5 Tricks To Master Division: 63 Divided By 7

Learning how to tackle division might seem daunting initially, but with the right strategies and a bit of practice, you can master it quickly. Today, let's dive into understanding the division of 63 by 7, but not just for the sake of division itself; we're here to uncover 5 clever tricks to solve any division problem effortlessly.

The Basics of Division

What is Division?

Division is the process of distributing a quantity into equal parts. When you divide 63 by 7, you're determining how many groups of 7 are in 63.

• Dividend: The number being divided (63)
• Divisor: The number dividing into the dividend (7)
• Quotient: The result after the division (9)
• Remainder: What's left after dividing (0 in this case)

Here's a simple markdown table to clarify:

Trick 1: Use Estimation for Quick Mental Math

When you're dealing with larger numbers, especially if they're close to multiples of your divisor, you can use estimation to make division easier.

Example Scenario

Let's estimate 63 divided by 7:

• We know that 7 times 10 equals 70, which is very close to 63.
• Since 63 is slightly less than 70, the answer will be a bit less than 10.

Practical Estimation:

• 7 * 9 = 63 (Which matches the precise answer)
• But if you're dividing a number like 75 by 7:
  • 7 * 10 = 70, so you know it's just over 10.

<p class="pro-note">💡 Pro Tip: Estimation can be your ally when doing quick mental calculations. Remember, the closer the dividend is to an easily divisible multiple, the more accurate your estimation will be.</p>

Trick 2: Check for Divisibility

Divisibility rules can significantly simplify division processes. Here are some basic ones to keep in mind:

• By 2: If a number ends in 0, 2, 4, 6, or 8, it's divisible by 2.
• By 3: If the sum of the digits is divisible by 3, then so is the number.
• By 5: If a number ends in 0 or 5, it's divisible by 5.
• By 7: No simple rule, but you can try halving and using the rule of 3.

Example Application:

Checking divisibility of 63 by 7:

• The sum of digits (6+3) equals 9, which isn't divisible by 7, but we know from our estimation that it works.

Trick 3: Use the Long Division Method

If mental tricks or estimation don't work, the classic long division method is always reliable:

• Write down the dividend (63) with the divisor (7) to the left.
• Determine how many times 7 fits into the first digit (6).
• 7 goes into 6 only once with a remainder. So write down 1 as the first digit of the quotient.
• Multiply 7 by 1, which equals 7, subtract from 6 (remainder 0), bring down the next digit (3).
• 7 goes into 30 four times (7 * 4 = 28, so 30 - 28 = 2). Write down 4 as the next digit of the quotient.

You now have your answer: 63 ÷ 7 = 9 with a remainder of 2.

Trick 4: Factorization

Finding common factors can make division much simpler:

Example:

• To divide 63 by 7:
  • Find common factors. Both numbers can be divided by 7.
  • 63 ÷ 7 = 9

Advanced Techniques:

• Prime Factorization: Break down both numbers into their prime factors, then divide the matching factors.
• Canceling: If both numbers have common factors, you can cancel them out first.

63 = 7 x 3 x 3
 7 = 7

Divide both by 7 to simplify:

= 3 x 3
= 9

Trick 5: The Cross-Multiplication Method for Dividing Fractions

When dividing fractions, you can use the cross-multiplication method:

• 63 ÷ 7 can be seen as dividing 63/1 by 7/1:
  • Flip the divisor (7/1) to 1/7 (as you do when dividing by a fraction).
  • Multiply the numerators (63 * 1) and the denominators (1 * 7) respectively.
  • Simplify if needed:

    63 / 7 = 63/7 = 9
  

<p class="pro-note">🧠 Pro Tip: For more advanced division scenarios, like fractions, remember that division is just multiplying by the reciprocal of the divisor. This mindset can simplify even the most complex divisions.</p>

Wrapping Up

Understanding division, whether you're splitting a pizza among friends or calculating ratios in a recipe, is fundamental. By learning these five tricks, you not only become quicker at doing mental math but also gain confidence in tackling more complex mathematical problems.

In the world of numbers, division isn't just about finding answers but understanding the relationships between values. Practice these methods, and soon you'll find division not only a necessary skill but an enjoyable challenge.

Don't stop here; explore related math tutorials to enhance your number skills even further. With practice and these techniques, you'll be a division pro in no time!

<p class="pro-note">🔍 Pro Tip: For an extra edge in your learning, dive into real-life applications of these division tricks. They're not only math problems but also problem-solving tools in daily life.</p>

<div class="faq-section"> <div class="faq-container"> <div class="faq-item"> <div class="faq-question"> <h3>Why use estimation for division?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>Estimation allows for quick mental calculations, helping you gauge approximate results without performing exact computations. This is especially useful in everyday situations where an exact number isn't necessary.</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>How can I make long division easier?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>Long division can be made simpler by understanding number patterns, practicing regularly, and breaking the problem down step-by-step. Also, using estimation to check your answers can help ensure accuracy.</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>Can these division tricks be applied to larger numbers?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>Absolutely! These tricks, especially factorization and divisibility rules, can be scaled up to handle larger numbers, making the division process much more manageable.</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>What if I need to divide by a fraction?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>Remember to flip the divisor fraction (reciprocate it) and then multiply. For instance, to divide by 3/4, you multiply by 4/3.</p> </div> </div> </div> </div>