Are use the proper use of operation enrollments for multiplying and dividing to solve what is -3/5×5/16×7/12÷-3/16×-5/7
To solve the expression (-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7), you can follow these steps:
Step 1: Begin with the numerator:
(-3) × (5) × (7) × (-5) = -525
Step 2: Proceed with the denominator:
(5) × (16) × (12) × (3) × (7) = 3,360
Step 3: Divide the numerator by the denominator:
-525 ÷ 3,360 ≈ -0.15625
Therefore, the result of the expression -3/5 × 5/16 × 7/12 ÷ -3/16 × -5/7 is approximately -0.15625.
To solve the expression: -3/5 × 5/16 × 7/12 ÷ -3/16 × -5/7, you can follow these steps:
Step 1: Simplify the multiplication operations from left to right:
-3/5 × 5/16 = -15/80
-15/80 × 7/12 = -105/960
Step 2: Simplify the division operations from left to right:
-105/960 ÷ -3/16 = -105/960 × -16/3
Step 3: Simplify the multiplication operation:
-105/960 × -16/3 = 1680/2880
Step 4: Simplify the fraction to its simplest form:
1680/2880 = 7/12
Therefore, the result of the expression -3/5 × 5/16 × 7/12 ÷ -3/16 × -5/7 is 7/12.
To solve the expression -3/5 × 5/16 × 7/12 ÷ -3/16 × -5/7, we need to follow the proper order of operations, which is commonly known as "PEMDAS" (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). Let's break it down step-by-step:
Step 1: Simplify multiplication and division from left to right.
-3/5 × 5/16 × 7/12 ÷ -3/16 × -5/7
= (-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7)
Step 2: Multiply the fractions.
= (-3 × 5 × 7) / (5 × 16 × 12) ÷ (-3 × -5) / (16 × 7)
= (-105) / (960) ÷ (15) / (112)
Step 3: Simplify the division by multiplying by the reciprocal.
= (-105) / (960) × (112) / (15)
= -112 × 105 / 960 × 15
Step 4: Simplify the numerators and denominators separately.
= -11760 / 14400
Step 5: Reduce the fraction, if possible.
To find the highest common factor (HCF) of 11760 and 14400, we can use prime factorization.
11760 = 2^5 × 3^2 × 5 × 7
14400 = 2^6 × 3^2 × 5^2
The HCF is 2^5 × 3^2 × 5 = 720.
= -11760 / 14400
= (-2^5 × 3^2 × 5 × 7) / (2^6 × 3^2 × 5^2)
= -7 / (2 × 5)
= -7 / 10
Therefore, the value of the expression -3/5 × 5/16 × 7/12 ÷ -3/16 × -5/7 is -7/10.