Problem 33 \(78.65 \div 11\)... [FREE SOLUTION]

Chapter 0: Problem 33

\(78.65 \div 11\)

Short Answer

Expert verified

7.15

Step by step solution

- Setup Division

Write down the division problem as a fraction: \[ \frac{78.65}{11} \] Move the decimal point two places to the right in both the numerator and the denominator to simplify division.

- Simplify the Expression

After shifting the decimal points, the expression becomes: \[ \frac{7865}{1100} \] This simplifies the calculation.

- Simplify the Division

Perform the division: \[ \frac{7865}{1100} = 7.15 \] Therefore, 78.65 divided by 11 equals 7.15.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

simplifying fractions

Converting a division problem into a fraction is a great first step to take. In the exercise of dividing 78.65 by 11, we start by writing it as the fraction: \( \frac{78.65}{11} \). This fraction form allows us to see the relationship between the dividend (78.65) and the divisor (11).

Simplifying fractions makes large or complex numbers easier to handle. It involves reducing the fraction to its smallest form, ensuring that the numerator and the denominator have no common factors other than 1. In our example, shifting the decimal point helps us simplify the division without physically changing the value of the numbers.

decimal point adjustment

Adjusting the decimal point is a critical step in dealing with decimals during division problems. By moving the decimal point two places to the right, both the numerator and the denominator are turned into whole numbers. This gives us the fraction: \( \frac{7865}{1100} \).

Moving the decimal in both numbers ensures that their relative value remains the same. For instance, 78.65 and 7865 still have the same ratio to each other after adjusting the decimal point to form the numbers 11 and 1100, respectively. This makes it easier to perform long division without confusing decimal calculations.

long division

Long division is a straightforward method to divide numbers, especially when dealing with large numbers. After adjusting the decimal points and forming the fraction \( \frac{7865}{1100} \), we perform long division.

In long division, divide the numerator (7865) by the denominator (1100) step by step. By doing so, we find that 7865 divided by 1100 equals 7.15.

This final answer means that when you divide 78.65 by 11, you get 7.15. Breaking down this process helps ensure clarity and accuracy in the calculation, making division with decimals much simpler.

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91影视

\(78.65 \div 11\)

Short Answer

Step by step solution

- Setup Division

- Simplify the Expression

- Simplify the Division

Key Concepts

simplifying fractions

decimal point adjustment

long division

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