Use properties of operations and rules for multiplying and dividing signed numbers to solve: (-4) × (7/5) × (- 3/4) ÷ (7/15)
To solve this problem, we will use the properties of operations and rules for multiplying and dividing signed numbers.
(-4) is a negative number, (7/5) is a positive number, (-3/4) is a negative number, and (7/15) is a positive number.
We can begin by multiplying the numbers together:
(-4) × (7/5) × (-3/4) ÷ (7/15)
Multiplying the integers:
= (-4) × (7) × (-3) ÷ (7/15)
Multiplying the fractions:
= (-4) × (7) × (-3) × (15/7)
Simplifying the multiplication:
= (-4) × (-3) × (15)
Multiplying the negative numbers:
= 12 × 15
= 180
Therefore, (-4) × (7/5) × (-3/4) ÷ (7/15) = 180.
To solve the expression (-4) × (7/5) × (-3/4) ÷ (7/15), we can follow the rules for multiplying and dividing signed numbers.
Step 1: Multiply the numbers together.
(-4) × (7/5) equals -28/5.
Step 2: Multiply the result by (-3/4).
(-28/5) × (-3/4) equals 84/20.
Step 3: Divide the result by (7/15).
(84/20) ÷ (7/15) can be simplified by multiplying the numerator by the reciprocal of the denominator.
(84/20) ÷ (7/15) equals (84/20) × (15/7).
To multiply, we multiply the numerators and denominators:
(84 × 15) / (20 × 7).
Calculating the numerator and denominator separately:
Numerator: 84 × 15 = 1260.
Denominator: 20 × 7 = 140.
So, (84/20) ÷ (7/15) equals 1260/140.
Step 4: Simplify the result.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD).
GCD of 1260 and 140 is 20.
Dividing by 20:
Numerator: 1260 ÷ 20 = 63.
Denominator: 140 ÷ 20 = 7.
So, 1260/140 simplifies to 63/7.
Thus, the expression (-4) × (7/5) × (-3/4) ÷ (7/15) simplifies to 63/7.
To solve (-4) × (7/5) × (- 3/4) ÷ (7/15), we can follow the rules for multiplying and dividing signed numbers.
Step 1: Simplify the multiplication
Starting with (-4) × (7/5) × (-3/4), we can simplify the multiplication as follows:
(-4) × (7/5) = -28/5
Then, multiply -28/5 by (-3/4):
(-28/5) × (-3/4) = 84/20
Step 2: Simplify the division
Now, we have to divide 84/20 by 7/15. To divide fractions, we can multiply by the reciprocal of the second fraction. The reciprocal of 7/15 is 15/7.
So, we have:
(84/20) ÷ (7/15) = (84/20) × (15/7)
Step 3: Simplify the final multiplication
Multiply the fractions:
(84/20) × (15/7) = 1260/140
Step 4: Simplify the resulting fraction
Simplify the fraction 1260/140. We can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 20:
(1260/20) ÷ (140/20) = 63/7
Step 5: Simplify the final result
Finally, reduce the fraction 63/7:
63/7 = 9
So, (-4) × (7/5) × (-3/4) ÷ (7/15) simplifies to 9.