Use the properties of operations and rules for multiplying and dividing to solve:
(−3)÷(3/4)×(2/7)×(−5/16)÷(5/7). Show your work.
To solve this expression, we'll need to simplify the multiplication and division as we go along.
First, let's start with the multiplication: (-3) * (2/7) * (-5/16).
To simplify this, we multiply the numerators together (-3 * 2 * -5) and the denominators together (7 * 16):
(-3 * 2 * -5) / (7 * 16) = 30 / 1120.
Next, let's move on to the division: (30/1120) / (5/7).
To divide, we multiply the first fraction by the reciprocal of the second fraction:
(30/1120) * (7/5).
Next, we simplify this multiplication:
(30 * 7) / (1120 * 5) = 210 / 5600.
Finally, let's simplify the fraction 210/5600. Both the numerator and denominator can be divided by 10:
(21/560) / (56/560) = 21/56.
So the final result is 21/56.
The answer needs to be a whole number.
Apologies for the mistake. Let's start over and solve the expression correctly.
(-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7)
First, let's simplify the division (-3) ÷ (3/4):
(-3) ÷ (3/4) = (-3) × (4/3) = -12/3 = -4
Now, let's simplify the remaining multiplication:
-4 × (2/7) × (-5/16) ÷ (5/7)
= -4 × 2/7 × -5/16 ÷ 5/7
= -4 × -5/7 × 2/16 ÷ 5/7
= 20/7 × 2/16 ÷ 5/7
Now, let's simplify the division:
20/7 × 2/16 ÷ 5/7 = 20/7 × 2/16 × 7/5
= 20/7 × 1/8 × 7/5
= (20 × 1 × 7) / (7 × 8 × 5)
= 20/8 = 10/4 = 5/2
So, the simplified expression is 5/2.
To solve the expression (-3)÷(3/4)×(2/7)×(-5/16)÷(5/7), we need to simplify each operation step by step. Let's break it down:
Step 1: Simplify the division (-3) ÷ (3/4):
To divide by a fraction, we can multiply by the reciprocal of the fraction. Thus, (-3) ÷ (3/4) can be rewritten as:
(-3) × (4/3)
Step 2: Simplify the multiplication (-3) × (4/3):
Multiplying a number by a fraction is the same as multiplying the number by the numerator and dividing it by the denominator. Thus, (-3) × (4/3) can be calculated as:
(-3) × 4 / 3
Step 3: Calculate (-3) × 4:
(-3) × 4 equals -12. So, we have:
-12 / 3
Step 4: Simplify -12/3:
Dividing a number by another number is the same as multiplying by its reciprocal. Therefore, -12/3 can be simplified as:
(-12) × (1/3)
Step 5: Calculate -12 × (1/3):
Multiplying -12 by 1/3 gives us:
-12 × 1 / 3
Step 6: Calculate -12 × 1:
-12 × 1 equals -12. So, we have:
-12 / 3
Step 7: Simplify -12/3:
Dividing -12 by 3 gives us:
-12 ÷ 3
Step 8: Calculate -12 ÷ 3:
-12 ÷ 3 equals -4.
Now we move on to the next part of the expression: (-4) × (2/7) × (-5/16) ÷ (5/7).
Step 9: Simplify the multiplication (-4) × (2/7):
Multiplying -4 by 2/7 gives us:
-4 × 2 / 7
Step 10: Calculate -4 × 2:
-4 × 2 equals -8. So, we have:
-8 / 7
Step 11: Simplify -8/7:
Dividing -8 by 7 gives us:
-8 ÷ 7
Finally, we multiply the result by (-5/16) ÷ (5/7):
Step 12: Simplify the division (-5/16) ÷ (5/7):
To divide by a fraction, we can multiply by its reciprocal. So, (-5/16) ÷ (5/7) can be written as:
(-5/16) × (7/5)
Step 13: Calculate (-5/16) × (7/5):
Multiplying a fraction by another fraction is done by multiplying the numerators and denominators separately. Thus, (-5/16) × (7/5) can be calculated as:
(-5) × (7) / (16) × (5)
Step 14: Calculate (-5) × (7):
(-5) × (7) equals -35. So, we have:
-35 / (16) × (5)
Step 15: Calculate (16) × (5):
(16) × (5) equals 80. So, we have:
-35 / 80
Step 16: Simplify -35/80:
Dividing -35 by 80 gives us:
-35 ÷ 80
Step 17: Calculate -35 ÷ 80:
-35 ÷ 80 can be simplified further, but since there are no common factors between the numerator and the denominator, we cannot simplify it any further.
Therefore, the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) simplifies to -35/80.