can anyone simplify and multiply the rational expressions 10m/11p x 44p/20k x 15k/8m? and then explain it to me?
have patience.
Of course! To simplify and multiply the rational expressions, we can follow these steps:
Step 1: Simplify each rational expression separately.
- The expression 10m/11p is already simplified, so we leave it as it is.
- The expression 44p/20k can be simplified by canceling out any common factors between the numerator and denominator. In this case, both 44 and 20 are divisible by 4. Also, both p and k do not have any common factors with the numerator or denominator. So, we simplify it to 11p/5k.
- The expression 15k/8m can be simplified by canceling out any common factors between the numerator and denominator. In this case, both 15 and 8 are divisible by 1. Also, both k and m do not have any common factors with the numerator or denominator. So, we simplify it to 15k/8m.
Now, we have the simplified forms of each expression:
10m/11p, 11p/5k, and 15k/8m.
Step 2: Multiply the simplified expressions together.
To multiply rational expressions, we can multiply the numerators to get the new numerator, and multiply the denominators to get the new denominator.
Multiplying the numerators: (10m) * (11p) * (15k) = 1650mpk
Multiplying the denominators: (11p) * (5k) * (8m) = 440pkm
Therefore, the resulting expression is 1650mpk/440pkm.
Step 3: Simplify the resulting expression, if possible.
In this case, we can see that both the numerator and denominator have a common factor of 10. By canceling out this common factor, we simplify it further to:
165m/44km.
So, the simplified and multiplied form of the given rational expressions is 165m/44km.
Please note that simplifying rational expressions involves canceling out common factors. It is essential to check if there are any restrictions on the variables involved (such as variables being non-zero) to ensure the solution is valid.