6. Paige decided to paint 4/5
of the rooms in her home last year. By the end of the year, Paige completed 2/3
of the rooms. How much of Paige’s home was painted last year ?(1 point)
Responses
2/3
2/9
6/15
8/15
1/3
To find out how much of Paige's home was painted last year, we need to add the fractions representing the rooms she painted in the first and second parts of the year.
First, we know that Paige painted 4/5 of the rooms in total.
Then, we need to find out how much of the remaining 1/5 of the rooms she painted by the end of the year, which is represented by 2/3.
To add the fractions, we need to have a common denominator, which in this case is 15.
4/5 = 12/15 (multiply the numerator and denominator by 3)
2/3 = 10/15 (multiply the numerator and denominator by 5)
Now, we can add the two fractions together:
12/15 + 10/15 = 22/15
Therefore, Paige painted 22/15 of her home last year, which is equivalent to 8/15 of her home.
The correct answer is 8/15.
7. What is 38÷2
?(1 point)
Responses
1/4
5/13
3/16
1/13
To find the value of 38 ÷ 2, we simply divide 38 by 2:
38 ÷ 2 = 19
Therefore, the answer is 19.
None of the given responses (1/4, 5/13, 3/16, 1/13) are correct.
7. What is 3/8÷2
?(1 point)
Responses
1/4
5/13
3/16
1/13
To find the value of (3/8) ÷ 2, we divide 3/8 by 2:
(3/8) ÷ 2 = (3/8) x (1/2)
= (3/8) * (1/2)
= 3/16
Therefore, the answer is 3/16.
The correct response is 3/16.
2/13÷2/5
(1 point)
Responses
14/15
4/5
5 5/6
9/16
To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction:
(2/13) ÷ (2/5) = (2/13) * (5/2)
To multiply fractions, we multiply the numerators together and the denominators together:
(2/13) * (5/2) = (2 * 5) / (13 * 2) = 10/26
This fraction can be simplified by dividing the numerator and denominator by their greatest common divisor, which is 2:
10/26 = 5/13
Therefore, (2/13) ÷ (2/5) = 5/13.
The correct response is 5/13.
Incorrect
2 1/3÷2/5
14/15
4/5
5 5/6
9/16
To divide a mixed number by a fraction, we first convert the mixed number to an improper fraction.
2 1/3 can be converted to an improper fraction as follows:
2 1/3 = (2 * 3 + 1) / 3 = 7/3
Now, we can divide 7/3 by 2/5:
(7/3) ÷ (2/5) = (7/3) * (5/2)
To multiply fractions, we multiply the numerators together and the denominators together:
(7/3) * (5/2) = (7 * 5) / (3 * 2) = 35/6
The fraction 35/6 can be simplified by dividing the numerator and denominator by their greatest common divisor, which is 1:
35/6 = 35/6
Thus, (2 1/3) ÷ (2/5) = 35/6.
None of the given responses (14/15, 4/5, 5 5/6, 9/16) are correct for this division.