Use the properties of operations and rules for multiplying and dividing signed numbers to solve:
..
(−4)×(7/5)×(−3/4)÷(7/15)
To solve this expression, we can simplify step-by-step using the properties of operations and rules for multiplying and dividing signed numbers.
First, let's simplify the multiplication:
(-4) × (7/5) × (-3/4) = (-4) × (-3) × (7/5) × (1/4)
= 12 × (7/5) × (1/4) [Since (-4) × (-3) = 12]
= (12 × 7 × 1) / (5 × 4)
= 84 / 20
= 4.2
Next, let's simplify the division:
4.2 ÷ (7/15) = 4.2 × (15/7) [Since division is equivalent to multiplication by the reciprocal]
= (4.2 × 15) / 7
= 63 / 7
= 9
Therefore, the solution to the expression (-4) × (7/5) × (-3/4) ÷ (7/15) is 9.
To solve this expression, we can follow the rules for multiplying and dividing signed numbers step by step. Let's begin:
Step 1: Multiply the numbers with the same signs.
(-4) × (7/5) × (-3/4) ÷ (7/15)
= -4 × 7/5 × -3/4 ÷ 7/15
= -28/5 × -3/4 ÷ 7/15
Step 2: Simplify the fractions.
-28/5 × -3/4 ÷ 7/15
= (-28 × -3)/(5×4) ÷ 7/15
= (84/20) ÷ 7/15
Step 3: Divide by multiplying the reciprocal of the divisor.
(84/20) ÷ 7/15
= (84/20) × (15/7)
= (84 × 15)/(20 × 7)
Step 4: Simplify the fraction.
(84 × 15)/(20 × 7)
= 1260/140
= 9
Therefore, the result of the expression (-4)×(7/5)×(-3/4)÷(7/15) is 9.
To solve the expression (-4) × (7/5) × (-3/4) ÷ (7/15), we can follow the order of operations.
First, let's simplify the multiplication and division of the numbers using the properties of operations and the rules for multiplying and dividing signed numbers.
Multiplication:
(-4) × (7/5) × (-3/4) can be simplified as follows:
Start by multiplying the whole numbers: -4 × -3 = 12.
Next, multiply the fractions: (7/5) × (1/4) = 7/20.
So, (-4) × (7/5) × (-3/4) equals 12 × (7/20) = 84/20.
Division:
Now, let's divide the resulting fraction by (7/15):
Before dividing fractions, we need to take the reciprocal of the second fraction. The reciprocal of (7/15) is (15/7).
Now, multiply (84/20) by (15/7):
Multiply the numerators: 84 × 15 = 1260.
Multiply the denominators: 20 × 7 = 140.
So, (84/20) ÷ (7/15) equals 1260/140.
Simplifying the fraction:
To simplify the fraction 1260/140, we can divide the numerator and denominator by their greatest common factor, which is 20:
Divide the numerator: 1260 ÷ 20 = 63.
Divide the denominator: 140 ÷ 20 = 7.
Therefore, (84/20) ÷ (7/15) simplifies to 63/7.
Final Answer:
The expression (-4) × (7/5) × (-3/4) ÷ (7/15) simplifies to 63/7.