Use the properties of operations and rules for multiplying and dividing to solve: (8/9) x (-3/4) divide (1/9) x (-4/5) divide (3/5)
To simplify the expression (8/9) x (-3/4) ÷ (1/9) x (-4/5) ÷ (3/5), we follow the order of operations (PEMDAS/BODMAS).
1. Simplify the multiplication:
(8/9) x (-3/4) = -24/36
2. Simplify the division:
(-24/36) ÷ (1/9) = -24/36 x 9/1 = -24/4 = -6
3. Simplify the second division:
-6 ÷ (3/5) = -6 x 5/3 = -30/3 = -10
Therefore, the value of the expression (8/9) x (-3/4) ÷ (1/9) x (-4/5) ÷ (3/5) is -10.
To solve this expression, we will simplify each part separately and then divide the results.
First, we simplify (8/9) x (-3/4).
To multiply fractions, we multiply the numerators together and the denominators together.
(8/9) x (-3/4) = (8 x -3) / (9 x 4) = -24/36
The fraction -24/36 can be simplified by dividing the numerator and denominator by their greatest common divisor, which is 12.
-24/36 = (-24 ÷ 12) / (36 ÷ 12) = -2/3
Now, we simplify (1/9) x (-4/5).
(1/9) x (-4/5) = (1 x -4) / (9 x 5) = -4/45
Finally, we divide (-2/3) by (-4/45).
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
(-2/3) ÷ (-4/45) = (-2/3) x (45/-4)
We can simplify before multiplying by dividing the numerator and denominator by their greatest common divisor, which is 1.
(-2/3) x (45/-4) = (-2 x 45) / (3 x -4) = -90/-12
Again, we simplify by dividing the numerator and denominator by their greatest common divisor, which is 6.
-90/-12 = (-90 ÷ 6) / (-12 ÷ 6) = 15/2
So, (8/9) x (-3/4) ÷ (1/9) x (-4/5) ÷ (3/5) simplifies to 15/2.
To solve the expression, we can follow the order of operations. Let's break down each step using the properties of operations and the rules for multiplying and dividing fractions.
Step 1: Multiply fractions
To multiply fractions, you multiply the numerators together and the denominators together. In this case, we need to multiply (8/9) and (-3/4):
(8/9) x (-3/4)
Multiplying the numerators gives us: 8 x (-3) = -24
Multiplying the denominators gives us: 9 x 4 = 36
Therefore, (8/9) x (-3/4) = -24/36
Step 2: Simplify the fraction
To simplify the fraction, we can reduce the numerator and the denominator by finding their greatest common factor (GCF). In this case, the GCF of -24 and 36 is 12:
-24/36 = (-24 ÷ 12) / (36 ÷ 12) = -2/3
So, (8/9) x (-3/4) simplifies to -2/3.
Step 3: Divide fractions
Now, let's move on to dividing fractions. To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction. Thus, we need to divide (-2/3) by (1/9):
(-2/3) ÷ (1/9)
Since dividing by a fraction is the same as multiplying by the reciprocal, we have:
(-2/3) x (9/1)
Multiplying the numerators gives us: -2 x 9 = -18
Multiplying the denominators gives us: 3 x 1 = 3
Thus, (-2/3) ÷ (1/9) simplifies to -18/3.
Step 4: Simplify the fraction
To simplify the fraction, we can reduce the numerator and the denominator by finding their greatest common factor (GCF). In this case, the GCF of -18 and 3 is 3:
-18/3 = (-18 ÷ 3) / (3 ÷ 3) = -6/1 = -6
So, (-2/3) ÷ (1/9) simplifies to -6.
Step 5: Divide fractions
Lastly, let's divide (-6) by (3/5):
(-6) ÷ (3/5)
To divide by a fraction, we can multiply the first number by the reciprocal of the fraction:
(-6) x (5/3)
Multiplying the numerators gives us: -6 x 5 = -30
Multiplying the denominators gives us: 1 x 3 = 3
Thus, (-6) ÷ (3/5) simplifies to -30/3.
Step 6: Simplify the fraction
To simplify the fraction, we can reduce the numerator and the denominator by finding their greatest common factor (GCF). In this case, the GCF of -30 and 3 is 3:
-30/3 = (-30 ÷ 3) / (3 ÷ 3) = -10/1 = -10
So, (-6) ÷ (3/5) simplifies to -10.
In conclusion, the expression (8/9) x (-3/4) ÷ (1/9) x (-4/5) ÷ (3/5) simplifies to -10.