.5 \div 1.61\)

Step-by-Step Solution

Answer

80.5 divided by 1.61 is 50.

Step 1: Understand the Operation

We need to perform a division operation where 80.5 is divided by 1.61. Division will tell us how many times 1.61 fits into 80.5.

Step 2: Rewrite the Division

Division can be expressed as a fraction, so we rewrite the problem as \( \frac{80.5}{1.61} \). This means dividing 80.5 by 1.61.

Step 3: Perform the Division

Using a calculator or long division, divide 80.5 by 1.61. Begin by seeing how many times 1.61 fits into 80.5. It fits approximately 50 times as 1.61 x 50 equals 80.5.

Step 4: Verify the Result

Multiply 1.61 by 50 to check the answer: \(1.61 \times 50 = 80.5\). The multiplication confirms the division result is accurate.

Key Concepts

Long Division

Long division is a method that helps us divide larger numbers more easily. It involves a series of steps, and we can do it on paper. Imagine trying to find out how many toy blocks fit into a box. In a way, that's what long division helps us understand with numbers. Each step of long division aims to make the number smaller until we figure out the whole division.

• First, we see how many times the divisor fits into the first part of the dividend.
• We multiply the divisor by the number we found, subtract the result from the dividend part, and then bring down the next digit.
• We repeat until we've processed all digits of the dividend.

Although calculators can do division quickly, understanding long division is crucial. It's foundational for more complex math skills. Practicing with examples like dividing 80.5 by 1.61 can build confidence in manual calculations.

Fraction Representation

Fraction representation in division is like showing the division differently. For instance, dividing 80.5 by 1.61 can be shown as a fraction: \(\frac{80.5}{1.61}\).
Fractions tell us how many times one number is contained within another. Here's why fractions are useful:

• Fractions help simplify division problems and make them easier to visualize.
• They let us see the division as a division of parts (numerator and denominator).
• Fractions can also help us understand ratios and proportions.

When we turn a division into a fraction, we create a visual and mathematical representation. It shows clearly what it means to "divide" in terms of parts and wholes. This helps simplify the problem and verify results quickly.

Verifying Division Results

Verifying division results is all about checking our work. Whenever you divide, it's a good idea to make sure the answer fits. For instance, dividing 80.5 by 1.61 gives a result. To check it, we do the reverse: multiply 1.61 by the result (50 in this case).

• Perform the multiplication: \(1.61 \times 50 = 80.5\).
• If the result matches the original number (80.5), the division was done correctly.

Verification serves multiple purposes:

• Ensures accuracy in calculations.
• Helps catch any possible errors early.
• Builds confidence in understanding the math involved.

Remember, verifying results is not just for math class. It's a useful habit in everyday life too, ensuring our calculations are reliable and accurate.