5 Simple Steps To Solve 90 Divided By 5/8

Are you someone who often finds yourself working on complex mathematical problems, even when it seems there's a simple trick to it? Don't worry, understanding how to solve problems like 90 divided by 5/8 can be a bit of a brain teaser, but it's actually quite straightforward once you get the hang of it. This article will guide you through 5 simple steps to solve 90 divided by 5/8, ensuring you're equipped with the knowledge to conquer similar equations in the future.

Understanding the Problem

Before we dive into the step-by-step process, let's clarify what we're trying to achieve here:

• We are dealing with division by a fraction, which might seem daunting at first, but essentially, you're dividing by a part or a ratio.
• 90 is the dividend, the number we're dividing.
• 5/8 is our divisor, but since it's a fraction, it changes how we usually perform division.

Step 1: Recognize It as Division by a Fraction

When you're dividing by a fraction, remember this golden rule: dividing by a fraction is the same as multiplying by its reciprocal. So instead of thinking about dividing by 5/8, think about multiplying by 8/5.

<p class="pro-note">🎓 Pro Tip: This rule applies to any situation where you're dividing by a fraction, not just in arithmetic but also in algebra and beyond.</p>

Step 2: Convert the Division to Multiplication

Now, let's apply that rule:

• 90 divided by 5/8 becomes 90 multiplied by 8/5.

This step simplifies our work considerably by turning the problem into a multiplication equation.

Step 3: Multiply the Numerators Together

First, we'll multiply the numerators:

• 90 x 8 = 720

Step 4: Multiply the Denominators Together

Now, let's handle the denominators:

• 1 x 5 = 5

Step 5: Simplify the Result

Our multiplication gives us 720/5. Now, we simplify:

• 720 ÷ 5 = 144

So, 90 divided by 5/8 is 144.

Practical Examples and Scenarios

Let's explore how this knowledge can be applied in real-life situations:

• Cooking: If a recipe calls for 3/4 of an ingredient and you need to adjust the recipe for 8 servings, where the original serves 5, you'll be dividing by 5/8 to find the new quantity.

• Scaling Plans: In architecture or graphic design, you might need to scale a plan or a design up or down by a fraction. This calculation is essential for ensuring the final product meets exact proportions.

Helpful Tips and Shortcuts

Here are some tips to make solving similar problems easier:

• Memorize the reciprocals of common fractions to quickly convert division to multiplication.
• Practice mental math to speed up simple conversions like in this example.
• Use division by fractions in different contexts to deepen your understanding and become more versatile in problem-solving.

<p class="pro-note">🔧 Pro Tip: Learning common fractions' reciprocals by heart will significantly speed up your calculations.</p>

Common Mistakes to Avoid

• Forgetting the reciprocal: This is the most common error. Always remember to invert the divisor when dividing by a fraction.
• Incorrect multiplication: Ensure you're multiplying the right numerators and denominators together.
• Not simplifying the final answer: Leaving the answer in fractional form when it can be simplified is not only redundant but also can lead to confusion.

Troubleshooting Tips

• Double-check your work: Especially in scenarios where the stakes are high, like in engineering or construction, verify your calculations.
• Understand the context: Sometimes, the problem might be worded in a way that suggests division, but multiplication or another operation might be more appropriate.

Now that you've followed these steps, let's wrap things up:

After delving into the steps to solve 90 divided by 5/8, it's clear that this isn't just about mastering a math problem. It's about understanding how to navigate through mathematical challenges with confidence. Remember, it's not just about the destination but also about the journey - each step in solving this equation teaches you more about the dynamics of numbers.

We encourage you to explore more tutorials on fraction operations, division techniques, and real-world applications of these mathematical concepts. The more you practice, the more second nature this process will become.

<p class="pro-note">🔍 Pro Tip: Always remember that dividing by a fraction is the same as multiplying by its reciprocal. Keep this in mind, and you'll conquer any similar equation with ease.</p>

<div class="faq-section"> <div class="faq-container"> <div class="faq-item"> <div class="faq-question"> <h3>Can I always solve division by a fraction by multiplying by its reciprocal?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>Yes, in basic algebra and arithmetic, this rule applies universally. However, in advanced math, the context might dictate other methods.</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>How can I remember the reciprocal of common fractions quickly?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>Create flashcards or mnemonic devices to aid in memorization. For instance, 5/8 can be recalled as '5 people sharing 8 slices of pizza, making each slice worth 8/5 of a person's portion'.</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>What if the fraction in the denominator has a numerator of 1?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>In such cases, the process is simplified since dividing by 1 does not change the value of the numerator. So, 90 divided by 1/8 becomes 90 times 8, giving you a straightforward multiplication.</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>Why is it useful to understand division by fractions in real life?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>This understanding helps in everyday tasks like scaling recipes, budgeting, time management, and more. It teaches you to think in terms of ratios, which is critical in many professional fields.</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>How can I simplify the final answer if it's a large fraction?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>Use the greatest common divisor (GCD) or prime factorization to find common factors in the numerator and the denominator. Divide both by the GCD to simplify the fraction.</p> </div> </div> </div> </div>