Problem 79 - Prealgebra

Question

Compute the quotient \(51 / 59\), and round your answer to the nearest tenth.

Step-by-Step Solution

Answer

The quotient is approximately 0.9.

Step 1: Division

First, divide 51 by 59. To do this division, set it up as a fraction: \(\frac{51}{59}\). The division gives you an approximate decimal result of about 0.8644067.

Step 2: Round to the Nearest Tenth

To round 0.8644067 to the nearest tenth, look at the first digit after the decimal point, which is 8. Then, look at the second digit, 6, to decide if the first digit should round up or stay the same. Since 6 is greater than or equal to 5, the 8 rounds up to 9.

Key Concepts

Fractions

Fractions represent a part of a whole. They consist of two parts: the numerator and the denominator. The numerator is the top number and shows how many parts you have. The denominator is the bottom number and tells you how many parts the whole is divided into. In the fraction \(\frac{51}{59}\), 51 is the numerator and 59 is the denominator. This fraction represents 51 parts out of 59 total parts. They are useful for solving problems involving division, since they can easily express portions and ratios.

• Great for dividing quantities
• Helpful in comparing ratios
• Fraction to decimal conversion makes calculation easier

Remember, fractions can be simplified or approximated by converting them into decimals to make them easier to handle in calculations.

Decimal Approximation

Decimal approximation involves converting fractions into decimal values to make them easier to interpret. To convert a fraction to a decimal, you divide the numerator by the denominator, just like in our example where \(51\) is divided by \(59\). The result is a decimal approximation of about \(0.8644067\).
When working with decimals, it often becomes easier to perform arithmetic calculations. Approximations are quite beneficial when exact fractions do not provide a clear visualization or easy computation. Use the fraction's division result to understand how much each pie slice or portion of a number represents in decimal terms.

• Convert fractions to decimals to simplify math
• Used when a rough estimate is needed
• Helps in visualizing and comparing sizes or amounts

Decimal approximations are particularly useful when complexity needs to be reduced, such as when using fractions in practical, real-world scenarios.

Rounding

Rounding is a method used to simplify numbers to make them easier to work with. It involves decreasing the number of digits after the decimal, thereby making a number shorter and simpler. To round decimals, identify which place value you need to round to and then use the digit immediately to the right to determine whether to round up or maintain the same digit.
In our case, we are rounding \(0.8644067\) to the nearest tenth. The first digit after the decimal is \(8\), and the next one is \(6\). Since 6 is greater than or equal to 5, \(8\) is increased by 1, resulting in \(0.9\).

• Simplifies complex numbers
• Makes calculations faster and easier
• Useful in estimates and quick assessments

Keep in mind that rounding helps get a quick estimate, but one should consider how much precision is needed in the context of the problem at hand.