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Chapter 6: Problem 6

Translate to a proportion. Do not solve. $$ 133 \% \text { of what is } 40 ? $$

Short Answer

Expert verified
\(\frac{1.33}{1} = \frac{40}{x}\)

Step by step solution

01

- Understand the problem

We need to translate the problem '133% of what is 40' into a proportion without solving it.
02

- Convert percentage to decimal

Recall that percentage can be converted to a decimal by dividing by 100. Thus, 133% becomes 1.33.
03

- Set up the proportion

Let the unknown value be represented by \( x \). The phrase '133% of what is 40' translates to the equation: 1.33 \times x = 40.
04

- Write as a proportion

To express this as a proportion, we can write: \( \frac{1.33}{1} = \frac{40}{x} \)

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Key Concepts

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

percentage conversion
Percentage conversion is a straightforward process.
It involves changing a percentage into a decimal value.
Understanding this conversion is crucial for solving many mathematical problems.
To convert a percentage to a decimal, you simply divide by 100.
For example, if you have 133%, you divide 133 by 100.
This will give you 1.33. So, 133% equals 1.33 in decimal form.
This conversion helps set up equations more easily and accurately.
setting up equations
Setting up equations involves translating a word problem into a mathematical statement.
This is done by identifying the relationship described in the problem.
Let's consider the example from the exercise:
'133% of what is 40?' We converted 133% to 1.33 earlier.
Now, we represent the unknown value as \( x \).
The phrase '133% of \( x \)' translates to 1.33 \( x \).
Therefore, the equation becomes 1.33 \( x \) = 40.
Setting up equations correctly is key to solving proportion problems.
understanding proportions
Proportions are equations that express two ratios as being equal.
In the context of our exercise, we need to turn the equation into a proportion.
We already have the equation 1.33 \( x \) = 40.
To express it as a proportion, follow these steps:
- Recognize that 1.33 is over 1 (since 1.33 is not a fraction).
- Write the corresponding ratio on the other side of the equation.
This gives us \( \frac{1.33}{1} = \frac{40}{x} \).
Now, we have our proportion:
\( \frac{1.33}{1} = \frac{40}{x} \).
Proportions make it easier to solve for unknowns using cross-multiplication.

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