Use the properties of operations and rules for multiplying and dividing to solve:
(−2)×(15)÷(23)×(−56)÷(34)
(1 point)
Responses
−23
negative Start Fraction 2 over 3 End Fraction
23
Start Fraction 2 over 3 End Fraction
−16
negative Start Fraction 1 over 6 End Fraction
16
To solve the expression (-2) × (15) ÷ (23) × (-56) ÷ (34), we will follow the order of operations.
First, we'll multiply -2 and 15, which equals -30.
Now, we'll divide -30 by 23, which gives approximately -1.304.
Next, we'll multiply -1.304 by -56, which equals approximately 72.864.
Finally, we'll divide 72.864 by 34, which gives approximately 2.144.
Therefore, the solution is approximately 2.144.
Use the properties of operations and rules for multiplying and dividing to solve:
(−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)
(1 point)
Responses
−2/3
negative Start Fraction 2 over 3 End Fraction
2/3
Start Fraction 2 over 3 End Fraction
−1/6
negative Start Fraction 1 over 6 End Fraction
1/6
To solve the expression (-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4), we follow the order of operations.
First, we'll multiply -2 and 1/5. The product is -2/5.
Next, we'll divide -2/5 by 2/3. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So, we multiply -2/5 by 3/2. The result is -6/10, which simplifies to -3/5.
Then, we'll multiply -3/5 by -5/6. When multiplying fractions, we multiply the numerators together and the denominators together. So, (-3/5) * (-5/6) = (15/30), which simplifies to 1/2.
Finally, we'll divide 1/2 by 3/4. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So, we multiply 1/2 by 4/3. The result is 4/6, which simplifies to 2/3.
Therefore, the solution is 2/3.
Question
Use the properties of operations and rules for multiplying and dividing to solve:
(9)÷(54)×(79)×(−5)÷(72)
(1 point)
Responses
1,2258
Start Fraction 1,225 over 8 End Fraction
8
8
−8
To solve the expression (9) ÷ (54) × (79) × (-5) ÷ (72), we will follow the order of operations.
First, we'll divide 9 by 54, which equals approximately 0.1667.
Next, we'll multiply 0.1667 by 79, which gives approximately 13.175.
Now, we'll multiply 13.175 by -5, which equals -65.875.
Finally, we'll divide -65.875 by 72, which gives approximately -0.9151.
Therefore, the solution is approximately -0.9151.
Question
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
8
−8
To solve the expression (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2), we will follow the order of operations.
First, we'll divide 9 by 5/4. To divide by a fraction, we multiply by its reciprocal. So, (9) divided by (5/4) is equivalent to (9) multiplied by (4/5). This gives us 36/5.
Next, we'll multiply 36/5 by 7/9. To multiply fractions, we multiply the numerators and denominators separately. (36/5) multiplied by (7/9) gives us (252/45).
Now, we'll multiply (252/45) by -5, which gives us (-1260/45).
Finally, we'll divide (-1260/45) by 7/2. To divide by a fraction, we multiply by its reciprocal. So, we'll multiply (-1260/45) by (2/7). This gives us (-2520/315), which simplifies to (-8/1).
Therefore, the solution is -8.
Solve this multi-step problem. A runner completes 1/4 of a 5-mile race every 8 minutes. At the same pace, how far can the runner go in 16 minutes?(1 point)
Responses
1/10 mile
Start Fraction 1 over 10 End Fraction mile
2/12 miles
2 Start Fraction 1 over 2 End Fraction miles
1/60 miles
1/60 miles
1/8 mile
To calculate how far the runner can go in 16 minutes at the same pace, we need to multiply their speed (1/4 mile every 8 minutes) by the number of sets of 8 minutes in 16 minutes.
Dividing 16 minutes by 8 minutes gives us 2 (16/8 = 2).
Now, if the runner completes 1/4 mile every 8 minutes, in 16 minutes they will cover 1/4 mile × 2 = 2/4 mile.
Simplifying 2/4 mile, we get 1/2 mile.
Therefore, the runner can go 1/2 mile in 16 minutes at the same pace.
Solve this multi-step problem. A runner completes 1/4 of a 5-mile race every 8 minutes. At the same pace, how far can the runner go in 16 minutes?(1 point)
Responses
1/10 mile
Start Fraction 1 over 10 End Fraction mile
2/12 miles
2 Start Fraction 1 over 2 End Fraction miles
160 miles
160 miles
1/8 mile