Select all that justify the following statement.
2 * 1/2 = 1
What are your choices?
To justify the statement "2 * 1/2 = 1," we need to determine the mathematical rules or properties that support this equation. Here are the steps to explain the justification:
Step 1: Understanding Multiplication
To explain the multiplication of fractions, we need to recall the rule that multiplying two fractions involves multiplying the numerators (top numbers) and multiplying the denominators (bottom numbers).
Step 2: Multiplying the Fractions
In this equation, we have the fraction 2 * 1/2. Multiplying the numerators (2 * 1) gives us 2, and multiplying the denominators (2) gives us 2 as well.
Step 3: Simplifying the Fraction
To simplify a fraction, we divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 2 and 2 is also 2.
Step 4: Simplification Result
Dividing the numerator 2 by the GCD of 2 gives us 1, and dividing the denominator 2 by the GCD of 2 gives us 1.
Therefore, the fraction 2/2 simplifies to 1/1, which is equal to 1. So, all the justifications that apply to the statement "2 * 1/2 = 1" are:
- The rule of multiplying fractions
- The simplification of fractions.