What is 4.65 converted to a fraction? The answer should be given in simplest form
a. 4 12/20
b. 4 65/100
c. 4 6/5
d. 4/65
The answer is c. 4 6/5
Use long division to convert 2 7/16 to a decimal
a. 0.4375
b. 2.4375
c. 2.716
d. 2.2857
To convert 2 7/16 to a decimal using long division, follow these steps:
1. Rewrite the mixed number as an improper fraction:
2 7/16 = (2 * 16 + 7) / 16 = 39/16
2. Perform long division: Divide the numerator (39) by the denominator (16) and write the quotient with a decimal point in front.
.24375 (The quotient starts with 2)
16 | 39.00
- 32
----
70
- 64
----
60
- 48
----
120
- 112
----
80
- 80
----
0
3. The decimal representation of 2 7/16 is 2.4375.
Therefore, the correct answer is b. 2.4375.
Use long division to convert 6 7/15 to a decimal
a. 6.47
b. 0.46
c. 6.14285
d. 6.715
To convert 6 7/15 to a decimal using long division, follow these steps:
1. Rewrite the mixed number as an improper fraction:
6 7/15 = (6 * 15 + 7) / 15 = 97/15
2. Perform long division: Divide the numerator (97) by the denominator (15) and write the quotient with a decimal point in front.
.6.47 (The quotient starts with 6)
15 | 97.00
- 90
----
70
- 60
----
100
- 90
----
10
0
3. The decimal representation of 6 7/15 is 6.47.
Therefore, the correct answer is a. 6.47.
A pilot is flying an airplane due to strong winds the pilot decides to fly 4000 feet lower to avoid excessive turbulence it takes the pilot 3.5 minutes to make this adjustment interpret the quotient to describe the rate of change in the planes altitude give your answer to the nearest hundredth and remember the plane is descending
The quotient that beat represents the rate of change in the planes altitude is (Blank) feet/minute
To find the rate of change in the plane's altitude, we divide the change in altitude (4000 feet) by the time it takes to make the adjustment (3.5 minutes).
Rate of change in altitude = Change in altitude / Time = 4000 feet / 3.5 minutes
Calculating this division, we get:
Rate of change in altitude ≈ 1142.86 feet/minute
Rounding to the nearest hundredth, the rate of change in the plane's altitude is approximately 1142.86 feet/minute.
Problem 2: Simplify the expression
2(a -3) + 4b - 2(a -b -3) + 5
To simplify the expression, we apply the distributive property and combine like terms:
2(a - 3) + 4b - 2(a - b - 3) + 5
Multiplying 2 by each term inside the first set of parentheses:
2a - 6 + 4b - 2(a - b - 3) + 5
Now, distribute the -2 to the terms inside the second set of parentheses:
2a - 6 + 4b - 2a + 2b + 6 + 5
Combining like terms:
(2a - 2a) + (4b + 2b) + (-6 + 6 + 5)
The terms 2a and -2a cancel each other out, and the terms 4b and 2b can be combined:
0 + 6b + 5
Finally, combining the remaining terms:
6b + 5
Thus, the expression 2(a - 3) + 4b - 2(a - b - 3) + 5 simplifies to 6b + 5.