Reggie writes the expression m + 8 × (2/3). Which expression is equivalent to the one Reggie writes?
A) (m+8)(2 ÷ 3)
B) 8 + m(2 ÷ 3)
C) m + (8×3 ÷ 2)
D) (8×2 ÷ 3) + m
D looks good to me since 2÷3 = 2/3
and multiplication is commutative
If you expand the others you can clearly see that they do not match
A) (m+8)(2 ÷ 3) = m*(2/3) + 8*(2/3)
B) 8 + m(2 ÷ 3) = 8 + m(2/3)
C) m + (8×3 ÷ 2) = m + 8(3/2)
THANK YOU!
thanks
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Reggie writes the expression m + 8 × (2/3). Which expression is equivalent to the one Reggie writes?
Responses
A (m+8)(2 ÷ 3)(m+8)(2 ÷ 3)
B (8×2 ÷ 3) + m(8×2 ÷ 3) + m
C 8 + m(2 ÷ 3)8 + m(2 ÷ 3)
D m + (8×3 ÷ 2)
The correct answer is D) m + (8×3 ÷ 2).
To simplify m + 8 × (2/3), we can first multiply 8 and 2/3 together:
8 × (2/3) = 16/3
So the expression becomes:
m + 16/3
To write this in a more common fraction form, we can convert the mixed number to an improper fraction:
16/3 = 5 1/3
So the expression is equivalent to:
m + 5 1/3
Now we can simplify the mixed number to a fraction:
m + (5×3 + 1)/3 = m + 16/3
So the answer is D) m + (8×3 ÷ 2) or m + 16/3.
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Solve
Responses
A AA
B BB
C DD
D C
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A grocery clerk put only packages of flour tortillas and packages of corn tortillas on a shelf. The ratio of the number of flour tortillas to the number of packages on the shelf was 5 to 9. Which number could be the number of packages of corn tortillas the clerk put on the shelf?
Responses
A 2323
B 1414
C 3232
D 1818
Let's call the number of packages of flour tortillas "5x" and the number of total packages on the shelf "9x", since we know that the ratio of flour tortillas to the total is 5 to 9.
This means that the number of packages of corn tortillas is:
9x - 5x = 4x
So the number of packages of corn tortillas must be a multiple of 4.
Out of the given choices, only 14 and 32 are multiples of 4.
Let's try 14 as the answer. If there are 14 packages of corn tortillas, then the total number of packages on the shelf is 5x + 14, and this must be a multiple of 9.
5x + 14 = 9n
where n is some integer. Rearranging this equation:
5x = 9n - 14
The right hand side is always even, so the left hand side must also be even. But 5x is only even if x is even. Therefore, n must be even as well.
If we try n = 2, then we get:
5x = 9(2) - 14 = 4
which doesn't work, since x must be a positive integer.
Therefore, 14 cannot be the answer.
Now let's try 32 as the answer. If there are 32 packages of corn tortillas, then the total number of packages on the shelf is 5x + 32, and this must be a multiple of 9.
5x + 32 = 9n
where n is some integer. Rearranging this equation:
5x = 9n - 32
The right hand side is always odd, so the left hand side must also be odd. But 5x is odd only if x is odd. Therefore, n must be odd as well.
If we try n = 3, then we get:
5x = 9(3) - 32 = 1
which works if x = 1/5. However, x must be a positive integer, so this doesn't work.
Therefore, 32 cannot be the answer either.
Since neither 14 nor 32 works, the answer is none of the above.