Multiply and divide rational numbers quick check use the properties of operations and rules for multiplying and dividing to solve -2×1/5÷2/3×5/6÷3/4
To solve this expression, we'll follow the order of operations (PEMDAS) and use the properties of operations and rules for multiplying and dividing.
Firstly, let's evaluate the expression from left to right:
-2 × 1/5 ÷ 2/3 × 5/6 ÷ 3/4
First, we'll simplify the multiplication and division from left to right:
-2 × 1/5 = -2/5 (simplifying the multiplication)
-2/5 ÷ 2/3 = -2/5 × 3/2 = (-2 × 3)/(5 × 2) = -6/10 = -3/5 (simplifying the division)
-3/5 × 5/6 = (-3 × 5)/(5 × 6) = -15/30 = -1/2 (simplifying the multiplication)
-1/2 ÷ 3/4 = -1/2 × 4/3 = (-1 × 4)/(2 × 3) = -4/6 = -2/3 (simplifying the division)
So, -2 × 1/5 ÷ 2/3 × 5/6 ÷ 3/4 simplifies to -2/3.
To solve the expression -2 × 1/5 ÷ 2/3 × 5/6 ÷ 3/4, we can follow these four steps:
Step 1: Apply the properties of multiplication and division.
Step 2: Simplify each multiplication and division separately.
Step 3: Multiply the simplified values together.
Step 4: Simplify the final result.
Let's solve it step by step:
Step 1: Apply the properties of multiplication and division.
-2 × 1/5 ÷ 2/3 × 5/6 ÷ 3/4 can be written as (-2) × (1/5) ÷ (2/3) × (5/6) ÷ (3/4).
Step 2: Simplify each multiplication and division separately.
(-2) × (1/5) ÷ (2/3) × (5/6) ÷ (3/4) simplifies to -2/5 ÷ 2/3 × 5/6 ÷ 3/4.
Step 3: Multiply the simplified values together.
Now, let's multiply -2/5 ÷ 2/3 × 5/6 ÷ 3/4:
= (-2/5) × (3/2) × (5/6) × (4/3)
Step 4: Simplify the final result.
Let's simplify (-2/5) × (3/2) × (5/6) × (4/3):
= (-2 × 3 × 5 × 4) / (5 × 2 × 6 × 3)
Now, we can cancel out any common factors:
= (-2 × 3 × 5 × 4) / (5 × 2 × 6 × 3)
= (-2 × 5 × 4) / (2 × 6)
= (-40) / 12
Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4:
= -10 / 3
Therefore, the final answer is -10/3.
To solve the expression -2 × 1/5 ÷ 2/3 × 5/6 ÷ 3/4, we can follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
Step 1: Start by simplifying within parentheses (if any). In this case, there are no parentheses, so we move to the next step.
Step 2: Simplify any exponents (if any). Again, there are no exponents, so we move to the next step.
Step 3: Perform multiplication and division from left to right. Let's break down the expression:
-2 × 1/5 can be simplified as -(2/1) × (1/5) = -2/5.
Next, we have ÷ 2/3. Dividing is the same as multiplying by the reciprocal, so we can write it as × 3/2. Thus, we have -2/5 × 3/2.
Now, multiplying fractions is done by multiplying the numerators and denominators separately. Therefore, -2/5 × 3/2 = (-2 × 3) / (5 × 2) = -6/10.
Continuing, we have × 5/6. Following the same steps as before, -6/10 × 5/6 = (-6 × 5) / (10 × 6) = -30/60.
Finally, we have ÷ 3/4, which is equivalent to multiplying by the reciprocal, i.e., × 4/3. Thus, we have -30/60 × 4/3.
Again, multiplying the numerators and denominators separately, we get (-30 × 4) / (60 × 3) = -120/180.
Step 4: Simplify the fraction, if possible. In this case, we can divide both the numerator and denominator by their greatest common divisor, which is 60.
-120/180 = (-120 ÷ 60) / (180 ÷ 60) = -2/3.
Therefore, the solution to the expression -2 × 1/5 ÷ 2/3 × 5/6 ÷ 3/4 is -2/3.