7/12 Divided By 2/9 In Simplest Form

7/12 Divided by 2/9 in Simplest Form: A Comprehensive Guide

Dividing fractions can seem daunting at first, but with a clear understanding of the process, it becomes straightforward. This article will guide you through the step-by-step solution to dividing 7/12 by 2/9, explaining the underlying principles and offering additional tips for mastering fraction division. We'll also explore related concepts and provide practice problems to solidify your understanding.

Understanding Fraction Division

Before diving into the specific problem, let's review the fundamental concept of dividing fractions. The core principle is to invert the second fraction (the divisor) and then multiply. This is equivalent to finding out how many times the second fraction fits into the first.

The Formula:

a/b ÷ c/d = a/b × d/c

Where 'a', 'b', 'c', and 'd' represent numbers, and 'b' and 'c' are not zero (division by zero is undefined).

Solving 7/12 Divided by 2/9

Now, let's apply this knowledge to our problem: 7/12 ÷ 2/9.

Step 1: Invert the Second Fraction (the Divisor)

The second fraction, 2/9, becomes its reciprocal, 9/2.

Step 2: Multiply the Fractions

Now, we multiply the first fraction (7/12) by the inverted second fraction (9/2):

7/12 × 9/2

Step 3: Multiply the Numerators and the Denominators

Multiply the numerators together (7 × 9 = 63) and the denominators together (12 × 2 = 24):

63/24

Step 4: Simplify the Fraction

The fraction 63/24 is not in its simplest form. To simplify, we need to find the greatest common divisor (GCD) of 63 and 24. The GCD is the largest number that divides both 63 and 24 without leaving a remainder. In this case, the GCD is 3.

Divide both the numerator and the denominator by the GCD (3):

63 ÷ 3 = 21 24 ÷ 3 = 8

Therefore, the simplified fraction is 21/8.

Expressing the Answer as a Mixed Number

The fraction 21/8 is an improper fraction (the numerator is larger than the denominator). It's often helpful to express improper fractions as mixed numbers (a whole number and a proper fraction).

To convert 21/8 to a mixed number, we divide the numerator (21) by the denominator (8):

21 ÷ 8 = 2 with a remainder of 5

This means that 21/8 is equivalent to 2 5/8.

Alternative Method: Simplifying Before Multiplying

We can sometimes simplify the fractions before multiplying, making the calculation easier. This is done by canceling out common factors between the numerators and denominators.

Let's revisit the multiplication step:

7/12 × 9/2

Notice that 9 (in the numerator) and 12 (in the denominator) share a common factor of 3. We can simplify:

(7/12) × (9/2) = (7/(12÷3)) × ((9÷3)/2) = (7/4) × (3/2)

Now, multiply the simplified fractions:

(7/4) × (3/2) = 21/8

This gives us the same result as before, but the multiplication was simpler.

Practical Applications of Fraction Division

Understanding fraction division is crucial in various real-world scenarios:

• Cooking and Baking: Scaling recipes up or down requires dividing fractions.
• Sewing and Tailoring: Calculating fabric requirements often involves fraction division.
• Construction and Engineering: Precise measurements in construction rely heavily on fraction calculations.
• Finance and Budgeting: Dividing your budget into portions often involves fractions.

Further Practice Problems

To solidify your understanding, try these practice problems:

1. 5/6 ÷ 1/3
2. 3/4 ÷ 2/5
3. 1/2 ÷ 3/8
4. 9/10 ÷ 3/5
5. 2/7 ÷ 4/14

Remember to follow the steps outlined above: invert the second fraction, multiply, and simplify. You can also try simplifying before multiplying to make the calculations easier.

Conclusion

Dividing fractions might seem challenging at first, but by understanding the process of inverting and multiplying, and by practicing regularly, you'll quickly master this essential skill. Remember to always simplify your answer to its simplest form, and consider converting improper fractions to mixed numbers for easier interpretation. Mastering fraction division opens doors to a broader understanding of mathematical concepts and their practical applications in various fields. Keep practicing, and you'll become confident in handling fraction division problems. Remember, the key is to break down the problem into manageable steps and to always double-check your work.