Use the properties of operations and rules for multiplying and dividing to solve:
(-3) ÷ (3/4) x (2/7) x (- 5/16) ÷ (5/7)
To solve the expression (-3) ÷ (3/4) x (2/7) x (-5/16) ÷ (5/7), we can follow the order of operations, which states that we should solve any operations inside parentheses first, then perform any multiplications or divisions from left to right, and finally, perform any additions or subtractions from left to right.
First, we have (-3) ÷ (3/4). To divide by a fraction, we can multiply by its reciprocal (flipping the numerator and denominator). So, we have:
(-3) ÷ (3/4) = (-3) x (4/3)
Next, we have (-3) x (4/3). Multiplying a negative number by a positive number gives a negative answer, so we have:
(-3) x (4/3) = -12/3
Now, we simplify -12/3. Since both -12 and 3 are divisible by 3, we can reduce the fraction:
-12/3 = -4/1 = -4
Next, we have -4 x (2/7). To multiply fractions, we multiply the numerators together and the denominators together. So, we have:
-4 x (2/7) = (-4 x 2) / 7 = -8/7
Now, we have -8/7 x (-5/16). When multiplying two negative fractions together, the result is positive. So, we have:
-8/7 x (-5/16) = 8/7 x 5/16 = (8 x 5) / (7 x 16) = 40/112
Finally, we have 40/112 ÷ (5/7). To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So, we have:
40/112 ÷ (5/7) = 40/112 x (7/5) = (40 x 7) / (112 x 5) = 280/560
Now, we simplify 280/560. Both 280 and 560 are divisible by 280, so we have:
280/560 = 1/2
Therefore, (-3) ÷ (3/4) x (2/7) x (-5/16) ÷ (5/7) = 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 the expression (8/9) x (-3/4) ÷ (1/9) x (-4/5) ÷ (3/5), we can follow the order of operations, which states that we should solve any operations inside parentheses first, then perform any multiplications or divisions from left to right, and finally, perform any additions or subtractions from left to right.
First, we have (8/9) x (-3/4). To multiply two fractions, we multiply the numerators together and the denominators together. So, we have:
(8/9) x (-3/4) = (8 x -3) / (9 x 4) = (-24) / 36
Next, we have (-24) / 36. Since both -24 and 36 are divisible by 12, we can divide both numbers by 12 to simplify the fraction:
(-24) / 36 = (-2 x 12) / (3 x 12) = -2/3
Now, we have -2/3 ÷ (1/9). To divide by a fraction, we multiply by its reciprocal (flipping the numerator and denominator). So, we have:
-2/3 ÷ (1/9) = -2/3 x (9/1) = (-2 x 9) / (3 x 1) = -18/3
Next, we simplify -18/3. Since both -18 and 3 are divisible by 3, we can simplify the fraction:
-18/3 = -6/1 = -6
Now, we have -6 x (-4/5). Multiplying a negative number by a positive number gives a negative answer, so we have:
-6 x (-4/5) = -6 x (4/5) = (-6 x 4) / 5 = -24/5
Finally, we have -24/5 ÷ (3/5). Dividing by a fraction is the same as multiplying by its reciprocal. So, we have:
-24/5 ÷ (3/5) = -24/5 x (5/3) = (-24 x 5) / (5 x 3) = -120/15
Now, we simplify -120/15. Both -120 and 15 are divisible by 15, so we have:
-120/15 = (-8 x 15) / (1 x 15) = -8/1 = -8
Therefore, (8/9) x (-3/4) ÷ (1/9) x (-4/5) ÷ (3/5) = -8.
wrong
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 can follow the order of operations as before.
First, we perform the multiplications and divisions from left to right.
(-3/5) x (5/16) = (-3 x 5) / (5 x 16) = -15/80 = -3/16
Next, we have (-3/16) x (-5/7) = (-3 x -5) / (16 x 7) = 15/112
Now, we have (7/12) ÷ (15/112). To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
(7/12) ÷ (15/112) = (7/12) x (112/15) = (7 x 112) / (12 x 15) = 784/180 = 98/22 = 49/11
Therefore, (-3/5) x (5/16) x (7/12) ÷ (-3/16) x (-5/7) = 49/11.
incorrect
Apologies for the mistake. Let's go through the calculations again.
To solve (-3/5) x (5/16) x (7/12) ÷ (-3/16) x (-5/7), we'll apply the properties of operations and rules for multiplying and dividing in the correct order.
First, let's simplify (-3/5) x (5/16) x (7/12):
(-3/5) x (5/16) x (7/12) = (-3 x 5 x 7) / (5 x 16 x 12)
= (-3 x 7) / (16 x 12)
= -21 / (192)
= -7 / (64)
Next, let's simplify (-7/64) ÷ (-3/16) x (-5/7):
(-7/64) ÷ (-3/16) x (-5/7) = (-7/64) x (16/-3) x (-5/7)
= (7/64) x (16/3) x (5/7)
= (7 x 16 x 5) / (64 x 3 x 7)
= (560 / (1344) = 5/12
Therefore, a correct solution to the expression is (-3/5) x (5/16) x (7/12) ÷ (-3/16) x (-5/7) = 5/12.