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Chapter 6: Problem 9

Translate to a proportion. Do not solve. $$ 70 \% \text { of } 660 \text { is what? } $$

Short Answer

Expert verified
\( \frac{70}{100} = \frac{x}{660} \)

Step by step solution

01

- Understand the Problem

The exercise is asking to find 70% of 660. This can be translated into a mathematical proportion.
02

- Set Up the Proportion

Set up a proportion where 70% (or 70 out of 100) is equal to an unknown value (let's call it 'x') out of 660. This can be written as: \[ \frac{70}{100} = \frac{x}{660} \]

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Key Concepts

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

Percentage Calculations
Percentage calculations are a common way to express parts of a whole. When we say 70% of 660, we mean we want to find 70 parts out of every 100 parts of 660. To calculate percentages, you typically multiply the total number by the percentage (expressed as a decimal). For example, to find 70% of 660, the calculation would be:
  • First convert the percentage to a decimal: 70% = 0.70
  • Then multiply the total by the decimal: 660 x 0.70
  • This gives the result: 462
In this particular exercise, however, we are asked to set up a proportion instead of directly solving the percentage calculation.
Setting Up Proportions
Proportions allow us to find unknown quantities by setting two ratios equal to each other. In the exercise, we're given 70% of 660, and we need to express this as a proportion. To set up the proportion, follow these steps:
  • First, understand what is given: 70% means 70 out of 100.
  • Identify what needs to be found: the unknown value (let's call it 'x') representing 70% of 660.
  • Write this as a fraction: \( \frac{70}{100} = \frac{x}{660} \)
This proportion states that the ratio of 70 to 100 is the same as the ratio of 'x' to 660. Proportions are powerful tools in mathematics to solve for unknowns when ratios are constant or known.
Basic Algebra
Basic algebra is the branch of mathematics dealing with symbols and the rules for manipulating those symbols to solve equations. In the context of proportions, algebra helps us solve for the unknown variable. For our exercise involving the proportion \(\frac{70}{100} = \frac{x}{660} \), we can solve for 'x' by cross-multiplying and then isolating 'x':
  • Cross multiply: 70 * 660 = 100 * x
  • Perform the multiplication: 46200 = 100x
  • Isolate 'x' by dividing both sides by 100: x = 462
While the exercise doesn't require us to solve the proportion, understanding this algebraic process is essential. It shows what happens when we do need to find the exact value. Basic algebra lays the groundwork for more complex mathematical concepts.

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