Use the properties of operations and rules for multiplying and dividing to solve: (−3)÷(3/4)×(2/7)×(−5 1/6)÷(5/7)
To solve this expression, follow the order of operations, which is parentheses, multiplication/division, and addition/subtraction (PEMDAS).
Step 1: Simplify within the parentheses:
(-3) ÷ (3/4) × (2/7) × (-5 1/6) ÷ (5/7)
= (-3) ÷ (3/4) × (2/7) × (-31/6) ÷ (5/7)
Step 2: Perform division:
= [(-3) × (4/3)] × (2/7) × (-31/6) ÷ (5/7)
= [-12/3] × (2/7) × (-31/6) ÷ (5/7)
= -4 × (2/7) × (-31/6) ÷ (5/7)
Step 3: Simplify the fractions:
= -4 × (2/7) × [(-31)/(6/1)] ÷ (5/7)
= -4 × (2/7) × (-31) ÷ (5/7)
= -4 × (2/7) × (-31) × (7/5)
= -4 × 2 × (-31) × 7 ÷ 7 × 5
Step 4: Perform multiplication and division from left to right:
= -8 × (-31) × 5
= 1240
Therefore, (-3) ÷ (3/4) × (2/7) × (-5 1/6) ÷ (5/7) equals 1240.
To solve the given expression step-by-step, we will use the properties of operations and rules for multiplying and dividing.
Step 1: Simplify the division:
(-3) ÷ (3/4) = (-3) * (4/3) = -4
Step 2: Multiply the result with the next fraction:
-4 * (2/7) = -8/7
Step 3: Multiply the result with the next mixed number:
-8/7 * (-5 1/6)
To multiply a fraction with a mixed number, we need to convert the mixed number into an improper fraction.
-5 1/6 = -5 + 1/6 = -30/6 + 1/6 = (-30 + 1)/6 = -29/6
Then, multiply the fractions:
-8/7 * (-29/6)
Step 4: Multiply the numerators and multiply the denominators:
(-8 * -29) / (7 * 6)
= 232 / 42
Step 5: Simplify the fraction if possible:
Both the numerator and denominator have a common factor of 2, so we can simplify the fraction:
232/42 = 116/21
Therefore, the solution to the given expression (-3) ÷ (3/4) × (2/7) × (-5 1/6) ÷ (5/7) is 116/21.
To solve the given expression (−3)÷(3/4)×(2/7)×(−5 1/6)÷(5/7), we need to follow the properties of operations and rules for multiplying and dividing:
Step 1: Simplify within parentheses:
The given expression can be simplified as follows:
(-3) ÷ (3/4) × (2/7) × (-5 1/6) ÷ (5/7)
= (-3) ÷ (3/4) × (2/7) × (-31/6) ÷ (5/7)
Step 2: Solve the Division operation:
When dividing fractions, we multiply the numerator of the first fraction by the reciprocal of the second fraction. In this case, we have (-3) ÷ (3/4) which can be written as (-3) × (4/3).
= (-3) × (4/3) × (2/7) × (-31/6) ÷ (5/7)
Step 3: Multiply the fractions and whole numbers:
Multiply the numerators together and the denominators together:
= -3 × 4 × 2 × -31 ÷ 3 × 7 × 6 × 5
Step 4: Perform the multiplication:
Multiply the numerators: -3 × 4 × 2 × -31 = 744
Multiply the denominators: 3 × 7 × 6 × 5 = 630
= 744 ÷ 630
Step 5: Simplify the fraction:
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD), which is 6 in this case:
744 ÷ 6 ÷ 630 ÷ 6 = 124 ÷ 105
Step 6: Divide the numbers:
Perform the division: 124 ÷ 105 = 1 remainder 19
Therefore, the solution is 1 remainder 19 or 1 19/105.
By following these steps, you can solve the given expression using the properties of operations and rules for multiplying and dividing.