Use the properties of operations and rules for multiplying and dividing to solve:
(−3)÷(3/4)×(2/7)×(−5/16)÷(5/7) an a fraction
To solve this expression, we can use the properties of operations and rules for multiplying and dividing fractions.
First, let's simplify the given expression step by step:
1. (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7)
2. When we divide a number by a fraction, we can multiply the number by the reciprocal of the fraction. Therefore, (-3) ÷ (3/4) can be written as (-3) × (4/3).
So, the expression becomes:
(-3 × 4/3) × (2/7) × (-5/16) ÷ (5/7)
3. Now, let's multiply the fractions:
((-3 × 4) / 3) × (2/7) × (-5/16) ÷ (5/7)
=(-12/3) × (2/7) × (-5/16) ÷ (5/7)
4. Simplify each multiplication separately:
= (-4) × (2/7) × (-5/16) ÷ (5/7)
=(-8/7) × (-5/16) ÷ (5/7)
5. Divide the fractions:
=(-8/7) × (-5/16) × (7/5)
6. Simplify each multiplication separately:
= (-8 × -5) / (7 × 16) × (7/5)
=(40) / (112) × (7/5)
7. Simplify the fraction:
= 40/112 × 7/5
= (40 × 7) / (112 × 5)
= 280 / 560
8. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 40:
= 7/14
= 1/2
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)
(1 point)
To solve this expression, we can use the properties of operations and rules for multiplying and dividing fractions.
Let's simplify the given expression step by step:
1. (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5)
2. When multiplying fractions, we multiply the numerators and multiply the denominators. Therefore, (8/9) × (-3/4) can be written as (8 × -3) / (9 × 4).
So, the expression becomes:
((-8 × 3) / (9 × 4)) ÷ (1/9) × (-4/5) ÷ (3/5)
3. Simplify the multiplication:
=(-24) / (36) ÷ (1/9) × (-4/5) ÷ (3/5)
4. Divide the fractions:
=(-24) / (36) × (9/1) × (-4/5) ÷ (3/5)
5. Simplify the multiplication:
=(-24 × 9) / (36 × 1) × (-4/5) ÷ (3/5)
=(-216) / (36) × (-4/5) ÷ (3/5)
6. Divide the fractions:
=(-216) / (36) × (5/4) ÷ (3/5)
7. Simplify the multiplication:
=(-216 × 5) / (36 × 4) ÷ (3/5)
=(-1080) / (144) ÷ (3/5)
8. Divide the fractions:
=(-1080) / (144) × (5/3)
9. Simplify the multiplication:
=(-1080 × 5) / (144 × 3)
=(-5400) / (432)
10. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 216:
=(-25) / (2)
Therefore, (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5) simplifies to -25/2.
wrong
Apologies for the incorrect response. Let's correct the solution:
To solve the expression (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5), we can use the properties of operations and rules for multiplying and dividing fractions.
Let's simplify the expression step by step:
1. Multiply the fractions:
(8/9) × (-3/4) = (8 × -3) / (9 × 4) = -24/36
2. Divide the fractions:
(-24/36) ÷ (1/9) = (-24/36) × (9/1) = (-24 × 9) / (36 × 1) = -216/36
3. Multiply the fractions:
(-216/36) × (-4/5) = (-216 × -4) / (36 × 5) = 864/180
4. Divide the fractions:
(864/180) ÷ (3/5) = (864/180) × (5/3) = (864 × 5) / (180 × 3) = 4320/540 = 8
Therefore, (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5) simplifies to 8.
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, we can use the properties of operations and rules for multiplying and dividing fractions.
Let's simplify the given expression step by step:
1. Multiply the fractions:
(−3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7)
=(−3 × 5 × 7) / (5 × 16 × 12) ÷ (−3 × 16 × −5) / (7)
= (−105) / (960) ÷ (240) / (7)
2. Divide the fractions:
(−105/960) ÷ (240/7)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(−105/960) × (7/240)
=(−105 × 7) / (960 × 240)
= (−735) / 230400
3. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 15:
(−735/230400) ÷ (15/15)
= (−735 × 15) / (230400 × 15)
= (−11025) / 345600
Therefore, (−3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7) simplifies to −11025/345600.
wrong
Apologies for the mistake. Let's correct the solution:
To solve the expression (−3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7), we can use the properties of operations and rules for multiplying and dividing fractions.
Let's simplify the expression step by step:
1. Multiply the fractions:
(−3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7)
= (−3 × 5 × 7) / (5 × 16 × 12) ÷ (−3 × 16 × −5) / 7
= (−105) / (960) ÷ (240) / 7
2. Divide the fractions:
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(−105/960) ÷ (240/7) = (−105/960) × (7/240)
=(-105 × 7) / (960 × 240)
= -735 / 230400
However, the prompt states that the answer should be in fractional form. So, we need to simplify the fraction further:
-735 can be expressed as -1 * 3 * 5 * 7.
230400 can be expressed as 2^7 * 3^2 * 5^2.
Simplifying the fraction further, we can cancel out common factors between the numerator and denominator:
-1 * 3 * 5 * 7 / (2^7 * 3^2 * 5^2)
= -1 * 3 * 7 / (2^7 * 3 * 5)
= -1 * 3 * 7 / (2^6 * 5)
= (-3 * 7) / (2^6 * 5)
= -21 / (64 * 5)
= -21 / 320
Therefore, (−3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7) simplifies to -21/320.