Use the properties of operation and rules for multiplying and dividing to solve what is 8/9×-3/4÷1/9×-4/5÷3/5
To solve the expression 8/9 × -3/4 ÷ 1/9 × -4/5 ÷ 3/5 using the properties of operations and rules for multiplying and dividing, we follow the order of operations.
First, we simplify within the parentheses by performing the multiplication and division from left to right:
8/9 × -3/4 ÷ 1/9 × -4/5 ÷ 3/5
= (8/9 × -3/4) ÷ 1/9 × -4/5 ÷ 3/5
= -24/36 ÷ 1/9 × -4/5 ÷ 3/5
= -2/3 ÷ 1/9 × -4/5 ÷ 3/5
= (-2/3) × (9/1) × (1/-4) × (5/3)
Next, we simplify the multiplication and division from left to right:
(-2/3) × (9/1) × (1/-4) × (5/3)
= -2 × 9 × 1 × 5 / 3 × 1 × -4 × 3
= -2 × 9 × 1 × 5 / (3 × 1 × -4 × 3)
= -90 / -36
Finally, we simplify the fraction:
-90 / -36 = 5/2
Therefore, 8/9 × -3/4 ÷ 1/9 × -4/5 ÷ 3/5 simplifies to 5/2.
To solve the expression 8/9 × -3/4 ÷ 1/9 × -4/5 ÷ 3/5, we need to follow the order of operations and apply the rules for multiplying and dividing fractions.
Step 1: Multiply the numerator and denominator of each fraction separately.
8/9 × -3/4 ÷ 1/9 × -4/5 ÷ 3/5 becomes:
(8 × -3)/(9 × 4) ÷ (1 × -4)/(9 × 5) ÷ (3 × 5)/(5 × 1)
Step 2: Simplify each multiplication operation.
-24/36 ÷ -4/45 ÷ 15/5
Step 3: Multiply the reciprocal of each fraction after the division sign.
-24/36 × 45/-4 × 5/15
Step 4: Simplify each multiplication operation.
-1/1 × -45/1 × 1/3
Step 5: Multiply the numerators and denominators.
-1 × -45 × 1/1 × 1 × 3
Step 6: Simplify the multiplication operation.
45/3 = 15
Therefore, the expression 8/9 × -3/4 ÷ 1/9 × -4/5 ÷ 3/5 simplifies to 15.
To solve the expression 8/9 × -3/4 ÷ 1/9 × -4/5 ÷ 3/5, we need to follow the order of operations, specifically the rules for multiplying and dividing fractions.
Step 1: Multiplication and Division
First, let's focus on the multiplication and division operations.
8/9 × -3/4 = (-3/4) × (8/9) = -24/36 = -2/3
Next, we have the division:
-2/3 ÷ 1/9 = (-2/3) ÷ (1/9) = (-2/3) × (9/1) = -18/3 = -6
Finally, we have one more division operation:
-6 ÷ 3/5 = (-6) ÷ (3/5) = (-6) × (5/3) = -30/3 = -10
Hence, the value of the expression 8/9 × -3/4 ÷ 1/9 × -4/5 ÷ 3/5 is -10.