Simplify The Expression: 7/1 × 2/21
Introduction
In mathematics, simplifying expressions is an essential skill that helps us solve problems efficiently and accurately. When dealing with fractions, we often need to multiply or divide them, which can lead to complex expressions. In this article, we will focus on simplifying the expression 7/1 × 2/21 using various mathematical techniques.
Understanding the Expression
The given expression is 7/1 × 2/21. To simplify this expression, we need to understand the rules of fraction multiplication. When multiplying fractions, we multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom).
Fraction Multiplication Rules
To multiply fractions, we follow these simple rules:
- Multiply the numerators: 7 × 2 = 14
- Multiply the denominators: 1 × 21 = 21
Simplifying the Expression
Now that we have multiplied the numerators and denominators, we can simplify the expression by dividing the numerator by the denominator. However, in this case, we can simplify the expression further by canceling out common factors.
Canceling Out Common Factors
To cancel out common factors, we need to find the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD of 14 and 21 is 7.
Simplifying the Expression Using GCD
Now that we have found the GCD, we can simplify the expression by dividing both the numerator and the denominator by the GCD.
- Numerator: 14 ÷ 7 = 2
- Denominator: 21 ÷ 7 = 3
Final Simplified Expression
After simplifying the expression using the GCD, we get:
2/3
Conclusion
In this article, we simplified the expression 7/1 × 2/21 using fraction multiplication rules and canceling out common factors. We found the GCD of the numerator and the denominator and used it to simplify the expression. The final simplified expression is 2/3.
Frequently Asked Questions
- Q: What is the rule for multiplying fractions? A: To multiply fractions, we multiply the numerators and multiply the denominators.
- Q: How do we simplify an expression using the GCD? A: We divide both the numerator and the denominator by the GCD.
- Q: What is the final simplified expression for 7/1 × 2/21? A: The final simplified expression is 2/3.
Additional Resources
- For more information on fraction multiplication, visit Math is Fun.
- For more information on canceling out common factors, visit [Khan Academy](https://www.khanacademy.org/math/algebra/x2f6b7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7ff7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f77f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7
Introduction
In our previous article, we simplified the expression 7/1 × 2/21 using fraction multiplication rules and canceling out common factors. We found the greatest common divisor (GCD) of the numerator and the denominator and used it to simplify the expression. In this article, we will answer some frequently asked questions related to simplifying expressions.
Q&A
Q: What is the rule for multiplying fractions?
A: To multiply fractions, we multiply the numerators and multiply the denominators.
Q: How do we simplify an expression using the GCD?
A: We divide both the numerator and the denominator by the GCD.
Q: What is the final simplified expression for 7/1 × 2/21?
A: The final simplified expression is 2/3.
Q: Can we simplify expressions with different denominators?
A: Yes, we can simplify expressions with different denominators by finding the least common multiple (LCM) of the denominators.
Q: How do we find the LCM of two numbers?
A: To find the LCM of two numbers, we list the multiples of each number and find the smallest multiple that is common to both.
Q: Can we simplify expressions with negative numbers?
A: Yes, we can simplify expressions with negative numbers by following the same rules as for positive numbers.
Q: How do we simplify expressions with variables?
A: To simplify expressions with variables, we follow the same rules as for numerical expressions.
Q: Can we simplify expressions with fractions and decimals?
A: Yes, we can simplify expressions with fractions and decimals by converting the decimals to fractions and then simplifying.
Q: How do we simplify expressions with exponents?
A: To simplify expressions with exponents, we follow the rules of exponentiation, such as multiplying exponents with the same base.
Q: Can we simplify expressions with radicals?
A: Yes, we can simplify expressions with radicals by following the rules of radical arithmetic.
Q: How do we simplify expressions with absolute values?
A: To simplify expressions with absolute values, we follow the rules of absolute value arithmetic.
Conclusion
In this article, we answered some frequently asked questions related to simplifying expressions. We covered topics such as multiplying fractions, simplifying expressions using the GCD, and simplifying expressions with different denominators, negative numbers, variables, fractions and decimals, exponents, radicals, and absolute values.
Additional Resources
- For more information on fraction multiplication, visit Math is Fun.
- For more information on canceling out common factors, visit [Khan Academy](https://www.khanacademy.org/math/algebra/x2f6b7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7fff7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f77f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7f7