Use the properties of operations and rules for multiplying and dividing to solve: (9)÷(5/4)×(7/9)×(−5)÷(7/2) (1 point) Responses −8 negative 8 1,2258 Start Fraction 1,225 over 8 End Fraction −1,225
To solve the expression (9)÷(5/4)×(7/9)×(−5)÷(7/2), we can use the properties of operations and rules for multiplying and dividing:
Step 1: Simplify the expression inside the parentheses by dividing 9 by (5/4):
(9) ÷ (5/4) = 9 × (4/5) = 36/5
Step 2: Simplify the expression by multiplying the fractions 36/5 and 7/9:
(36/5) × (7/9) = (36 × 7) / (5 × 9) = 252/45 (or 28/5 in simplified form)
Step 3: Simplify the expression by multiplying the fraction 28/5 and -5:
(28/5) × (-5) = (28 × -5) / 5 = -140/5 (or -28 in simplified form)
Step 4: Simplify the expression by dividing -140/5 by (7/2):
(-140/5) ÷ (7/2) = (-140/5) × (2/7) = (-140 × 2) / (5 × 7) = -280/35 (or -8 in simplified form)
Therefore, the answer to the expression (9)÷(5/4)×(7/9)×(−5)÷(7/2) is -8 or negative 8.
To solve the expression `(9)÷(5/4)×(7/9)×(−5)÷(7/2)`, we follow the properties of operations and rules for multiplying and dividing step by step:
Step 1: Start with division:
• Divide 9 by 5/4:
9 ÷ (5/4)
To divide by a fraction, we multiply by its reciprocal:
9 × (4/5)
The 5 in the denominator cancels with the 5 in the numerator:
= 9 × (4/1)
= 36
Step 2: Continue with multiplication:
• Multiply the answer from step 1 by 7/9:
36 × (7/9)
Now we multiply the numerators together and denominators together:
= (36 × 7) / (1 ×9)
= 252/9
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which in this case is 9:
= 28/1
= 28
Step 3: Multiply by -5:
• Multiply the answer from step 2 by -5:
28 × (-5)
= -140
Step 4: Finally, divide by 7/2:
• Divide -140 by 7/2:
-140 ÷ (7/2)
To divide by a fraction, we multiply by its reciprocal:
-140 × (2/7)
= (-140 × 2) / 7
= -280/7
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which in this case is 7:
= -40
Therefore, the value of the expression (9)÷(5/4)×(7/9)×(−5)÷(7/2) is -40.
To solve the expression (9)÷(5/4)×(7/9)×(-5)÷(7/2), we need to follow the properties of operations and rules for multiplying and dividing. Let's break it down step by step:
Step 1: Simplify the expression inside the parentheses.
(9) ÷ (5/4) = 9 × (4/5) = 36/5
Step 2: Multiply the fractions:
(36/5) × (7/9) = (36 × 7) / (5 × 9) = 252/45
Step 3: Multiply by -5:
(252/45) × (-5) = (252 × -5) / 45 = -1260/45
Step 4: Divide by the fraction:
-1260/45 ÷ (7/2) = -1260/45 × (2/7)
Step 5: Multiply the fractions:
(-1260/45) × (2/7) = (-1260 × 2) / (45 × 7) = -2520/315
Step 6: Simplify the fraction:
-2520/315 can be simplified by dividing both numerator and denominator by their greatest common divisor, which is 315:
-2520 ÷ 315 = -8
So, the answer to the expression (9)÷(5/4)×(7/9)×(-5)÷(7/2) is -8.