(−4)×(
7
5
)×(−
3
4
)÷(
7
15
To solve this expression, we follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
First, let's simplify the expression inside the parentheses: (−3/4) × (7/15)
To multiply fractions, we multiply the numerators together and multiply the denominators together.
(-3/4) × (7/15) = (-3 × 7) / (4 × 15)
= -21 / 60
= -7 / 20
Now we substitute this value back into the original expression and perform the remaining steps:
(-4) × (-7/20) = 28/20
= 7/5
So the simplified result of the expression is 7/5.
To perform the given calculation step-by-step:
Step 1: Evaluate the multiplication of the two negative numbers:
(−4) × (−3/4) = 12/4 = 3
Step 2: Evaluate the multiplication of the fraction with the whole number:
3 × (7/5) = (3 × 7) / 5 = 21/5
Step 3: Evaluate the division of the fraction by another fraction:
(21/5) ÷ (7/15) = (21/5) × (15/7)
To simplify further, we can cancel out the common factors:
(21/5) × (15/7) = (3/1) × (3/1) = 9/1 = 9
Therefore, the final answer is 9.
To simplify the given expression, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Let's break down the given expression step by step:
1. Begin by multiplying the numbers within the parentheses:
-4 × 7 = -28
-3 × -4 = 12
So, the expression becomes: -28 × 12 ÷ (7/5) ÷ (7/15)
2. Next, simplify the division by multiplying the numerator by the reciprocal of the denominator:
(7/5) ÷ (7/15) = (7/5) × (15/7)
Multiply the numerators (7 × 15) and the denominators (5 × 7):
= 105/35
3. Now we have:
-28 × 12 ÷ (105/35)
4. Divide -28 by 12:
-28 ÷ 12 = -2.3333 (rounded to four decimal places)
5. Finally, divide the result from step 4 by (105/35):
-2.3333 ÷ (105/35)
To divide by a fraction, we multiply by its reciprocal:
= -2.3333 × (35/105)
Perform the multiplication:
= -2.3333 × (1/3)
Divide -2.3333 by 3:
= -0.7777 (rounded to four decimal places)
So, the simplified value of the expression is approximately -0.7777.