Use the properties of operations and rules for multiplying and dividing to solve: (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7)
??????
To solve this expression, we should follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
First, we have the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7).
Let's simplify the division first:
(-3) ÷ (3/4) = (-3) × (4/3) = -12/3 = -4
Next, let's multiply the remaining numbers:
-4 × (2/7) × (-5/16) = (-4) × (2/7) × (-5/16)
Multiplying the numerators and denominators separately:
= (-4 * 2) / (7 * 16) * (-5)
= (-8/112) * (-5)
= 40/112
Finally, divide this result by (5/7):
(40/112) ÷ (5/7) = (40/112) * (7/5)
Multiplying the numerators and denominators separately:
= (40 * 7) / (112 * 5)
= 280/560
= 1/2
Therefore, the simplified expression is 1/2.
Use the properties of operations and rules for multiplying and dividing to solve: (8/9) x (-3/4) ÷ (1/9) x (-4/5) ÷ (3/5)
To solve this expression, we need to follow the order of operations:
First, we have the expression (8/9) x (-3/4) ÷ (1/9) x (-4/5) ÷ (3/5).
Let's simplify the multiplication first:
(8/9) x (-3/4) = (8 x -3) / (9 x 4) = -24/36 = -2/3
Next, let's divide by (1/9):
(-2/3) ÷ (1/9) = (-2/3) x (9/1)
Multiplying the numerators and denominators separately:
= (-2 x 9) / (3 x 1) = -18/3 = -6
Now, let's divide by (-4/5):
-6 ÷ (-4/5) = -6 x (5/-4)
Multiplying the numerators and denominators separately:
= (-6 x 5) / (-4 x 1) = -30/-4 = 15/2
Lastly, let's divide by (3/5):
(15/2) ÷ (3/5) = (15/2) x (5/3)
Multiplying the numerators and denominators separately:
= (15 x 5) / (2 x 3) = 75/6 = 25/2
Therefore, the simplified expression is 25/2.
u sure?
Apologies for the mistake in my previous response. Let's correct it:
To solve the expression (8/9) x (-3/4) ÷ (1/9) x (-4/5) ÷ (3/5), we need to follow the order of operations:
First, let's simplify the multiplication:
(8/9) x (-3/4) = (8 x -3) / (9 x 4) = -24/36 = -2/3
Next, let's simplify the division:
(-2/3) ÷ (1/9) = (-2/3) x (9/1) = -2/3 x 9/1 = -18/3 = -6
Now let's continue with the next division:
-6 x (-4/5) = -6 x (-4/5) = 24/5
Finally, let's divide by (3/5):
24/5 ÷ (3/5) = 24/5 x 5/3 = 24/3 = 8
Therefore, the simplified expression is 8.
Use the properties of operations and rules for multiplying and dividing to solve: (-3/5) x (5/16) x (7/12) ÷ (-3/16) x (-5/7)
To solve the expression (-3/5) x (5/16) x (7/12) ÷ (-3/16) x (-5/7), we will follow the order of operations:
First, let's simplify the multiplication:
(-3/5) x (5/16) x (7/12) = (-3 x 5 x 7) / (5 x 16 x 12)
Simplifying the numerator and denominator separately:
= -105 / 960
Next, let's simplify the division:
(-105 / 960) ÷ (-3/16) = (-105 / 960) x (16 / -3)
Multiplying the numerators and denominators separately:
= (-105 x 16) / (960 x -3)
Simplifying the numerator and denominator:
= -1680 / -2880
Since there is a negative sign in both the numerator and denominator, they cancel each other out.
= 1680 / 2880
Dividing the numerator and denominator by 240:
= 7 / 12
Finally, let's divide by (-5/7):
(7/12) ÷ (-5/7) = (7/12) x (-7/5)
Multiplying the numerators and denominators separately:
= (7 x -7) / (12 x 5)
= -49 / 60
Therefore, the simplified expression is -49/60.
r u sure
Apologies for the mistake in my previous response. Let's correct it:
To solve the expression (-3/5) x (5/16) x (7/12) ÷ (-3/16) x (-5/7), we will follow the order of operations:
First, let's simplify the multiplication:
(-3/5) x (5/16) x (7/12) = -3/5 * 5/16 * 7/12
Multiplying the numerators and denominators separately:
= (-3 * 5 * 7) / (5 * 16 * 12)
= -105/960
Next, let's simplify the division:
(-105/960) ÷ (-3/16) = -105/960 * 16/-3
Multiplying the numerators and denominators separately:
= (-105 * 16) / (960 * -3)
= -1680/-2880
Since there is a negative sign in both the numerator and denominator, they cancel each other out:
= 1680/2880
Now, let's simplify the next division:
1680/2880 ÷ (-5/7) = 1680/2880 * 7/-5
Multiplying the numerators and denominators separately:
= (1680 * 7) / (2880 * -5)
= 11760/-14400
Since there is a common factor of 240 in both the numerator and denominator, we can simplify the fraction:
= 49/60
Therefore, the simplified expression is 49/60.