Use the properties of operations and rules for multiplying and dividing to solve: (−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7) (1 point)
To solve this expression, let's start by multiplying the fractions:
(-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7)
= (-3 × 5 × 7 × -5) / (5 × 16 × 12 × -3 × -5 × 7 × 16)
= (-105 × -5) / ( -/5 × -12 × -3 × -7)
= 525 / (5 × 12 × 3 × 7)
Now, let's simplify further:
525 / (5 × 12 × 3 × 7) = 525 / (5 × 36 × 7)
= 525 / (180 × 7)
= 525 / 1260
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 105:
525 / 1260 = (525 ÷ 105) / (1260 ÷ 105)
= 5 / 12
So, the solution is 5/12.
Use the properties of operations and rules for multiplying and dividing to solve: (−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)
To solve this expression, let's start by multiplying the fractions and numbers:
(-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4)
= (-2/1) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4) (change the whole numbers to fractions)
= (-2/1) × (1/5) × (3/2) × (-5/6) × (4/3)
Now, let's simplify:
= (-2 × 1 × 3 × -5 × 4) / (1 × 5 × 2 × 6 × 3 × 4)
= (-120) / (720)
= -120/720
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 120:
-120/720 = (-120 ÷ 120) / (720 ÷ 120)
= -1/6
So, the solution is -1/6.
Use the properties of operations and rules for multiplying and dividing to solve: (9)÷(5/4)×(7/9)×(−5)÷(7/2) (1 point) Responses 1,2258 Start Fraction 1,225 over 8 End Fraction −8 negative 8 8 8 −1,2258
Use the properties of operations and rules for multiplying and dividing to solve: (9)÷(5/4)×(7/9)×(−5)÷(7/2) (1 point) Responses 1,2258 Start Fraction 1,225 over 8 End Fraction −8 negative 8 8 8 −1,2258
To solve this expression, let's start by converting the division to multiplication by taking the reciprocal of the divisor:
(9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2)
= (9) × (4/5) × (7/9) × (-5) × (2/7)
Now, let's simplify:
= (9 × 4 × 7 × -5 × 2) / (5 × 9 × 7 × 2)
= (-9 × 4 × 7 × 5 × 2) / (5 × 9 × 7 × 2)
= (-9 × 4 × 5 × 2) / (5 × 9)
= (-18 × 5 × 2) / 9
= (-180) / 9
= -20
So, the solution is -20.
To solve the given expression \((-3/5)×(5/16)×(7/12)÷(-3/16)×(-5/7)\), we can simplify it step by step using the properties of operations and the rules for multiplying and dividing fractions.
Step 1: Start with the numerator multiplication first.
\((-3/5)×(5/16)×(7/12)÷(-3/16)×(-5/7)\)
Step 2: Multiply the numerators together.
\((-3×5×7)/5×16×12÷(-3/16)×(-5/7)\)
Step 3: Multiply the denominators together.
\((-3×5×7)/(5×16×12)÷(-3/16)×(-5/7)\)
Step 4: Simplify the numerator and denominator.
\(-105/(5×16×12)÷(-3/16)×(-5/7)\)
\(-105/960÷(-3/16)×(-5/7)\)
Step 5: For division, we can convert it into multiplication by taking the reciprocal of the second fraction.
\(-105/960×(16/-3)×(-5/7)\)
Step 6: Simplify the multiplication.
\(-105/960×(-16/3)×(-5/7)\)
Step 7: Multiply the numerators and denominators.
\((-105×-16×-5)/(960×3×7)\)
Step 8: Simplify the numerator and denominator.
\((-13440)/(20160)\)
Step 9: Divide the numerator by the denominator.
\(-13440/20160 = -2/3\)
Thus, the simplified form of the expression \((-3/5)×(5/16)×(7/12)÷(-3/16)×(-5/7)\) is \(-2/3\).