use the properties of operations and rules for multiplying and dividing to solve: (-3) divided by (3/4) x (2/7) x (-5/16) divided by (5/7)
To solve the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7), let's follow the order of operations and simplify step by step:
Step 1: Simplify the multiplication and division within the expression starting from left to right.
Starting with the first set of parentheses:
(-3) ÷ (3/4) = (-3) × (4/3) = -12/3 = -4
Next set of parentheses:
(-4) × (2/7) = -8/7
Now, let's simplify the division:
-8/7 ÷ (5/16) = -8/7 × (16/5) = -128/35
Lastly:
-128/35 ÷ (5/7) = -128/35 × (7/5) = -896/175
Therefore, the simplified expression is -896/175.
To solve the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7), we can start by simplifying each fraction individually.
First, let's simplify (-3) ÷ (3/4):
We can rewrite this expression as (-3) × (4/3) since division is the same as multiplying by the reciprocal of the divisor.
Now, multiplying these two values (-3) × (4/3) gives us -12/3, which simplifies to -4.
Next, let's simplify (-5/16) ÷ (5/7):
Similarly, we can rewrite this expression as (-5/16) × (7/5).
Multiplying these two values (-5/16) × (7/5) gives us -35/80, which can be further simplified.
By dividing both the numerator and denominator by 5, we get -7/16.
Finally, we have -4 × (2/7) × (-7/16):
We can multiply these fractions together directly, without simplifying further:
(-4) × (2/7) × (-7/16) = (-8/7) × (-7/16).
When we multiply two negative numbers together, the result is positive.
So, (-8/7) × (-7/16) = 8/7 × 7/16.
Now, we can cancel out common factors:
8/7 × 7/16 = (8/1 × 1/7) × (1/1 × 1/16) = 8/112.
Lastly, we can simplify the resulting fraction:
8/112 can be reduced by dividing both the numerator and denominator by 8, resulting in 1/14.
Therefore, the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) simplifies to 1/14.
To solve the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7), we can simplify it step by step using the properties of operations and the rules for multiplying and dividing fractions.
Step 1: Start with the division operation: (-3) ÷ (3/4)
To divide a number by a fraction, we multiply the numerator by the reciprocal of the fraction. The reciprocal of (3/4) is (4/3).
So, (-3) ÷ (3/4) is the same as (-3) × (4/3).
Step 2: Simplify the multiplication: (-3) × (4/3)
Multiply the numerators and denominators: (-3) × 4 = -12, and 1 × 3 = 3.
Therefore, (-3) × (4/3) is equal to -12/3 or -4.
Step 3: Continue with the multiplication: -4 × (2/7) × (-5/16)
Multiply the numerators together and the denominators together: -4 × 2 × (-5) = 40.
And multiply the denominators: 7 × 16 = 112.
So, -4 × (2/7) × (-5/16) is equal to 40/112.
Step 4: Simplify the final division: 40/112 ÷ (5/7)
To divide a fraction by another fraction, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of (5/7) is (7/5).
So, 40/112 ÷ (5/7) is the same as 40/112 × (7/5).
Step 5: Simplify the multiplication: 40/112 × (7/5)
Multiply the numerators and denominators together: 40 × 7 = 280, and 112 × 5 = 560.
Therefore, 40/112 × (7/5) is equal to 280/560, which can be simplified to 1/2.
Therefore, the solution to the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) is 1/2.