Question

In the first paragraph of an essay, Carmen wrote 70 words in 6 sentences. Which answer expresses this as a unit rate? A. \(11 \frac{2}{3} \frac{\text { words }}{\text { sentence }}\) B. \(\frac{35 \text { words }}{3 \text { sentences }}\) C. \(\frac{3 \text { sentences }}{35 \text { words }}\) D. \(11 \frac{2}{3} \frac{\text { sentences }}{\text { word }}\)

Short answer

The correct answer is A: \(11 \frac{2}{3} \frac{\text{words}}{\text{sentence}}\).

Step-by-step solution

Understand the problem

The problem asks us to express the given information as a unit rate. The unit rate we need to find is words per sentence.

Identify the given values

Carmen wrote 70 words in 6 sentences. Therefore, the given values are 70 words and 6 sentences.

Calculate the unit rate

Divide the total number of words by the total number of sentences to find the unit rate in words per sentence: \[ \text{Unit Rate} = \frac{70 \text{ words}}{6 \text{ sentences}} = 11.67 \text{ words per sentence} \]

Simplify the unit rate

Express the decimal as a mixed number: \(11.67 \approx 11 \frac{2}{3}\). Therefore, the unit rate in mixed number form is \(11 \frac{2}{3} \frac{\text{words}}{\text{sentence}}\).

Choose the correct answer

Among the options given, option A represents the unit rate of \(11 \frac{2}{3} \frac{\text{words}}{\text{sentence}}\).

Key concepts

Ratios and Proportions

Ratios and proportions are fundamental concepts in mathematics that help us compare quantities and understand the relationship between them. A ratio is a way to express how one quantity relates to another. For example, in the exercise, the ratio is the number of words to the number of sentences Carmen wrote.

A proportion, on the other hand, is an equation that states two ratios are equivalent. Proportions allow us to solve problems where we need to find an unknown quantity by comparing it to a known ratio. In our problem, we start with the ratio of 70 words to 6 sentences. To find the unit rate (words per sentence), we divide the total words by the total sentences.

This gives us a ratio of 11.67 words per sentence, which simplifies to a mixed number, giving us a better understanding of how many words are in each sentence Carmen wrote. Understanding the concept of ratios and proportions makes solving such problems straightforward and manageable.

Mathematical Reasoning

Mathematical reasoning involves understanding and thinking through problems to come up with solutions. This includes identifying the information given, determining what needs to be found, and logically working through the steps to reach the answer. In the given problem, we use mathematical reasoning to find the unit rate.

First, we understand the problem by identifying the given values - 70 words and 6 sentences. Next, we calculate the unit rate by dividing the total words by the total sentences. This process involves basic arithmetic but requires logical thinking to ensure we perform the correct operation and interpret the result appropriately.

Good mathematical reasoning is essential for solving problems accurately and efficiently. It helps us break down complex problems into simpler, more manageable steps.

GED Math

The GED math test assesses a range of mathematical skills, from basic arithmetic to algebra and geometry. One core aspect is understanding and calculating unit rates, ratios, and proportions—concepts we’ve already addressed in our exercise. Mastering these skills is crucial because they are relevant to real-life situations, such as calculating speed (miles per hour) or price (cost per item).

The exercise provided is an excellent example of the type of problem you might encounter on the GED math test. It requires you to find a unit rate which tests your ability to perform division, interpret results, and simplify fractions. Practicing these types of problems helps build confidence and improve your mathematical abilities.

To do well on the GED math section, focus on understanding the concepts, practicing various problems, and developing your problem-solving skills. Always double-check your calculations and ensure your answers make sense in the context of the problem.