What Fraction Of The Original Bag Of Fertilizer Did Anita Use?

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Introduction

In mathematics, fractions are a way to represent a part of a whole. They are used to describe a proportion of a quantity. In this article, we will explore a problem involving fractions and proportions. We will use the concept of equivalent ratios to find the fraction of the original bag of fertilizer that Anita used.

Problem Statement

Anita had a bag of fertilizer that contained 120 pounds of fertilizer. She used 1/4 of the fertilizer to fertilize her garden. How much fertilizer did she use in total, and what fraction of the original bag did she use?

Step 1: Understand the Problem

To solve this problem, we need to understand the concept of fractions and proportions. A fraction is a way to represent a part of a whole. In this case, Anita used 1/4 of the fertilizer, which means she used one-fourth of the total amount of fertilizer in the bag.

Step 2: Calculate the Amount of Fertilizer Used

To find the amount of fertilizer Anita used, we need to multiply the total amount of fertilizer in the bag (120 pounds) by the fraction she used (1/4).

# Define the total amount of fertilizer in the bag
total_fertilizer = 120

fraction_used = 1/4

fertilizer_used = total_fertilizer * fraction_used

Step 3: Calculate the Fraction of the Original Bag Used

To find the fraction of the original bag that Anita used, we need to divide the amount of fertilizer she used by the total amount of fertilizer in the bag.

# Calculate the fraction of the original bag used
fraction_of_original_bag = fertilizer_used / total_fertilizer

Step 4: Simplify the Fraction

To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator.

# Import the math module
import math

gcd = math.gcd(int(fertilizer_used), total_fertilizer)

simplified_fraction = str(int(fertilizer_used / gcd)) + "/" + str(total_fertilizer // gcd)

Conclusion

In this article, we used the concept of equivalent ratios to find the fraction of the original bag of fertilizer that Anita used. We calculated the amount of fertilizer she used and then divided it by the total amount of fertilizer in the bag to find the fraction of the original bag used. We then simplified the fraction by finding the greatest common divisor of the numerator and denominator.

Final Answer

The final answer is that Anita used 30 pounds of fertilizer, which is 1/4 of the original bag.

What is a Fraction?

A fraction is a way to represent a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts, and the denominator represents the total number of parts.

Types of Fractions

There are two types of fractions: proper fractions and improper fractions.

  • Proper Fractions: A proper fraction is a fraction where the numerator is less than the denominator. For example, 1/2 is a proper fraction.
  • Improper Fractions: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, 3/2 is an improper fraction.

Equivalent Ratios

Equivalent ratios are ratios that have the same value. For example, 1/2 and 2/4 are equivalent ratios because they have the same value.

Adding and Subtracting Fractions

To add or subtract fractions, we need to have the same denominator. We can then add or subtract the numerators and keep the denominator the same.

Multiplying and Dividing Fractions

To multiply fractions, we multiply the numerators and denominators separately. To divide fractions, we invert the second fraction and multiply.

Real-World Applications of Fractions

Fractions are used in many real-world applications, such as:

  • Cooking: Fractions are used to measure ingredients in recipes.
  • Building: Fractions are used to measure materials and calculate quantities.
  • Science: Fractions are used to measure quantities and calculate proportions.

Conclusion

In conclusion, fractions are an important concept in mathematics. They are used to represent a part of a whole and are used in many real-world applications. We have discussed the concept of fractions, equivalent ratios, and how to add, subtract, multiply, and divide fractions. We have also discussed the real-world applications of fractions and how they are used in cooking, building, and science.