(−3)÷(3/4)×(2/7)×(−5/16)÷(5/7)
To solve this expression, let's simplify it step by step:
First, let's simplify the division of -3 by 3/4:
(-3) ÷ (3/4) = -3 × (4/3)
Next, let's multiply the result by 2/7:
-3 × (4/3) × (2/7)
Now, let's multiply the result by -5/16:
-3 × (4/3) × (2/7) × (-5/16)
Finally, let's divide the result by 5/7:
-3 × (4/3) × (2/7) × (-5/16) ÷ (5/7)
Now, let's simplify:
-3 × (4/3) = -4
-4 × (2/7) = -8/7
-8/7 × (-5/16) = 40/112 = 5/14
5/14 ÷ (5/7) = 5/14 × (7/5) = 35/70 = 1/2
Therefore, (-3)÷(3/4)×(2/7)×(−5/16)÷(5/7) = 1/2.
To solve this expression, you need to follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
Let's break down the expression step by step:
1. Start by simplifying the division first. Remember that dividing by a fraction is equivalent to multiplying by its reciprocal.
So, (−3) ÷ (3/4) is the same as (−3) x (4/3).
Simplifying this expression gives you: −12/3 = -4.
2. Next, multiply this result by the next fraction: -4 x (2/7) = -8/7.
3. Then, multiply the previous result by the next fraction: (-8/7) x (−5/16).
To multiply these fractions, you can multiply the numerators together and multiply the denominators together:
(-8 x -5) / (7 x 16).
This simplifies to: 40 / 112.
4. Finally, divide this result by the last fraction: (40/112) ÷ (5/7).
Remember, dividing by a fraction is the same as multiplying by its reciprocal:
(40/112) x (7/5).
Multiplying these fractions together gives you:
(40 x 7) / (112 x 5).
Simplifying this expression, you get: 280 / 560.
5. Finally, simplify the fraction 280/560 by dividing both the numerator and the denominator by their greatest common divisor, which is 280:
280 / 560 = 1/2.
Therefore, the value of the expression (−3)÷(3/4)×(2/7)×(−5/16)÷(5/7) is 1/2.
To calculate this expression step-by-step, let's follow the order of operations (PEMDAS) and start with parentheses:
1. Begin by simplifying the expression inside the parentheses: (3/4).
- No simplification is needed: (3/4).
Now let's proceed with the division operation:
2. Calculate: (-3) ÷ (3/4).
- Dividing a number by a fraction is the same as multiplying by its reciprocal, so this expression becomes: (-3) × (4/3).
- Multiply the numerators: (-3) × (4) = -12.
- Multiply the denominators: (1) × (3) = 3.
- The result is: -12/3 = -4.
Next, let's multiply the remaining fractions:
3. Multiply: -4 × (2/7) × (-5/16) × (5/7).
- Multiply the numerators: (-4) × (2) × (-5) × (5) = 200.
- Multiply the denominators: (1) × (7) × (16) × (7) = 784.
- The result is: 200/784.
Finally, let's simplify the fraction:
4. Simplify 200/784.
- Divide both the numerator and denominator by their greatest common divisor (GCD), which is 8.
- Divide the numerator: 200 ÷ 8 = 25.
- Divide the denominator: 784 ÷ 8 = 98.
- The result is: 25/98.
So, the final simplified result of the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) is 25/98.