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Chapter 6: Problem 7

Translate to a proportion. Do not solve. $$ \text { What is } 76 \% \text { of } 90 ? $$

Short Answer

Expert verified
\(\frac{76}{100} = \frac{x}{90}\)

Step by step solution

01

Understanding Percentage

Recall that percent means 'per hundred.' So, 76% is equivalent to the fraction \(\frac{76}{100}\).
02

Setting Up the Proportion

Set up the proportion to represent the exercise. For 'What is 76% of 90?' let \(x\) be the unknown number that represents 76% of 90. Write the proportion as: \[\frac{76}{100} = \frac{x}{90}\]

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Key Concepts

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

proportions
Understanding proportions is essential in solving many types of math problems, including those involving percentages. A proportion is simply an equation that states that two ratios are equivalent. For example, in our exercise, we translated 'What is 76% of 90?' into a proportion. The proportion we used was \[ \frac{76}{100} = \frac{x}{90} \]. Notice how each fraction represents the same relationship: 76 out of 100 is the same as some number (x) out of 90. When you have a proportion like this, it means that the ratio of 76 to 100 is equivalent to the ratio of x to 90. Proportions are useful because you can solve for the unknown value (x) once the proportion is set up correctly.
fractions
Fractions are a way to represent parts of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). In the context of percentages, fractions become incredibly helpful. Consider the fraction \[ \frac{76}{100} \]. This represents 76 out of 100 and is equivalent to 76%. It helps us to understand the portion of a whole quantity. For our problem, converting 76% to \[ \frac{76}{100} \] was the first step. This allowed us to easily set up a proportion. Always remember, practicing with fractions can help simplify complex problems and make them more manageable.
translating word problems
Translating word problems into mathematical equations or expressions is a critical skill. It involves breaking down the text into smaller parts and identifying the mathematical operations required. In our example, the problem asked, 'What is 76% of 90?' To translate this, we followed these steps:
  • Identify the percentage and the whole number (76% and 90).
  • Recall that percentages can be written as fractions, so 76% becomes \[ \frac{76}{100} \].
  • Set up a proportion where the percentage fraction equals the fraction of the part over the whole: \[ \frac{76}{100} = \frac{x}{90} \].
Breaking down word problems and translating them into mathematical expressions can simplify the process of finding a solution. Practice regularly to improve this skill.

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