Use the properties of operations and rules for multiplying and dividing to solve:
(−3)÷(3/4)×(2/7)×(−5/16)÷(5/7)
(1 point)
To solve the expression, we can simplify it step by step:
Step 1: Simplify the division (−3) ÷ (3/4)
To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 3/4 is 4/3.
So, (−3) ÷ (3/4) = (−3) × (4/3)
Multiplying -3 by 4 gives us -12, and multiplying 3 by 3 gives us 9.
Therefore, (−3) ÷ (3/4) = -12/9.
Step 2: Simplify the multiplication -12/9 × (2/7) × (−5/16) ÷ (5/7)
To multiply fractions, we multiply their numerators together and their denominators together. Similarly, to divide fractions, we multiply by the reciprocal of the second fraction.
So, -12/9 × (2/7) × (−5/16) ÷ (5/7) = (-12 × 2 × -5) / (9 × 7 × 16) × (7/5)
Multiplying -12 by 2 by -5 gives us 120, and multiplying 9 by 7 by 16 gives us 1008.
Therefore, -12/9 × (2/7) × (−5/16) ÷ (5/7) = 120/1008 × (7/5) = (12/84) × (7/5)
Step 3: Simplify the multiplication (12/84) × (7/5)
To simplify this multiplication, we can first simplify the fractions by cancelling out any common factors in their numerators and denominators.
The numerator 12 has a common factor of 4 with 84, and the denominator 84 has a common factor of 4 with 5.
So, (12/84) × (7/5) = (12/4) × (7/1) / (84/4) × (5/1)
Canceling out the common factor of 4 gives us:
(3/1) × (7/1) / (21/1) × (5/1)
Now, we can multiply the numerators and denominators directly:
(3 × 7) / (21 × 5)
This simplifies to:
21 / 105
So, the final answer is 21/105, which can be simplified further to 1/5.
To solve this expression, we can follow the order of operations (also known as PEMDAS) and simplifying as we go along. Here's the step-by-step process:
Step 1: Simplify the division operations first:
(−3) ÷ (3/4) = −3 × (4/3)
Step 2: Simplify the multiplication of fractions:
(4/3) × (2/7) × (−5/16) = (4 × 2 × −5) / (3 × 7 × 16)
Step 3: Simplify the division of fractions:
[(4 × 2 × −5) / (3 × 7 × 16)] ÷ (5/7) = [(4 × 2 × −5) / (3 × 7 × 16)] × (7/5)
Step 4: Perform the remaining multiplication:
[(4 × 2 × −5) × 7] / [(3 × 7 × 16) × 5]
Step 5: Multiply the numbers together:
[-40 × 7] / [336 × 5]
Step 6: Continue simplifying:
[-280] / [1680]
Step 7: Divide the numbers:
-280 ÷ 1680
Step 8: Simplify the division:
-1/6
Therefore, the solution is -1/6.
To solve the expression (−3)÷(3/4)×(2/7)×(−5/16)÷(5/7), we need to follow the properties and rules for multiplying and dividing fractions.
Step 1: Simplify the division within the expression.
To divide fractions, we multiply the first fraction by the reciprocal (or multiplicative inverse) of the second fraction.
(−3) ÷ (3/4) can be rewritten as (−3) × (4/3).
Step 2: Multiply the fractions together.
To multiply fractions, we simply multiply the numerators together and multiply the denominators together.
(−3) × (4/3) × (2/7) × (−5/16) ÷ (5/7) can be simplified to:
((-3) × 4 × 2 × (−5)) ÷ (3 × 7 × 16 × 5)
Step 3: Perform the arithmetic operations.
We multiply the numbers in the numerator and multiply the numbers in the denominator.
((-3) × 4 × 2 × (−5)) ÷ (3 × 7 × 16 × 5) can be calculated as:
((-3) × 4 × 2 × (−5)) ÷ (3 × 7 × 16 × 5) = (-120) ÷ (1680)
Step 4: Simplify the fraction.
To simplify the fraction, we divide the numerator by the denominator.
(-120) ÷ (1680) = -0.07142857143
So, the value of the expression (−3)÷(3/4)×(2/7)×(−5/16)÷(5/7) is approximately -0.07142857143.