(−3/5)×(5 1/6)×(7 1/2)÷(−3 1/6)×(−5/7)
To solve this expression, we can follow the order of operations, which is parentheses, multiplication/division (from left to right), and then addition/subtraction (from left to right).
Starting with the parentheses, we have:
(-3/5) × (5 1/6) × (7 1/2) ÷ (-3 1/6) × (-5/7)
Next, let's convert the mixed numbers into improper fractions:
(-3/5) × (31/6) × (15/2) ÷ (-19/6) × (-5/7)
Now, multiplying the fractions together:
((-3) × 31 × 15 × (-5)) / ((5) × (6) × (2) × (-19)) × (7)
Simplifying the numerator and denominator separately:
(-1395) / (-1140) × 7
Canceling out the negative signs:
(1395) / (1140) × 7
Simplifying the fraction:
(465/380) × (7)
Multiplying the fractions:
(465 × 7) / 380
Simplifying the fraction:
(3255) / 380
So, the simplified expression is 3255/380.
To solve the expression (−3/5)×(5 1/6)×(7 1/2)÷(−3 1/6)×(−5/7), we'll break it down into steps and simplify each step.
Step 1: Convert mixed numbers to improper fractions:
5 1/6 = (6*5 + 1)/6 = 31/6
7 1/2 = (2*7 + 1)/2 = 15/2
-3 1/6 = (6*(-3) + 1)/6 = -19/6
The expression becomes:
(−3/5) × (31/6) × (15/2) ÷ (−19/6) × (−5/7)
Step 2: Multiply the fractions from left to right in the numerator and the denominators.
[(-3/5) × (31/6)] × (15/2) ÷ [(-19/6) × (-5/7)]
Step 3: Simplify the numerator and denominator of each fraction:
[-3 × 31] / [5 × 6] × [15 / (2 × 1)] ÷ [(-19 × -5) / (6 × 7)]
The expression becomes:
[-93 / 30] × [15 / 2] ÷ [95 / 42]
Step 4: Simplify further by multiplying and dividing the fractions:
[(-93 × 15) / (30 × 2)] ÷ [(95 / 42)]
Step 5: Simplify the numerator and denominator:
[-1395 / 60] ÷ [95 / 42]
Step 6: To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
[-1395 / 60] × [42 / 95]
Step 7: Multiply the numerators and denominators:
[-1395 × 42] / [60 × 95]
Step 8: Simplify the numerator and denominator:
-58410 / 5700
Step 9: Divide both the numerator and denominator by the greatest common divisor (GCD) to simplify the fraction:
(-58410 ÷ 30) / (5700 ÷ 30) = -1947 / 190
Therefore, the expression (−3/5)×(5 1/6)×(7 1/2)÷(−3 1/6)×(−5/7) simplifies to -1947 / 190.
To solve this expression, we can follow these steps:
1. Let's start by simplifying the fractions involved.
The fraction 5 1/6 can be converted to an improper fraction as:
5 1/6 = (6 × 5 + 1) / 6 = 31 / 6
The fraction 7 1/2 can be converted to an improper fraction as:
7 1/2 = (2 × 7 + 1) / 2 = 15 / 2
The fraction -3 1/6 can be converted to an improper fraction as:
-3 1/6 = (6 × (-3) + 1) / 6 = -19 / 6
2. Now we can perform the multiplication and division operations. Remember that multiplying two fractions is done by multiplying the numerators and multiplying the denominators. Dividing two fractions is done by multiplying the first fraction by the reciprocal of the second fraction.
(-3/5) × (31/6) × (15/2) ÷ (-19/6) × (-5/7)
Multiplying the numerators:
(-3 × 31 × 15 × (-5)) = 13950
Multiplying the denominators:
(5 × 6 × 2 × 19 × 7) = 3990
Thus, the expression becomes: 13950 / 3990.
3. Finally, simplify the fraction if possible. To do this, find the greatest common divisor (GCD) of the numerator and denominator and divide both by it.
GCD(13950, 3990) = 30
Dividing both the numerator and denominator by 30, we get:
13950 / 3990 = 465 / 133
Therefore, the result of the expression (-3/5) × (5 1/6) × (7 1/2) ÷ (-3 1/6) × (-5/7) is 465 / 133.