Simplify negative 4 and 1 over 4 − negative 9 and 1 over 2

Question

(5 points)

Group of answer choices

5 and 1 over 4

negative 13 and 1 over 3

13 and 1 over 3

negative 5 and 1 over 4

Answer 1

To simplify the expression, we need to find the difference between negative 4 and 1/4 and negative 9 and 1/2.

Negative 4 and 1/4 can be written as -4 1/4.

Negative 9 and 1/2 can be written as -9 1/2.

To find the difference between these two numbers, we subtract them:

(-4 1/4) - (-9 1/2) = -4 1/4 + 9 1/2

To add these fractions, we need to find a common denominator. The least common denominator for 4 and 2 is 4. We can rewrite the fractions with this denominator:

(-4 1/4) = -4 1/4 * 2/2 = -9/4

(9 1/2) = 9 1/2 * 4/4 = 19/2

Now we can add the fractions:

-9/4 + 19/2

To add these fractions, we need to find a common denominator. The least common denominator for 4 and 2 is 4. We can rewrite the fractions with this denominator:

(-9/4) = -9/4 * 2/2 = -18/8

(19/2) = 19/2 * 4/4 = 76/8

Now we can add the fractions:

-18/8 + 76/8 = 58/8

To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 2:

58/8 = 29/4

So, -4 1/4 - (-9 1/2) simplifies to -29/4.

Therefore, the answer is negative 29 over 4, which corresponds to "negative 7 and 1/4" from the options given.