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Chapter 1: Problem 24

Use mathematical symbols to translate each phrase. One hundred words per every sixty seconds

Short Answer

Expert verified
The expression is \( \frac{5W}{3S} \).

Step by step solution

01

Identify Known Values

Recognize the key values in the phrase. In this case, 'one hundred words' and 'every sixty seconds'.
02

Define Variables

Choose variables to represent the quantities. Let \( W \) represent words and \( S \) represent seconds.
03

Translate the Phrase

Translate 'one hundred words per every sixty seconds' into a mathematical expression. This can be written as \( \frac{100W}{60S} \).
04

Simplify the Expression

Simplify the fraction \( \frac{100}{60} \) to its lowest term by dividing both the numerator and the denominator by their greatest common divisor, which is 20. This results in \( \frac{5W}{3S} \).

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Key Concepts

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

Variables Definition
In math, we use variables to represent unknown quantities or values. Variables are usually represented by letters like x, y, or z. In the given problem, we defined two variables:

  • W represents the number of words.
  • S represents the number of seconds.
Using variables helps simplify and solve problems more efficiently. By assigning these variables, we can transform complex phrases into manageable mathematical expressions. Always choose letters that make sense for what they're representing to make it easier to follow.
Fraction Simplification
Simplifying fractions is about making them as simple as possible. You do this by dividing the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD).

In the example problem, the fraction is \(\frac{100}{60}\). We find the GCD of 100 and 60, which is 20. Then we divide both the numerator and the denominator by 20:

  • 100 梅 20 = 5
  • 60 梅 20 = 3
This simplifies the fraction to \(\frac{5}{3}\).

Always make sure your final fraction is in its simplest form. This way, it鈥檚 more efficient and easier to understand.
Mathematical Expressions
A mathematical expression is a combination of numbers, variables, and operators (like +, -, 脳, 梅) that represents a value. In this exercise, we translated a phrase into a mathematical expression.

The original phrase was 'one hundred words per every sixty seconds.' This is represented by:
  • 100 words = 100W
  • 60 seconds = 60S

This can be written as \(\frac{100W}{60S}\).

After simplification, we get \(\frac{5W}{3S}\). Expressions are essential in math because they help us describe relationships between different quantities clearly and concisely.

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Most popular questions from this chapter

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