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Chapter 4: Problem 2

Express the following fractions as ratios. Reduce to lowest terms. $$\frac{1}{9}$$

Short Answer

Expert verified
The fraction \( \frac{1}{9} \) expressed as a ratio is 1:9.

Step by step solution

01

Understand the Fraction

A fraction like \( \frac{1}{9} \) can be expressed as a ratio by writing it in the form of 'a:b'. 'a' is the numerator and 'b' is the denominator.
02

Write as a Ratio

Write the fraction \( \frac{1}{9} \) as a ratio. This can be expressed as 1:9.
03

Convert to Lowest Terms

Check whether the ratio 1:9 can be simplified further by determining the greatest common divisor (GCD) of 1 and 9. Since the GCD is 1, the ratio is already in its lowest terms.

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Key Concepts

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

Numerator
The numerator is the top part of a fraction. In a fraction like \( \frac{1}{9} \), the number 1 represents the numerator. It tells us how many parts of the whole are considered.
Think of a pie: if it's cut into 9 equal pieces, the numerator indicates how many pieces you have.
  • In \( \frac{1}{9} \), the numerator is 1.
  • It indicates 1 part out of a total of 9 parts.
When expressing fractions as ratios, the numerator becomes the first number in the ratio, like in "1:9." Understanding the numerator's role is crucial, as it helps define the portion of the whole being represented.
Denominator
The denominator is the bottom part of a fraction. It shows into how many equal parts the whole is divided. In the fraction \( \frac{1}{9} \), the number 9 is the denominator.
Let's imagine a chocolate bar cut into 9 pieces:
  • The denominator tells you there are 9 pieces in total.
  • In the ratio "1:9," the denominator is the second number, showing the total number of parts.
Understanding denominators helps us grasp how fractions represent parts of a whole. It is essential for comparing fractions and simplifying them when needed.
Greatest Common Divisor (GCD)
The greatest common divisor is a mathematical concept used to simplify fractions. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. Finding the GCD is an essential step in reducing fractions.
To determine if a fraction like \( \frac{1}{9} \) can be simplified further:
  • List the divisors of the numerator (1) and denominator (9).
  • Common divisors for both numbers are identified.
  • In \( \frac{1}{9} \), the GCD is 1.
When the GCD is 1, it means the fraction is already as simple as possible or in its lowest terms.
Reduce to Lowest Terms
Reducing a fraction to its lowest terms means simplifying it so that the numerator and the denominator have no common factors other than 1. This usually involves dividing both numbers by their greatest common divisor (GCD).
Consider our example, \( \frac{1}{9} \):
  • Find the GCD of the numerator and denominator, which is 1.
  • Divide both the numerator and denominator by their GCD.
  • The fraction \( \frac{1}{9} \) remains unchanged because it's already simplified.
Simplifying fractions makes them easier to work with and understand. It ensures you're working with the most straightforward version of the fraction or ratio possible.

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Most popular questions from this chapter

Solve for x in the following proportions. Carry division two decimal places as necessary. $$\frac{16}{40}=\frac{22}{x}$$

Set up the following problems as a proportion and solve. Include labels in the set up and on the answer. If one glass of milk contains 280 milligrams (mg) of calcium, how many mg of calcium is in 2陆 glasses of milk? ________________________

Set up the following word problems as proportions and solve. Include labels in the set up and on the answer. If 100 grams (g) of ice cream contains 20 g of fat, how many g of fat are in 275 g of ice cream? __________________________

Express the following strengths as ratios. 1 part medication to 50 parts solution ___________________________

Express the following fractions as ratios. Reduce to lowest terms. $$\frac{1}{5}$$
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