Use the properties of operations and rules for multiplying and dividing to solve: (−3)÷(3/4)×(2/7)×(−5/16)÷(5/7)
To solve this problem, we will use the properties of operations and rules for multiplying and dividing.
First, let's simplify the expression step by step:
=(-3)/(3/4)×(2/7)×(-5/16)/(5/7) [Using the division rule a/b ÷ c/d = a/b × d/c]
=(-3) × (4/3) × (2/7) × (-5/16) × (7/5) [Multiplying fractions: (a/b) × (c/d) = (a × c) / (b × d)]
=(-3×4×2×(-5)×7) / (3×7×16×5) [Cancelling out common factors]
=(-3×4×2×(-1)×7) / (1×7×16×1) [Simplifying negative signs]
=(-3×4×2×(-1)×7) / (1×7×16)
=(-3×4×2×(-1)×1)/(1×16) [Cancelling out common factors]
=(-3×4×2×(-1)) / (16×1)
=(-24×2×(-1)) / 16
=(48/16)
=3
Therefore, (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) = 3.
To solve the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7), follow these steps:
Step 1: Simplify the division (-3) ÷ (3/4):
To divide by a fraction, you multiply by its reciprocal. The reciprocal of 3/4 is 4/3.
So, (-3) ÷ (3/4) can be rewritten as (-3) × (4/3).
Step 2: Multiply (-3) × (4/3):
Multiply the numerators (-3) × (4) to get -12, and multiply the denominators (1) × (3) to get 3.
So, (-3) × (4/3) equals -12/3 or -4.
Step 3: Simplify the multiplication -4 × (2/7) × (-5/16) ÷ (5/7):
Multiply the numerators (-4) × (2) × (-5) to get 40, and multiply the denominators (7) × (16) × (5) to get 560.
So, the expression becomes 40/560.
Step 4: Simplify 40/560:
Divide both the numerator and the denominator by their greatest common divisor, which is 40.
40 ÷ 40 = 1, and 560 ÷ 40 = 14.
So, 40/560 simplifies to 1/14.
Therefore, (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) equals 1/14.
To solve the given expression:
(-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7)
We will follow the order of operations, which states that we should perform operations inside parentheses first, then perform multiplication and division from left to right, and finally perform addition and subtraction from left to right.
First, let's simplify the division:
(-3) ÷ (3/4) = (-3) × (4/3)
To multiply two fractions, we simply multiply the numerators together and multiply the denominators together:
(-3) × (4/3) = (-3 × 4) / (1 × 3) = (-12) / 3
Next, let's simplify the other fractions:
(2/7) × (-5/16) ÷ (5/7) = (2 × -5) / (7 × 16) × (7/5) = (-10) / 112 × (7/5)
To multiply two fractions, we simply multiply the numerators together and multiply the denominators together:
(-10) / 112 × (7/5) = (-10 × 7) / (112 × 5) = (-70) / 560
Now, let's simplify the division:
(-12) / 3 ÷ (-70) / 560 = (-12) / 3 × (560/(-70))
To divide one fraction by another, we take the reciprocal of the second fraction and multiply the two fractions:
(-12) / 3 × (560/(-70)) = (-12) / 3 × (-560/70) = (-12 × -560) / (3 × 70)
Finally, let's simplify the multiplication:
(-12 × -560) / (3 × 70) = 6720 / 210 = 32
Therefore, (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) simplifies to 32.