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Chapter 6: Problem 31

Solve. Round to the nearest hundredth. $$\frac{1.2}{0.44}=\frac{y}{14.2}$$

Short Answer

Expert verified
After performing the calculations and rounding off, a reliable calculator should produce \( y \approx 38.73 \)

Step by step solution

01

Re-arrange the equation

In any proportion, the product of the means equals the product of the extremes. So you can express this mathematically by cross-multiplying: \( 1.2 * 14.2 = 0.44 * y \)
02

Solve for y

Now to isolate y, divide both sides of the equation by 0.44. Therefore, \( y = (1.2 * 14.2) / 0.44 \)
03

Calculate y and round off to nearest hundredths

After performing the operation, y returns a long decimal number. Round this off to the nearest hundredth following standard rounding rules.

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Key Concepts

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

Cross-Multiplication
Cross-multiplication is a valuable tool in solving proportion problems. When you have a proportion of the form \( \frac{a}{b} = \frac{c}{d} \), cross-multiplication allows you to multiply the inner terms (means) and the outer terms (extremes) and set them equal: \( a \times d = b \times c \).

This process simplifies solving for a variable, particularly when it is in a fraction. For example, in the problem \( \frac{1.2}{0.44} = \frac{y}{14.2} \), cross-multiply to get:

  • Multiply \( 1.2 \times 14.2 \) to handle the extremes first.
  • Multiply \( 0.44 \times y \) to manage the means.
  • Set them equal: \( 1.2 \cdot 14.2 = 0.44 \cdot y \).
Understanding this concept helps you move variables and simplify proportion equations efficiently.
Rounding Decimals
Rounding decimals is essential when dealing with complex calculations to provide a clearer, more precise result. After solving for a variable, the result may be a long decimal number that needs smoothing out through rounding.

Here's how to round off to the nearest hundredth:

  • First identify the hundredths place: This is the second digit to the right of the decimal point.
  • Look at the next number in the thousandths place: If it is 5 or more, round the number in the hundredths place up.
  • If it's less than 5, leave the hundredths place as it is.
For instance, if after calculating \( y \) you get 38.726, rounding to the nearest hundredth delivers 38.73. Proper rounding provides solutions with the precision needed.
Solving Equations
Solving equations often involves a step-by-step process to isolate your variable. In this case, following cross-multiplication, the next step is to solve for \( y \).

Using our equation: \( 1.2 \cdot 14.2 = 0.44 \cdot y \), the goal is to get \( y \) alone on one side:

  • Calculate \( 1.2 \times 14.2 \) to find the total of the expression for the left side.
  • Divide the result by 0.44 to isolate \( y \).
This sequence ensures you methodically break down the calculation without error. When such steps are followed meticulously, finding the correct, rounded solution becomes straightforward.

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Solve. Use the basic percent equation. \(26 \%\) of 19.5 is what?

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Of the travelers who, during a recent year, allowed their children to miss school to go on a trip, approximately 1.738 million allowed their children to miss school for more than a week. This represented \(11 \%\) of the travelers who allowed their children to miss school. (Source: Travel Industry Association) About how many travelers allowed their children to miss school to go on a trip?
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