Use the properties of operations and rules for multiplying and dividing to solve: (−2)×(1/5)÷(2/3)×(−5/6)÷(3/4) (1 point)
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To solve this expression, we can use the properties of operations and rules for multiplying and dividing.
First, we need to simplify the expression by performing the multiplication and division from left to right.
To multiply -2 by 1/5, we multiply the numerators (-2 × 1) to get -2 and multiply the denominators (5 × 1) to get 5. So, -2 × 1/5 = -2/5.
Next, we divide -2/5 by 2/3. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 2/3 is 3/2. So, -2/5 ÷ 2/3 = -2/5 × 3/2.
To multiply fractions, we multiply the numerators (-2 × 3) to get -6 and multiply the denominators (5 × 2) to get 10. So, -2/5 × 3/2 = -6/10.
Next, we multiply -6/10 by -5/6. Again, we multiply the numerators (-6 × -5) to get 30 and multiply the denominators (10 × 6) to get 60. So, -6/10 × -5/6 = 30/60.
Finally, we divide 30/60 by 3/4. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 3/4 is 4/3. So, 30/60 ÷ 3/4 = 30/60 × 4/3.
To simplify 30/60 × 4/3, we can reduce 30/60 to 1/2. So, 1/2 × 4/3 = 4/6.
To further simplify 4/6, we can divide the numerator and denominator by their greatest common factor, which is 2. So, 4/6 = 2/3.
Therefore, (-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4) = 2/3.
Use the properties of operations and rules for multiplying and dividing to solve: (9)÷(5/4)×(7/9)×(−5)÷(7/2)
To solve this expression, we will use the properties of operations and rules for multiplying and dividing.
First, we will simplify the division of the number 9 by the fraction 5/4:
9 ÷ (5/4)
To divide a number by a fraction, we multiply the number by the reciprocal of the fraction. The reciprocal of 5/4 is 4/5.
Therefore, 9 ÷ (5/4) = 9 × (4/5) = 36/5.
Next, we need to multiply the fraction 36/5 by the fraction 7/9:
(36/5) × (7/9)
To multiply fractions, we multiply the numerators (36 × 7) to get 252 and multiply the denominators (5 × 9) to get 45.
Therefore, (36/5) × (7/9) = 252/45.
Next, we need to multiply the fraction 252/45 by the number -5:
(252/45) × (-5).
To multiply a fraction by a number, we simply multiply the numerator of the fraction by the number. In this case, we multiply 252 by -5.
Therefore, (252/45) × (-5) = -1260/45.
Finally, we need to divide the fraction -1260/45 by the fraction 7/2:
(-1260/45) ÷ (7/2).
To divide a fraction by another fraction, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 7/2 is 2/7.
Therefore, (-1260/45) ÷ (7/2) = (-1260/45) × (2/7) = -2520/315.
To simplify the fraction -2520/315, we can divide both the numerator and denominator by their greatest common divisor, which is 45.
Therefore, -2520/315 = -56/7 = -8.
Therefore, (9)÷(5/4)×(7/9)×(−5)÷(7/2) = -8.
To solve the given expression, we can use the properties of operations and rules for multiplying and dividing.
Step 1: Simplify the numerator and denominator separately.
Numerator:
(-2) × (1/5) × (-5/6) = (2/1) × (1/5) × (-5/6)
= (2 × 1 × -5) / (1 × 5 × 6)
= -10/30
= -1/3
Denominator:
(2/3) × (3/4) = (2 × 3) / (3 × 4)
= 6/12
= 1/2
Step 2: Divide the numerator by the denominator.
(-1/3) ÷ (1/2) = (-1/3) × (2/1)
= (-1 × 2) / (3 × 1)
= -2/3
Therefore, the solution to the given expression is -2/3.
To solve the expression (-2)×(1/5)÷(2/3)×(-5/6)÷(3/4), we can follow the order of operations (PEMDAS/BODMAS) which states that we should perform calculations inside parentheses/brackets first, then exponents/powers, then multiplication and division from left to right, and finally addition and subtraction from left to right.
Let's break down the expression step by step:
1. Start by dealing with the negative signs. Multiply the first two negative signs (-2)×(1/5), which gives us -2/5.
2. For the next step, we divide -2/5 by (2/3) and multiply the result by (-5/6).
Remember that division is equivalent to multiplying by the reciprocal. To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
-2/5 ÷ (2/3) can be rewritten as -2/5 × (3/2), taking the reciprocal of (2/3) which is (3/2) or (3/2) ÷ 1.
When multiplying fractions, multiply the numerators together to get the new numerator and multiply the denominators together to get the new denominator.
(-2/5) × (3/2) gives us (-2×3) / (5×2) which simplifies to -6/10 or -3/5.
3. Finally, we have to divide (-3/5) multiplied by (3/4).
Again, we can rewrite (-3/5) ÷ (3/4) as (-3/5) × (4/3) or (-3×4) / (5×3) which simplifies to -12/15 or -4/5.
Thus, the solution to the expression (-2)×(1/5)÷(2/3)×(-5/6)÷(3/4) is -4/5.