Use the properties of operations and rules for multiplying and dividing to solve:
(−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7)
Make sure to get a positive number, not a fraction.
To solve this expression, we will follow the rules for multiplying and dividing fractions:
First, multiply all the numerators together and multiply all the denominators together:
(-3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7) = -3 × 5 × 7 × -3 × -5 / 5 × 16 × 12 × 16 × 7
Next, simplify the expression:
(-3 × 5 × 7 × -3 × -5) / (5 × 16 × 12 × 16 × 7)
= (none of the denominators and numerators have common factors)
= (3 × 5 × 7 × 3 × 5) / (5 × 2 × 2 × 2 × 2 × 3 × 7 × 2 × 2 × 2 × 2 × 7)
= (3 × 3 × 5 × 5) / (2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 7 × 7)
= (3 × 3 × 5 × 5) / (64 × 49)
Now, notice that 3 × 3 = 9 and 5 × 5 = 25:
= (9 × 25) / (64 × 49)
Next, simplify further by finding common factors between the numerator and the denominator:
= (3 × 3 × 5 × 5) / (2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 7)
= (3 × 3 × 5 × 5) / (2^8 × 7^3)
Finally, we can see that 3 × 3 = 9 and 5 × 5 = 25, and 2^8 = 256 and 7^3 = 343:
= (9 × 25) / (256 × 343)
Now, we can calculate the division:
= 225 / (256 × 343)
Finally, calculate the multiplication:
= 225 / 87552
Since we want a positive number, not a fraction, we can divide 225 by 87552:
225 ÷ 87552 ≈ 0.00257
So the positive value for the expression is approximately 0.00257.
To solve the expression (−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7), we can follow the order of operations (PEMDAS/BODMAS) and apply the properties of operations and rules for multiplying and dividing as follows:
1. Simplify the numerator and denominator of the expression separately.
- Numerator: (−3/5)×(5/16)×(7/12) = (−3×5×7)/(5×16×12) = (−105)/(960)
- Denominator: (−3/16)×(−5/7) = (−3×−5)/(16×7) = 15/112
2. Divide the simplified numerator by the simplified denominator.
- (−105)/(960) ÷ (15/112) = (−105)/(960) × (112/15)
3. Simplify the multiplication of the numerators and the denominators.
- (−105)/(960) × (112/15) = (−105×112)/(960×15) = (−11760)/(14400)
4. Simplify the fraction by canceling out the common factors.
- (−11760)/(14400) = (−98×120)/(12×120) = (−98)/(12)
5. Multiply the numerator and denominator by the same value to make the numerator positive.
- (−98)/(12) × (−1)/(−1) = 98/(−12)
Therefore, the simplified expression is 98/(-12), which can be further simplified as -49/6 or -8.16 (rounded to two decimal places).
To solve the expression:
(-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7),
We can start by simplifying the expression step by step using the properties of operations and rules for multiplying and dividing.
Step 1: Simplify multiplication as you go
Multiply the numerators and denominators of the fractions across the expression.
(-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7)
= (-3 × 5 × 7 × -3 × -5) / (5 × 16 × 12 × 16 × 7)
= 1575 / (9,600 × 2,688)
Step 2: Simplify the fractions
To simplify the fraction 1575 / (9,600 × 2,688), we can look for common factors. In this case, 1575, 9600, and 2688 have a common factor of 336.
So we can rewrite the expression as:
(336 × 4.6875) / (336 × 28.3333)
Step 3: Cancel out common factors
We can see that we have a common factor of 336 in both the numerator and denominator of the fraction.
Canceling out the common factor, we get:
4.6875 / 28.3333
Step 4: Evaluate the division
Divide the numerator by the denominator:
4.6875 / 28.3333 = 0.165
The final result is 0.165 (rounded to three decimal places).
By following these steps and using the properties of operations and rules for multiplying and dividing, we simplified the given expression to a positive decimal number.