To simplify the expression “1 divided by 2⁄3”, we need to follow the order of operations (PEMDAS):
- Divide 2 by 3: 2⁄3 = 0.67
- Divide 1 by the result: 1 ÷ 0.67 = 1.5
So, 1 divided by 2⁄3 is equal to 1.5.
Alternatively, we can simplify the expression by multiplying 1 by the reciprocal of 2⁄3, which is 3⁄2:
1 ÷ (2⁄3) = 1 × (3⁄2) = 3⁄2 = 1.5
Either way, the result is the same: 1 divided by 2⁄3 is equal to 1.5.
Step-by-Step Explanation
The order of operations is crucial in simplifying mathematical expressions. In this case, we first need to simplify the fraction 2⁄3, which equals approximately 0.67. Then, we divide 1 by this result to get 1.5.
Alternative Method
We can also simplify the expression by using the reciprocal of 2⁄3, which is 3⁄2. By multiplying 1 by 3⁄2, we get 3⁄2, which is equal to 1.5. This method is often more straightforward and efficient.
| Method | Result |
|---|---|
| Divide 1 by 2/3 | 1.5 |
| Multiply 1 by 3/2 | 1.5 |
Key Points
- To simplify the expression "1 divided by 2/3", follow the order of operations (PEMDAS).
- First, divide 2 by 3 to get 0.67.
- Then, divide 1 by the result (0.67) to get 1.5.
- Alternatively, multiply 1 by the reciprocal of 2/3 (3/2) to get 1.5.
- Both methods yield the same result: 1 divided by 2/3 equals 1.5.
Understanding how to simplify expressions involving division by fractions is a fundamental skill in mathematics. By following the order of operations and using the reciprocal of fractions when necessary, you can efficiently simplify complex expressions and arrive at the correct solution.
What is the order of operations when simplifying expressions?
+The order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
How do you simplify an expression that involves division by a fraction?
+To simplify an expression that involves division by a fraction, you can either follow the order of operations or multiply by the reciprocal of the fraction. Both methods will yield the same result.
What is the reciprocal of a fraction?
+The reciprocal of a fraction is obtained by swapping its numerator and denominator. For example, the reciprocal of 2⁄3 is 3⁄2.
