When it comes to dividing fractions, many people find it challenging to understand the concept and perform the calculations. However, with a clear understanding of the rules and procedures, dividing fractions can be made easier. In this article, we will explore the concept of dividing fractions, specifically the problem 7/9 ÷ 7/2, and provide a step-by-step guide on how to simplify it.
What is dividing fractions?
Dividing fractions is the process of splitting a fraction into equal parts or groups. It is the opposite operation of multiplying fractions. When dividing fractions, we are essentially finding how many times one fraction fits into another.
How to divide fractions
To divide fractions, we need to follow a simple rule: invert the second fraction (i.e., flip the numerator and denominator) and then multiply. This rule is based on the concept of multiplying by the reciprocal of the second fraction.
Step-by-step guide to simplifying 7/9 ÷ 7/2
Now, let's apply the rule to simplify the problem 7/9 ÷ 7/2.
Step 1: Invert the second fraction
In this step, we invert the second fraction 7/2 by flipping the numerator and denominator, resulting in 2/7.
Step 2: Multiply the fractions
Now, we multiply the first fraction 7/9 by the inverted second fraction 2/7.
Multiply the numerators and denominators
Multiplying the numerators (7 × 2) gives us 14, and multiplying the denominators (9 × 7) gives us 63.
Step 3: Simplify the result
The resulting fraction is 14/63. To simplify this fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator.
Find the GCD of 14 and 63
The GCD of 14 and 63 is 7.
Divide both numerator and denominator by the GCD
Dividing both the numerator (14) and denominator (63) by 7 gives us 2/9.
Simplified answer
Therefore, the simplified answer to the problem 7/9 ÷ 7/2 is 2/9.
Gallery of Dividing Fractions
FAQs
What is the rule for dividing fractions?
+The rule for dividing fractions is to invert the second fraction (i.e., flip the numerator and denominator) and then multiply.
How do I simplify a fraction?
+To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator and divide both by the GCD.
What is the greatest common divisor (GCD)?
+The greatest common divisor (GCD) is the largest number that divides both the numerator and denominator of a fraction without leaving a remainder.
Conclusion
In conclusion, dividing fractions can be made easier by following the simple rule of inverting the second fraction and multiplying. By applying this rule and simplifying the result, we can find the answer to complex fraction division problems like 7/9 ÷ 7/2. We hope this article has helped you understand the concept of dividing fractions and provided you with a step-by-step guide on how to simplify them.
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