Dividing Fractions: 7/9 ÷ 8/15 Made Easy
Table of Contents :
To divide fractions, one of the most effective methods is to multiply by the reciprocal of the divisor. In this article, we will explore how to divide the fractions ( \frac{7}{9} ) by ( \frac{8}{15} ) step-by-step, making the process easy to understand and follow.
Understanding the Division of Fractions
When dividing fractions, it can be a bit confusing at first, but the process can be simplified using the following steps:
- Find the reciprocal of the second fraction (the divisor).
- Change the division sign to multiplication.
- Multiply the numerators of the two fractions together.
- Multiply the denominators of the two fractions together.
- Simplify the resulting fraction if possible.
Let’s illustrate this with our specific example of ( \frac{7}{9} \div \frac{8}{15} ).
Step 1: Find the Reciprocal
The reciprocal of a fraction is obtained by swapping its numerator and denominator.
For the fraction ( \frac{8}{15} ):
- Reciprocal: ( \frac{15}{8} )
Step 2: Change the Division Sign to Multiplication
Now that we have the reciprocal, we can rewrite the division as multiplication:
[ \frac{7}{9} \div \frac{8}{15} = \frac{7}{9} \times \frac{15}{8} ]
Step 3: Multiply the Numerators
Next, we multiply the numerators (the top numbers of the fractions):
- ( 7 \times 15 = 105 )
Step 4: Multiply the Denominators
Now we multiply the denominators (the bottom numbers of the fractions):
- ( 9 \times 8 = 72 )
Putting it all together, we have:
[ \frac{7 \times 15}{9 \times 8} = \frac{105}{72} ]
Step 5: Simplify the Resulting Fraction
To simplify ( \frac{105}{72} ), we need to find the greatest common divisor (GCD) of the numerator and denominator.
- The factors of ( 105 ) are ( 1, 3, 5, 7, 15, 21, 35, 105 ).
- The factors of ( 72 ) are ( 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 ).
The common factors are ( 1 ) and ( 3 ), and the GCD is ( 3 ).
Now, we divide both the numerator and denominator by ( 3 ):
- Numerator: ( 105 \div 3 = 35 )
- Denominator: ( 72 \div 3 = 24 )
So, the simplified form of ( \frac{105}{72} ) is:
[ \frac{35}{24} ]
This fraction can also be expressed as a mixed number:
- ( 35 \div 24 = 1 ) remainder ( 11 ), which means ( 1 \frac{11}{24} ).
Summary
The final answer for ( \frac{7}{9} \div \frac{8}{15} ) is:
[ \frac{35}{24} \quad \text{or} \quad 1 \frac{11}{24} ]
Key Takeaways
- Division of fractions is easy once you know how to find the reciprocal and change the operation to multiplication.
- Always simplify your final answer to its lowest terms for clarity.
Now you have a step-by-step method for dividing fractions, and specifically, you can confidently say that dividing ( \frac{7}{9} ) by ( \frac{8}{15} ) is as straightforward as following these five simple steps! 🎉