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Chapter 6: Problem 3

Write the ratio in two other ways. 5 to 6

Short Answer

Expert verified
5:6, \(\frac{5}{6}\)

Step by step solution

01

Identify the Given Ratio

Start with the ratio provided: 5 to 6.
02

Express the Ratio as a Fraction

Rewrite the ratio 5 to 6 as a fraction. This gives \(\frac{5}{6}\).
03

Express the Ratio Using a Colon

Another way to write the ratio is by using a colon. Therefore, express 5 to 6 as 5:6.

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Key Concepts

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

fraction
A fraction is a way to represent a part of a whole or a division of quantities. In our exercise, we converted the ratio 5 to 6 into a fraction, which is represented as \(\frac{5}{6}\).
The number on top is called the numerator, and the one on the bottom is called the denominator.
The numerator tells us how many parts we have, while the denominator tells us how many equal parts make up the whole.

It's important to remember that fractions can also be simplified, meaning both numerator and denominator can be divided by the same number if possible. However, in this case, 5 and 6 have no common factors other than 1. So, \(\frac{5}{6}\) is already in its simplest form.
colon notation
Colon notation is another way to express a ratio. Instead of using fractions, we write the numbers separated by a colon. In our example, the ratio 5 to 6 is written as 5:6.
This notation is particularly useful because it is straightforward and easy to read.
Here are some points to remember about colon notation:
  • It's used to compare two quantities directly.
  • It doesn't imply one part is larger than the other.
  • It's frequently used in contexts like maps (1:1000) and cooking recipes.

Using different ways to write ratios helps us understand the relationships between numbers in various contexts.
mathematical expressions
Mathematical expressions are combinations of numbers, variables, and operators that represent values and relationships. When we deal with ratios, we essentially create simple mathematical expressions.
In this exercise, we started with a verbal expression: '5 to 6'. Then we turned it into two different mathematical expressions:
  • As a fraction: \(\frac{5}{6}\).
  • Using colon notation: 5:6.
Creating these expressions helps us see the ratio in different formats, making it easier to use in calculations.

Understanding these expressions is crucial because they are foundational to more complex mathematics like algebra and calculus. Knowing multiple ways to write ratios allows flexibility and clarity in problem-solving and communication.

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