To simplify the expression 1/5 * 3/4 * 4/5 using the commutative property, rearrange and group similar fractions, multiply numerators and denominators respectively, and simplify the result to get 3/25.
To simplify the expression 1/5 * 3/4 * 4/5 using the commutative property of multiplication, we can rearrange the terms in the expression. The commutative property allows us to multiply numbers in any order and still get the same result. In this case, we can group the similar fractions to make the calculation easier.
Here's how we can simplify the expression step by step:
- First, we will rearrange the terms: (1/5 * 4/5) * (3/4).
- Now, we multiply the numerators together and the denominators together for the terms (1/5 * 4/5): (1*4)/(5*5) = 4/25.
- Then, we multiply this result by the remaining fraction: (4/25) * (3/4).
- Again, we multiply the numerators together and the denominators together: (4*3)/(25*4) = 12/100.
- Lastly, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which in this case is 4: 12/100 = 3/25.
So, the simplified expression is 3/25.