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Chapter 6: Problem 7

Write the ratio in two other ways. $$\frac{1}{2}$$

Short Answer

Expert verified
\frac{1}{2}, 1:2, 1 to 2

Step by step solution

01

Understanding the Ratio

A ratio compares values. The given ratio is \( \frac{1}{2} \) which compares 1 part to 2 parts.
02

Express as a Fraction

The ratio \( \frac{1}{2} \) is already expressed as a fraction. It signifies 1 part out of 2 total parts.
03

Express in Colon Notation

The ratio can also be written using colon notation. So, \( \frac{1}{2} \) can be written as 1:2.
04

Express in Words

Another way to represent the ratio \( \frac{1}{2} \) is writing it in words: '1 to 2'.

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Key Concepts

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

fractions
A fraction represents a part of a whole.
It's one way to express ratios.
In our example, the fraction is \( \frac{1}{2} \).
This means one part out of a total of two parts or halves.
Fractions are a versatile way to show ratios because they are used in various areas of math.
When writing fractions:
  • The top number is the numerator, representing the number of parts you have.
  • The bottom number is the denominator, representing the total number of parts.

So, in \( \frac{1}{2} \), '1' is the numerator and '2' is the denominator.
colon notation
Colon notation is another way to express ratios.
In this form, the values are separated by a colon (:).
For example, the ratio \( \frac{1}{2} \) can be written as 1:2.
Colon notation is often used in real-world scenarios,
such as mixing ingredients or comparing quantities.
It's a straightforward way to make comparisons:
  • The first value (1) comes before the colon.
  • The second value (2) comes after the colon.

This tells you that for every 1 part of the first quantity,
you have 2 parts of the second quantity.
word notation
Word notation translates numerical ratios into words.
This can make ratios easy to understand, especially for beginners.
Taking our example, the ratio \( \frac{1}{2} \) or 1:2 can be written as '1 to 2'.
In word notation, simply state the two values with the word 'to' between them.
Word notation helps in verbal communication of ratios and is especially useful in descriptions,
recipes, or any context where clear explanation is needed.
As a recap in word notation:
  • '1' is the first value.
  • The word 'to' connects the two values.
  • '2' is the second value.

So, \( \frac{1}{2} \) becomes '1 to 2'.

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Most popular questions from this chapter

Solve the proportion. Be sure to check your answers. $$\frac{3}{40}=\frac{w}{10}$$

Determine whether the ratios form a proportion. $$\frac{16}{24} \triangleq \frac{2}{3}$$

Write a proportion for each statement. Then solve for the variable. 9 is to 12 as \(w\) is to 30

A cheetah can run \(120 \mathrm{m}\) in 4.1 sec. An antelope can run \(50 \mathrm{m}\) in 2.1 sec. Compare their unit speeds to determine which animal is faster. Round to the nearest whole unit.

Write a proportion for each statement. Then solve for the variable. 15 is to 20 as \(t\) is to 10
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