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.
(−4) × (7/5 ) × (− 3/4) ÷ (7/15)
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