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Writing ratios involves expressing a relationship between two numbers. This is key in many areas of math, expressing how one quantity is related to another.

For instance, to write the ratio of an integer, you can simply use the integer itself as the numerator and 1 as the denominator. This transforms the integer into a fraction.

• Example: The integer 8 can be written as the ratio \(\frac{8}{1}\).

When you write a ratio, ensure that you correctly represent how the quantities relate.

Ratios are versatile and appear in many contexts, including rates, proportions, and scaling problems in different fields.

Converting decimals to fractions is a crucial skill. It allows you to work with decimal numbers in the form of fractions, which can be easier for some calculations. You follow these steps:

First, write the decimal as a fraction with 1 as the denominator. For the decimal 1.61, write it as \[ \frac{1.61}{1} \].

Next, multiply both the numerator and the denominator by 10 raised to a power that removes the decimal point. Since 1.61 has two decimal places, you multiply by 100:

\[1.61 \times 100 = 161 \text{ and } 1 \times 100 = 100 \].

So, \[ \frac{1.61}{1} \text{ becomes } \frac{161}{100} \]. This is the decimal converted to a fraction.

Understanding this conversion is essential for solving problems where fractions are more convenient or necessary to use.

Simplifying fractions is about reducing them to their simplest form. A fraction is in its simplest form when the numerator and denominator can't be divided by any common factor other than 1.

To simplify a fraction, follow these steps:

• Find the greatest common divisor (GCD) of the numerator and denominator.
• Divide both the numerator and the denominator by the GCD.

For example, let's examine the fraction \(\frac{161}{100}\):

1. The numerator is 161, and the denominator is 100.
2. Check the factors of 161 and 100. The common factor is only 1.
3. Since there's no other common factor, \(\frac{161}{100}\) is already simplified.

Understanding how to simplify fractions helps you make calculations easier and results in more precise answers.