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Chapter 3: Problem 42

Estimate each of the following as \(0, \frac{1}{2},\) or 1 . $$ \frac{5}{12} $$

Short Answer

Expert verified
The estimate for \(\frac{5}{12}\) is \(\frac{1}{2}\).

Step by step solution

01

Understand the problem

The task is to estimate the fraction \(\frac{5}{12}\) as \(0\), \(\frac{1}{2}\), or \(1\). We need to decide which of these three values \(\frac{5}{12}\) is closest to.
02

Convert the fraction to a decimal

Divide the numerator by the denominator: \(\frac{5}{12} = 0.4167\) (rounded to four decimal places).
03

Compare the decimal to 0, \(\frac{1}{2}\), and 1

Compare \(\frac{5}{12} = 0.4167\) to the given values: \(\frac{1}{2} = 0.5\). Since \0.4167\ is closest to \0.5\, we estimate \(\frac{5}{12}\) to \(\frac{1}{2}\).

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Key Concepts

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

Fraction to Decimal Conversion
When working with fractions, it's often easier to understand their value by converting them to decimals. This is done by dividing the numerator (top number) by the denominator (bottom number). For example, for \(\frac{5}{12}\), you divide 5 by 12, giving you approximately 0.4167. This process helps in visually comparing and understanding the fractional values against common reference points like 0, \(\frac{1}{2}\), and 1. Knowing how to convert fractions to decimals aids in many areas of mathematics, including estimation and calculations involving real numbers.
Comparing Decimals
Once you have converted a fraction to a decimal, comparing it becomes straightforward. You simply look at the digits and check their place value. Here, comparing the decimal 0.4167 to other standard decimals such as 0 (which represents zero), 0.5 (representing one half), and 1 (a whole one) can help.
  • 0.4167 is greater than 0 and less than 0.5.
  • It鈥檚 also closer to 0.5 than to 0, making \(\frac{5}{12}\) closer to \(\frac{1}{2}\).
This simple comparison tells us where the fraction lies in relation to these benchmark values.
Estimating Values
Estimation simplifies complex calculations and makes mental math more manageable. The goal is to determine which of 0, \(\frac{1}{2}\), or 1 a fraction or decimal is closest to. In our example, we estimated \(\frac{5}{12}\) by:
  • Converting the fraction to its decimal form, 0.4167.
  • Comparing 0.4167 to 0, 0.5, and 1.
We found that 0.4167 is closer to 0.5, so \(\frac{5}{12}\) is estimated as \(\frac{1}{2}\).
This technique helps in quick approximations & is useful in everyday math like budgeting, measurements, and even in scientific calculations.

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Most popular questions from this chapter

Consider only the numbers \(3,4,5,\) and 6 each can be placed in a blank in the following. $$ \square+\frac{\square}{\square} \cdot \square=? $$ What placement of the numbers in the blanks yields the largest sum?

A cubic meter of concrete mix contains \(420 \mathrm{~kg}\) of cement, \(150 \mathrm{~kg}\) of stone, and \(120 \mathrm{~kg}\) of sand. What is the total weight of a cubic meter of the mix? What part is cement? stone? sand? Add these fractional amounts. What is the result?

Add and simplify. $$ \frac{3}{8}+\frac{1}{8}+\frac{2}{8} $$

Estimate each of the following as \(0, \frac{1}{2},\) or 1 . $$ \frac{7}{8} $$

Estimate each of the following as \(0, \frac{1}{2},\) or 1 . $$ \frac{7}{100} $$
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