Use the properties of operations and rules for multiplying and dividing to solve:
(−3) ÷(3/4) × (2/7) × (−5/16) ÷ (5/7)
To solve this, we can follow the order of operations and use the properties of multiplication and division.
Step 1: Begin by simplifying the division of -3 ÷ (3/4):
To divide a number by a fraction, we can multiply by its reciprocal. The reciprocal of 3/4 is 4/3.
So, -3 ÷ (3/4) becomes -3 x (4/3).
Multiplying, we get -12/3, which simplifies to -4.
Step 2: Now, let's multiply -4 by (2/7):
Multiplying -4 by 2/7, we get (-4)*(2/7) = -8/7.
Step 3: Next, multiply -8/7 by (-5/16):
Multiplying -8/7 by -5/16, we get (-8/7)*(-5/16) = 40/112.
This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 8:
40/112 simplifies to 5/14.
Step 4: Lastly, divide 5/14 by 5/7:
To divide a fraction by another fraction, we multiply by the reciprocal. The reciprocal of 5/7 is 7/5.
So, 5/14 divided by 5/7 becomes (5/14)*(7/5).
Multiplying, we get 35/70, which simplifies to 1/2.
Therefore, (-3) ÷(3/4) × (2/7) × (−5/16) ÷ (5/7) = 1/2.
Use the properties of operations and rules for multiplying and dividing to solve:
(8/9)×(−3/4)÷(1/9)×(−4/5)÷(3/5)
To solve this, we can follow the order of operations and use the properties of multiplication and division.
Step 1: Begin by multiplying the numerators and denominators:
(8/9) × (−3/4) ÷ (1/9) × (−4/5) ÷ (3/5) = (-24/36) ÷ (4/45) ÷ (12/25)
Step 2: Simplify the division:
To divide fractions, we invert the second fraction and multiply.
(-24/36) ÷ (4/45) ÷ (12/25) = (-24/36) * (45/4) * (25/12)
Step 3: Multiply the numerators and denominators:
(-24/36) * (45/4) * (25/12) = (-24*45*25)/(36*4*12) = -2700/1728
Step 4: Simplify the fraction:
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 72.
-2700/1728 simplifies to -37.5/24.
Therefore, (8/9)×(−3/4)÷(1/9)×(−4/5)÷(3/5) equals -37.5/24.
Use the properties of operations and rules for multiplying and dividing to solve:
(8/9) × (− 3/4) ÷ (1/9) × (− 4/5) ÷ (3/5)
To solve this expression, we can follow the order of operations and use the properties of multiplication and division.
Step 1: Begin by multiplying the numerators and denominators:
(8/9) × (− 3/4) ÷ (1/9) × (− 4/5) ÷ (3/5) = (8 × -3 × -4)/(9 × 4 × 5 × 3)
Step 2: Simplify the multiplication:
(8 × -3 × -4)/(9 × 4 × 5 × 3) = (8 × 3 × 4)/(9 × 4 × 5 × 3)
Step 3: Cancel out common factors in the numerator and denominator:
In the numerator, we can cancel out a factor of 4 with one in the denominator, and in the denominator, we can cancel out a factor of 3 with one in the numerator.
Therefore, we have: (8 × 3 × 4)/(9 × 4 × 5 × 3) = (8 × 3)/(9 × 5)
Step 4: Multiply the numerators and denominators:
(8 × 3)/(9 × 5) = 24/45
Step 5: Simplify the fraction:
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 3.
24/45 simplifies to 8/15.
Therefore, (8/9) × (− 3/4) ÷ (1/9) × (− 4/5) ÷ (3/5) equals 8/15.
not right
Apologies for the mistake.
Let's solve it again step by step:
(8/9) × (− 3/4) ÷ (1/9) × (− 4/5) ÷ (3/5)
Step 1: Multiply the numerators together and the denominators together:
= (8 × -3 × -4) / (9 × 4 × 5 × 3)
Step 2: Simplify the multiplication:
= (96) / (540)
Step 3: Divide the numerator by the denominator:
= 96 / 540
Step 4: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 12:
= (8 × 12) / (45 × 12)
Step 5: Simplify further:
= 96 / 540
= 8 / 45
Therefore, (8/9) × (− 3/4) ÷ (1/9) × (− 4/5) ÷ (3/5) equals 8/45.
nope
Apologies for the continued confusion. Let's try to solve it step by step again:
(8/9) × (− 3/4) ÷ (1/9) × (− 4/5) ÷ (3/5)
Step 1: Perform the multiplications and divisions from left to right:
(8/9) × (− 3/4) = -24/36 = -2/3
Next, divide by (1/9):
(-2/3) ÷ (1/9) = (-2/3) × (9/1) = -18/3 = -6
Then, multiply by (− 4/5):
-6 × (− 4/5) = 24/5
Step 2: Simplify the resulting fraction:
24/5 cannot be simplified any further.
Therefore, the solution to (8/9) × (− 3/4) ÷ (1/9) × (− 4/5) ÷ (3/5) is 24/5.
To solve the expression (−3) ÷ (3/4) × (2/7) × (−5/16) ÷ (5/7), we can follow the properties and rules for multiplying and dividing.
Step 1: Simplify the division:
(−3) ÷ (3/4) can be written as (−3) × (4/3). This is because dividing by a fraction is equivalent to multiplying by its reciprocal.
Step 2: Simplify the multiplications:
(−3) × (4/3) × (2/7) × (−5/16) × (5/7)
When multiplying fractions, we multiply the numerators together and the denominators together.
Numerators: (-3) × (4) × (2) × (-5) × (5) = -600
Denominators: 3 × 7 × 16 × 7 = 2352
Step 3: Simplify the fraction:
The fraction -600/2352 can be simplified by dividing both the numerator and denominator by their greatest common divisor.
The greatest common divisor of 600 and 2352 is 24. Dividing both numerator and denominator by 24 gives:
-600 ÷ 24 = -25
2352 ÷ 24 = 98
Therefore, the expression (−3) ÷ (3/4) × (2/7) × (−5/16) ÷ (5/7) simplifies to -25/98.