Finding a Fraction of a Number: A Step-by-Step Guide with Sara's Journey

Introduction

Suppose you encounter a situation like Sara, who was asked to find 7/8ths of a number. Determining a fraction of a number is crucial in various fields such as mathematics, physics, and economics. In this comprehensive article, we'll guide you through Sara's journey and provide a step-by-step process for finding a fraction of a number.

Step 1: Convert the Fraction to a Decimal

To work with fractions easily, we often represent them as decimals. To convert 7/8ths to a decimal, divide the numerator (7) by the denominator (8):

7 ÷ 8 = 0.875

Step 2: Multiply the Fraction (Decimal) by the Number

Once you have the fraction in decimal form, multiply it by the number you want to find the fraction of. Let's call this number x:

0.875 x x = y

Where y is the result of finding 7/8ths of the number x.

Step 3: Solve for the Unknown Number (x)

If you know the result (y) and the fraction (0.875), you can solve for the unknown number x:

x = y ÷ 0.875

Sara's Example

Let's return to Sara's situation. She was asked to find 7/8ths of 128. Using the steps above, here's how she solved it:

1. Convert 7/8 to a decimal: 7 ÷ 8 = 0.875
2. Multiply 0.875 by 128: 0.875 x 128 = 112
3. Solve for x: x = 112 ÷ 0.875 = 128

Therefore, 7/8ths of 128 is 112.

Transition Words and Connecting Ideas

To enhance the flow and coherence of your writing, use transition words to connect ideas. For example:

• First, convert the fraction to a decimal.
• Next, multiply the fraction (decimal) by the number.
• Finally, solve for the unknown number.

Importance of Finding Fractions

Understanding how to find fractions is essential in many aspects of life, including:

• Mathematics: Fractions are used in operations such as addition, subtraction, multiplication, and division.
• Physics: Fractions help us measure physical quantities like speed, force, and energy.
• Economics: Fractions are used to express percentages, ratios, and proportions in financial transactions.

Benefits of Understanding Fractions

• Improved problem-solving skills: Fractions help us analyze and solve complex problems.
• Enhanced numeracy: Understanding fractions improves our overall numerical literacy.
• Increased confidence in STEM fields: Proficiency in fractions is crucial for success in science, technology, engineering, and mathematics.

Tables for Reference

Humorous Stories and Lessons Learned

Story 1:

A chef needed to bake 3/4ths of a cake for a party. He mistakenly used 7/4ths of the recipe. What happened?

Lesson Learned: Pay attention to the fraction you are using. Otherwise, you might end up with a cake that's too big for the pan!

Story 2:

Two friends decided to split a pizza equally. They cut the pizza into 8 slices. One friend ate 3/8ths of the pizza, while the other ate 5/8ths. Who ate more?

Lesson Learned: Fractions can be used to compare parts of a whole. It's important to consider the denominators when comparing fractions.

Story 3:

A store sold 1/5th of its inventory on Monday and 2/5ths on Tuesday. What fraction of its inventory remains unsold?

Lesson Learned: Fractions can be used to represent and combine parts of a whole. In this case, the remaining inventory is found by subtracting the fractions sold.

Tips and Tricks

• Practice regularly to improve your skills.
• Use calculators or online resources if needed.
• Break down complex fractions into smaller ones.
• Visualize the fraction using diagrams or graphs.

Call to Action

Now that you have a comprehensive understanding of finding fractions, test your skills by solving the following problems:

1. Find 5/8ths of 160.
2. Convert 3/5ths to a decimal.
3. If 1/3rd of a car is blue, what fraction of the car is not blue?

Remember, practice is key to mastering this concept. Keep practicing and you'll be a fraction expert in no time!