Use the properties of operations and rules for multiplying and dividing to solve:
(−3)÷(34)×(27)×(−516)÷(57)
To solve the expression (-3) ÷ (34) × (27) × (-516) ÷ (57), we can apply the properties of operations and the rules for multiplying and dividing:
First, let's start with the division part of the expression: (-3) ÷ (34).
Dividing a negative number by a positive number results in a negative quotient.
So, (-3) ÷ (34) = -3/34.
Next, let's move on to the multiplication part: (-3/34) × (27) × (-516) ÷ (57).
When multiplying or dividing negative and positive numbers, we follow these rules:
- A negative number times a positive number is negative.
- A positive number times a negative number is negative.
- A negative number divided by a negative number is positive.
- A positive number divided by a negative number is negative.
Applying these rules, we can simplify the expression step by step:
(-3/34) × (27) × (-516) ÷ (57)
= (-3/34) × (-516) × (27) ÷ (57) (Rearranging the terms)
= ((-3) × (-516) × (27)) ÷ (34 × 57) (Remember that division takes precedence over multiplication)
Now, let's calculate each part separately:
(-3) × (-516) × (27) = 39,816 (Multiplying the numbers)
(34 × 57) = 1,938 (Multiplying the numbers)
Substituting these values back into the expression, we have:
39,816 ÷ 1,938
= 20.53 (Dividing the numbers)
Therefore, (-3) ÷ (34) × (27) × (-516) ÷ (57) simplifies to 20.53.
Use the properties of operations and rules for multiplying and dividing to solve:
(−3)÷(3/4)×(2/7)×(−5/16)÷(5/7)
To solve the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7), we can apply the properties of operations and the rules for multiplying and dividing:
First, let's start with the division part of the expression: (-3) ÷ (3/4).
Dividing by a fraction is the same as multiplying by its reciprocal.
So, (-3) ÷ (3/4) = (-3) × (4/3) = (-12/3) = -4.
Next, let's move on to the multiplication part: -4 × (2/7) × (-5/16) ÷ (5/7).
When multiplying or dividing negative and positive numbers, we follow these rules:
- A negative number times a positive number is negative.
- A positive number times a negative number is negative.
- A negative number divided by a negative number is positive.
- A positive number divided by a negative number is negative.
Applying these rules, we can simplify the expression step by step:
-4 × (2/7) × (-5/16) ÷ (5/7)
= -4 × 2/7 × (-5/16) × 7/5 (Rearranging and multiplying the terms)
Now, let's calculate each part separately:
-4 × 2/7 × (-5/16) × 7/5
= -8/7 × (-5/16) × 7/5 (Multiplying the numbers)
= -40/112 × 7/5 (Simplifying fractions)
= -280/560 (Multiplying the numbers)
= -1/2 (Simplifying the fraction)
Therefore, (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) simplifies to -1/2.
Use the properties of operations and rules for multiplying and dividing to solve:
(8/9)×(−3/4)÷(1/9)×(−4/5)÷(3/5)
To solve the expression (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5), we can apply the properties of operations and the rules for multiplying and dividing:
First, let's start with the multiplication and division parts of the expression:
(8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5)
Multiplying fractions is done by multiplying the numerators together and the denominators together:
= (8 × -3) / (9 × 4) ÷ (1 × -4) / (9 × 5) ÷ (3 × 5)
Simplifying the numerators and denominators, we have:
= (-24) / (36) ÷ (-4) / (45) ÷ (15)
Dividing fractions is done by multiplying the first fraction by the reciprocal of the second fraction:
= (-24) / (36) × (45) / (-4) × (15)
= (-1) / (1) × (15)
= -15
Therefore, (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5) simplifies to -15.
Use the properties of operations and rules for multiplying and dividing to solve:
(−3/5)×(5 1/6)×(7 1/2)÷(−3 1/6)×(−5/7)
To solve the expression (-3/5) × (5 1/6) × (7 1/2) ÷ (-3 1/6) × (-5/7), we can apply the properties of operations and the rules for multiplying and dividing:
Let's begin by converting the mixed numbers to improper fractions:
5 1/6 = (5 * 6 + 1) / 6 = 31/6
7 1/2 = (7 * 2 + 1) / 2 = 15/2
-3 1/6 = (-3 * 6 + 1) / 6 = -19/6
Now, let's simplify the expression using the rules for multiplication and division:
(-3/5) × (31/6) × (15/2) ÷ (-19/6) × (-5/7)
Multiplying fractions is done by multiplying the numerators together and the denominators together:
= (-3 * 31 * 15 * -5) / (5 * 6 * 2 * 19 * 7 * 6)
= 1395 / 99720
Simplifying this fraction is not possible since there are no common factors between the numerator and denominator.
Therefore, the expression (-3/5) × (5 1/6) × (7 1/2) ÷ (-3 1/6) × (-5/7) remains as 1395/99720.