Simplify The Expression:${ 5 \div 1 \frac{7}{9} }$
Introduction
When dealing with mathematical expressions, it's essential to understand the order of operations and how to simplify complex fractions. In this article, we will focus on simplifying the expression 5 ÷ 1 7/9. We will break down the steps involved in simplifying this expression and provide a clear understanding of the mathematical concepts used.
Understanding the Expression
The given expression is 5 ÷ 1 7/9. To simplify this expression, we need to understand the concept of dividing by a mixed number. A mixed number is a combination of a whole number and a fraction. In this case, 1 7/9 is a mixed number where 1 is the whole number and 7/9 is the fraction.
Converting the Mixed Number to an Improper Fraction
To simplify the expression, we need to convert the mixed number 1 7/9 to an improper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. We then write the result as the new numerator over the denominator.
In this case, we multiply 1 by 9 and add 7 to get 16. So, the mixed number 1 7/9 is equivalent to the improper fraction 16/9.
Simplifying the Expression
Now that we have converted the mixed number to an improper fraction, we can simplify the expression 5 ÷ 16/9. To divide by a fraction, we multiply by the reciprocal of the fraction. The reciprocal of 16/9 is 9/16.
So, we can rewrite the expression as 5 × 9/16. To simplify this expression, we multiply the numerator 5 by 9 to get 45. The denominator remains the same, which is 16.
Final Answer
Therefore, the simplified expression is 45/16.
Conclusion
In this article, we simplified the expression 5 ÷ 1 7/9 by converting the mixed number to an improper fraction and then dividing by the fraction. We used the concept of multiplying by the reciprocal of a fraction to simplify the expression. The final answer is 45/16.
Frequently Asked Questions
- What is the order of operations when dealing with mathematical expressions?
- How do you convert a mixed number to an improper fraction?
- What is the concept of dividing by a fraction?
- How do you simplify an expression involving a mixed number and a fraction?
Step-by-Step Solution
- Convert the mixed number 1 7/9 to an improper fraction.
- Rewrite the expression 5 ÷ 16/9 as 5 × 9/16.
- Multiply the numerator 5 by 9 to get 45.
- The denominator remains the same, which is 16.
- The simplified expression is 45/16.
Additional Resources
- Khan Academy: Dividing Fractions
- Mathway: Simplifying Expressions
- IXL: Dividing Fractions
Final Answer
The final answer is 45/16.
Introduction
In our previous article, we simplified the expression 5 ÷ 1 7/9 by converting the mixed number to an improper fraction and then dividing by the fraction. We used the concept of multiplying by the reciprocal of a fraction to simplify the expression. In this article, we will answer some frequently asked questions related to simplifying expressions involving mixed numbers and fractions.
Q&A
Q: What is the order of operations when dealing with mathematical expressions?
A: The order of operations when dealing with mathematical expressions is:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do you convert a mixed number to an improper fraction?
A: To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and add the numerator. You then write the result as the new numerator over the denominator.
For example, to convert the mixed number 1 7/9 to an improper fraction, you multiply 1 by 9 and add 7 to get 16. So, the mixed number 1 7/9 is equivalent to the improper fraction 16/9.
Q: What is the concept of dividing by a fraction?
A: When you divide by a fraction, you are essentially multiplying by the reciprocal of the fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
For example, to divide 5 by 16/9, you multiply 5 by the reciprocal of 16/9, which is 9/16.
Q: How do you simplify an expression involving a mixed number and a fraction?
A: To simplify an expression involving a mixed number and a fraction, you need to follow these steps:
- Convert the mixed number to an improper fraction.
- Rewrite the expression using the improper fraction.
- Multiply by the reciprocal of the fraction.
- Simplify the resulting expression.
Q: What is the difference between a mixed number and an improper fraction?
A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator.
For example, 1 7/9 is a mixed number, while 16/9 is an improper fraction.
Q: How do you add and subtract fractions with different denominators?
A: To add or subtract fractions with different denominators, you need to find the least common multiple (LCM) of the denominators. You then convert each fraction to have the LCM as the denominator. Finally, you add or subtract the numerators and keep the same denominator.
Q: What is the concept of equivalent fractions?
A: Equivalent fractions are fractions that have the same value, but different numerators and denominators. For example, 1/2 and 2/4 are equivalent fractions.
Q: How do you compare fractions with different denominators?
A: To compare fractions with different denominators, you need to find the least common multiple (LCM) of the denominators. You then convert each fraction to have the LCM as the denominator. Finally, you compare the numerators.
Conclusion
In this article, we answered some frequently asked questions related to simplifying expressions involving mixed numbers and fractions. We covered topics such as the order of operations, converting mixed numbers to improper fractions, dividing by fractions, and comparing fractions with different denominators.
Frequently Asked Questions
- What is the order of operations when dealing with mathematical expressions?
- How do you convert a mixed number to an improper fraction?
- What is the concept of dividing by a fraction?
- How do you simplify an expression involving a mixed number and a fraction?
- What is the difference between a mixed number and an improper fraction?
- How do you add and subtract fractions with different denominators?
- What is the concept of equivalent fractions?
- How do you compare fractions with different denominators?
Step-by-Step Solution
- Convert the mixed number to an improper fraction.
- Rewrite the expression using the improper fraction.
- Multiply by the reciprocal of the fraction.
- Simplify the resulting expression.
Additional Resources
- Khan Academy: Dividing Fractions
- Mathway: Simplifying Expressions
- IXL: Dividing Fractions
Final Answer
The final answer is 45/16.