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Chapter 5: Problem 8

Write ratio as a fraction and simplify. \(5 \mathrm{cm}\) to \(1 \mathrm{m}\)

Short Answer

Expert verified
\(\frac{1}{20}\)

Step by step solution

01

Understand the Units

Identify the units involved in the ratio. Here, the units are centimeters (cm) and meters (m).
02

Convert Units to the Same Units

Convert meters to centimeters for easy comparison. Since 1 meter = 100 centimeters, convert 1 meter to 100 centimeters.
03

Set Up the Ratio as a Fraction

Rewrite the given ratio using the same units: 5 cm to 100 cm becomes the fraction \(\frac{5}{100}\).
04

Simplify the Fraction

Simplify \(\frac{5}{100}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 5. \(\frac{5 \div 5}{100 \div 5} = \frac{1}{20}\).

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Key Concepts

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

Unit Conversion
Understanding how to convert units is essential in simplifying ratios. When dealing with different units, like in our example where we have centimeters (cm) and meters (m), converting them into the same unit is crucial.
To convert meters to centimeters, you need to know the conversion factor. In this case, 1 meter equals 100 centimeters.
By using this conversion, you can easily rewrite 1 meter as 100 centimeters, making the ratio more manageable.
Practicing unit conversion can help you avoid errors and make the steps easier to follow. Always double-check your conversion factors for accuracy.
Fraction Simplification
Once you've converted all measurements into the same unit, the next step is to write them as a fraction.
In our example, the ratio of 5 cm to 100 cm is written as \(\frac{5}{100}\). Here, the fraction represents the relationship between the two quantities.
This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). Simplifying fractions makes them easier to understand and work with in further calculations.
Always look for common factors in the numerator and the denominator, and use them to reduce the fraction to its simplest form.
Greatest Common Divisor
The greatest common divisor (GCD) is vital for simplifying fractions. It is the largest integer that divides both the numerator and the denominator without leaving a remainder.
In our example, the fraction \(\frac{5}{100}\), the GCD of 5 and 100 is 5.
By dividing both 5 and 100 by their GCD (which is 5), we obtain the simplified fraction \(\frac{1}{20}\).
Finding the GCD can be done by listing the factors of each number and choosing the largest one they have in common.
Understanding how to find and use the GCD ensures your fractions are simplified correctly, making your math work more accurate and efficient.

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Most popular questions from this chapter

Write ratio as a fraction and simplify. \(150 \mathrm{mi}\) in \(5 \mathrm{hr}\)

In Exercises \(1-8,\) use the Pythagorean Theorem to find the length of the missing side in right triangle \(\triangle A B C\) with right angle \(C\). If \(a=12 \mathrm{cm}\) and \(c=20 \mathrm{cm},\) find \(b\)

Explain why it is impossible to construct a triangle with sides 3 inches, 4 inches, and 8 inches.

The measures of two complementary angles are in the ratio of \(2: 3,\) find the measures of each angle.

State whether the polygons are always, sometimes, or never similar. A right triangle and an acute triangle.
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