Simplify the expression.
the expression negative three fifths times k minus 9 plus the expression 6 plus one fourth times k
negative 7 over 20 times k plus negative 3
7 over 20 times k plus negative 3
negative 2 over 9 times k plus negative 15
negative 17 over 20 times k plus negative 15
The simplified expression is:
negative 17 over 20 times k plus negative 15
To simplify the given expression, let's break it down step by step:
1. Start with the expression "negative three fifths times k minus 9."
To multiply a number by a fraction, multiply the number by the numerator and then divide by the denominator. So, multiplying "-3" by "k" and dividing the result by "5" gives you: "(-3k)/5"
Next, subtract 9 from the previous result: "(-3k)/5 - 9"
2. Now, let's simplify the second expression: "6 plus one fourth times k."
First, multiply "1/4" by "k," which gives you "(k/4)."
Next, add 6 to the previous result: "(k/4) + 6"
3. Combine both expressions: "(-3k)/5 - 9 + (k/4) + 6"
4. To add or subtract fractions, they should have a common denominator. To find a common denominator, we need to find the least common multiple (LCM) of 4 and 5, which is 20.
5. Now, we can rewrite the expression with a common denominator:
(-3k)/5 - 9 + (k/4) + 6 = (-12k)/20 - 180/20 + 5k/20 + 120/20
6. Combine the like terms:
(-12k + 5k - 180 + 120)/20 = (-7k - 60)/20
So, the simplified expression is "(-7k - 60)/20."
To simplify the expression, we will combine like terms and perform any necessary operations.
The expression is:
(-3/5 * k) - 9 + (6 + 1/4 * k)
First, let's focus on the terms involving k. The two terms are (-3/5 * k) and (1/4 * k). To combine these terms, we need to find a common denominator.
The common denominator of 5 and 4 is 20. Therefore, we can rewrite the expression as:
(-12/20 * k) - 9 + (6 + 5/20 * k)
Now, let's simplify these terms:
(-12/20 * k) = -12k/20 = -3k/5
(5/20 * k) = 5k/20 = k/4
The expression now becomes:
(-3k/5) - 9 + (6 + k/4)
Next, let's combine the constant terms:
-9 + 6 = -3
Now, our expression becomes:
(-3k/5) - 3 + k/4
To simplify further, let's find a common denominator for the terms involving k. The common denominator of 5 and 4 is 20.
(-3k/5) = (-12k/20)
(k/4) = (5k/20)
Therefore, the expression can be rewritten as:
(-12k/20) - 3 + (5k/20)
Now, we can combine these terms:
(-12k/20) + (5k/20) = (-12k + 5k)/20 = -7k/20
The expression is now:
-7k/20 - 3
So, the simplified expression is:
-7k/20 - 3