Use the properties of operations and rules for multiplying and dividing to solve:
(−3/5)×(5 1/6)×(7 1/2)÷(−3 /16)×(−5/7)
To solve this expression, we can follow the order of operations and use the properties of operations and rules for multiplying and dividing.
First, let's simplify the expression step by step:
(-3/5) × (5 1/6) × (7 1/2) ÷ (-3/16) × (-5/7)
Step 1: Convert mixed numbers to improper fractions:
(5 1/6) = (6 × 5 + 1)/6 = 31/6
(7 1/2) = (2 × 7 + 1)/2 = 15/2
Our expression becomes:
(-3/5) × (31/6) × (15/2) ÷ (-3/16) × (-5/7)
Step 2: Simplify the multiplication and division from left to right:
(-3/5) × (31/6) = -93/30
(-93/30) × (15/2) = -1395/60
Now our expression becomes:
-1395/60 ÷ (-3/16) × (-5/7)
To divide fractions, we invert the divisor and multiply:
-1395/60 ÷ (-3/16) = (-1395/60) × (-16/3) = 23240/180
Now our expression becomes:
23240/180 × (-5/7)
Step 3: Multiply the fractions:
23240/180 × (-5/7) = (23240 × -5)/(180 × 7) = -116200/1260
Finally, simplify the fraction:
-116200/1260 = -580/6 = -290/3
Therefore, the solution to (-3/5)×(5 1/6)×(7 1/2)÷(-3/16)×(-5/7) is -290/3.
did you use PEMDAS
No, I did not specifically use PEMDAS in this case, as there were no parentheses, exponents, or radical symbols in the expression. Instead, I followed the order of operations by simplifying the expression from left to right, performing multiplication and division before addition and subtraction.
WELL ITS WRONG
Apologies for the mistake in my previous response. Let's solve the expression correctly using the order of operations.
(-3/5) × (5 1/6) × (7 1/2) ÷ (-3/16) × (-5/7)
First, let's convert the mixed numbers into improper fractions:
(5 1/6) = (6 × 5 + 1)/6 = 31/6
(7 1/2) = (2 × 7 + 1)/2 = 15/2
Now, the expression becomes:
(-3/5) × (31/6) × (15/2) ÷ (-3/16) × (-5/7)
Next, let's simplify the multiplication and division from left to right:
(-3/5) × (31/6) = -93/30
(-93/30) × (15/2) = -465/4
Now, the expression becomes:
-465/4 ÷ (-3/16) × (-5/7)
To divide fractions, we invert the divisor and multiply:
-465/4 ÷ (-3/16) = (-465/4) × (-16/3) = 23280/12
Now, the expression becomes:
23280/12 × (-5/7)
Next, multiply the fractions:
23280/12 × (-5/7) = (23280 × -5)/(12 × 7) = -116400/84
Finally, simplify the fraction:
-116400/84 = -1450/1 = -1450
Therefore, the correct solution to (-3/5) × (5 1/6) × (7 1/2) ÷ (-3/16) × (-5/7) is -1450.