(−4) × (7/5 ) × (− 3/4) ÷ (7/15)
To simplify the expression, we can follow the order of operations (also known as PEMDAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
First, we'll simplify the multiplication part:
(-4) × (7/5) × (-3/4) ÷ (7/15)
(-4) × (7/5) = -28/5
Next, we'll divide by (7/15):
(-28/5) ÷ (7/15)
To divide fractions, we can multiply the first fraction by the reciprocal (multiplicative inverse) of the second fraction:
(-28/5) × (15/7)
The negative signs cancel out:
-28/5 × 15/7
Multiplying the numerators and denominators:
(-28 × 15) / (5 × 7)
Simplifying:
-420 / 35
The numerator is divisible by 35, and the denominator is also divisible by 35:
(-420 ÷ 35) / (35 ÷ 35)
-12 / 1
The expression simplifies to -12.
Step 1: Multiply the first two numbers: (-4) * (7/5) = -28/5.
Step 2: Multiply the result from step 1 by the third number: (-28/5) * (-3/4) = 84/20.
Step 3: Divide the result from step 2 by the fourth number: (84/20) / (7/15).
To divide by a fraction, we need to multiply by its reciprocal. The reciprocal of 7/15 is 15/7, so we can rewrite the expression as (84/20) * (15/7).
Step 4: Simplify the expression by canceling out common factors: (84/20) * (15/7) = (2 * 2 * 3 * 7 / 2 * 2 * 5) * (3 * 5 / 7) = (3 * 3) / (2 * 5) = 9/10.
So, (-4) * (7/5) * (-3/4) ÷ (7/15) = 9/10.
To simplify the expression (-4) × (7/5) × (-3/4) ÷ (7/15), we can follow the order of operations (also known as PEMDAS).
Step 1: Multiply the numbers
(-4 × 7/5 × -3/4) ÷ (7/15)
Multiplying the numbers gives us -84/20 ÷ 7/15.
Step 2: Divide the numbers
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.
(-84/20) × (15/7)
Step 3: Simplify the fraction
To simplify the fraction further, we can cancel out any common factors between the numerator and denominator.
(-6/1) × (15/7)
Multiplying the numerators and denominators gives us -90/7.
Therefore, (-4) × (7/5) × (-3/4) ÷ (7/15) simplifies to -90/7.