Fraction Word Problems: Calculate Water Usage For Watering Flowers

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Hey guys! Let's dive into solving some cool word problems involving fractions. Word problems can seem tricky at first, but don't worry, we'll break it down step by step. This time, we're tackling a problem about calculating water usage for watering flowers. So grab your pencils, and let’s get started!

Understanding the Problem

In this section, we'll go through the problem together, making sure we fully understand what it's asking before we jump into solving it. Understanding the core of the problem is the most important thing, so we can develop a strategic approach to finding the solution. Remember, word problems are just stories with math hidden inside, and our job is to uncover that math!

Deconstructing the Word Problem

The problem states: "To water the flowers, 3/4 of 74 liters of water was used. How many liters of water were used? Express the answer as a mixed number." Let’s break down each part:

  • Fraction of water used: 3/4
  • Total amount of water available: 74 liters
  • What we need to find: The amount of water actually used (in liters), expressed as a mixed number.

Identifying Key Information

The key here is to recognize that we're finding a fraction of a whole. In this case, we want to find 3/4 of 74 liters. The word "of" often indicates multiplication in math problems. So, we know we need to multiply the fraction (3/4) by the total amount of water (74 liters).

Before we jump into the calculations, let's think about what a mixed number is. A mixed number is a whole number combined with a proper fraction (where the numerator is less than the denominator), like 2 1/2. We'll need to convert our final answer into this form.

Step-by-Step Solution

Alright, now that we've dissected the problem and know exactly what we're looking for, let's walk through the solution step by step. We will use basic arithmetic operations, focusing on fraction multiplication and conversion to mixed numbers. This process will not only give us the answer but also clarify how we arrived at it. So, let's get to work!

Multiplying the Fraction by the Whole Number

First, we need to multiply the fraction (3/4) by the whole number (74). To do this, we can rewrite 74 as a fraction (74/1) and then multiply the numerators and the denominators:

(3/4) * (74/1) = (3 * 74) / (4 * 1) = 222/4

So, we have 222/4 liters. But this is an improper fraction (the numerator is larger than the denominator), and we need to express our answer as a mixed number.

Converting the Improper Fraction to a Mixed Number

To convert the improper fraction 222/4 to a mixed number, we'll perform division. We divide the numerator (222) by the denominator (4):

222 ÷ 4 = 55 with a remainder of 2

This tells us that 4 goes into 222 fifty-five times, with 2 left over. So, our mixed number will have a whole number part of 55. The remainder (2) becomes the numerator of the fractional part, and we keep the same denominator (4). This gives us:

55 2/4

Simplifying the Fraction

We're almost there, but we can simplify the fraction 2/4. Both 2 and 4 are divisible by 2, so we can reduce the fraction:

2/4 = (2 ÷ 2) / (4 ÷ 2) = 1/2

So, our simplified mixed number is 55 1/2.

The Final Answer

Woo-hoo! We made it! After carefully solving the problem step by step, we've found our answer. Now, let's put it all together and clearly state the final result.

Stating the Solution

Therefore, 55 1/2 liters of water were used to water the flowers. This is the final answer, expressed as a mixed number, just like the problem asked.

Verifying the Answer

It's always a good idea to double-check our work, guys! Does 55 1/2 liters make sense in the context of the problem? We used 3/4 of 74 liters. Since 3/4 is a little less than the whole, we'd expect our answer to be a little less than 74. And 55 1/2 liters fits that description. We can be confident in our solution.

Practice Problems

Okay, now it's your turn to shine! To really nail this concept, let's try a couple of practice problems. Remember the steps we followed: understand the problem, identify the key information, multiply (if needed), and express the answer in the correct form. Let's do this!

Problem 1

A baker used 2/5 of a 10 kg bag of flour to make bread. How many kilograms of flour were used?

Problem 2

Sarah read 1/3 of a 240-page book on Monday. How many pages did she read?

Tips for Solving Fraction Word Problems

Alright, let's wrap things up by sharing some handy tips and tricks that will make tackling fraction word problems a breeze. These strategies will help you approach any problem with confidence and make sure you get the right answer every time. Let’s make you guys pros at these!

Read Carefully and Understand the Problem

This might sound obvious, but it's super important. Read the problem carefully, maybe even a couple of times. Identify what the problem is asking you to find. What information are you given, and what are you trying to figure out? Underlining key information can be a helpful strategy.

Identify Key Words

Certain words often indicate specific mathematical operations. For example:

  • "Of" usually means multiplication.
  • "In all" or "total" often means addition.
  • "Difference" means subtraction.
  • "Each" or "per" might suggest multiplication or division.

Recognizing these keywords can give you a clue about what operation to use.

Draw a Diagram or Model

Visual aids can be incredibly helpful for understanding fraction problems. Try drawing a diagram to represent the problem. You could use a bar model, a circle, or any other visual that makes sense to you. Seeing the problem visually can make it easier to grasp.

Break Down the Problem into Smaller Steps

Complex word problems can feel overwhelming, but if you break them down into smaller, manageable steps, they become much easier. Identify each step you need to take, and solve them one at a time. This makes the whole process less daunting.

Estimate Your Answer

Before you start calculating, try to estimate what a reasonable answer might be. This can help you catch mistakes later on. For example, if you're finding a fraction of a number, your answer should be smaller than the original number.

Check Your Answer

Once you've found an answer, take a moment to check it. Does it make sense in the context of the problem? Did you answer the question that was asked? If possible, try working backward to see if your answer leads back to the original information.

Practice Regularly

The more you practice, the better you'll become at solving fraction word problems. Work through examples in your textbook, online resources, or create your own problems to solve. Consistent practice builds confidence and skills.

Don't Be Afraid to Ask for Help

If you're struggling with a problem, don't hesitate to ask for help. Talk to your teacher, a classmate, or a family member. Sometimes, explaining the problem to someone else can help you understand it better yourself.

Conclusion

And there you have it, guys! We've successfully navigated a fraction word problem, broken down each step, and even learned some awesome tips for tackling these problems like pros. Remember, the key is to take your time, read carefully, and don't be afraid to break the problem down into smaller, more manageable parts. With a little practice, you'll be solving fraction word problems in no time. Keep up the great work, and happy problem-solving!