what is 1/4(5y-3)+1/16(12y+17)?
Which group shows all the whole answer number factors of a composite number?
A. 1,2,3,4,5,8,16
B. 1,2,3,4,5,6,10,20
C. 1,2,3,4,6,8,12,24
D. 1,2,3,4,7,14,28
To evaluate the expression 1/4(5y-3)+1/16(12y+17), you need to follow the order of operations, which is also called the PEMDAS rule (Parentheses, Exponents, Multiplication and Division - from left to right, and Addition and Subtraction - from left to right).
Step 1: Distribute the fractions
First, distribute the 1/4 to (5y-3) and distribute the 1/16 to (12y+17).
(1/4) * (5y-3) + (1/16) * (12y+17)
Step 2: Simplify inside the parentheses
Multiply 1/4 by each term inside the first parentheses (5y and -3) and multiply 1/16 by each term inside the second parentheses (12y and 17).
(5y/4 - 3/4) + (12y/16 + 17/16)
Step 3: Simplify the fractions (if possible)
Next, you need to simplify the fractions. To do this, find the least common denominator (LCD), which in this case is 16. Multiply the numerator and the denominator of each fraction by the necessary factor to make the denominator 16.
For the first fraction, multiply the numerator and the denominator by 4, and for the second fraction, multiply them by 1.
(5y * 4/4 - 3 * 4/4) + (12y * 1/16 + 17 * 1/16)
(20y/16 - 12/16) + (12y/16 + 17/16)
Now that the fractions have a common denominator, you can combine like terms.
Step 4: Combine like terms
Add the terms with y's separately and the terms without y's separately.
(20y/16 + 12y/16) + (-12/16 + 17/16)
(32y/16) + (5/16)
(2y) + (5/16)
Therefore, 1/4(5y-3) + 1/16(12y+17) simplifies to (2y) + (5/16).