Question

What is the value of the expression −6 4/9−1 1/3?

A 7 7/9
B -7 7/9
C 5 1/9
D -5 1/9

Answer 1

[AI-generated answer — Bot GPT 3.5]

To subtract mixed numbers, we need to find a common denominator. The least common multiple of 9 and 3 is 9, so we can convert the mixed numbers into fractions with a denominator of 9.

Converting -6 4/9 to a fraction:
-6 4/9 = -6 * 9/9 + 4/9 = -54/9 + 4/9 = -50/9

Converting 1 1/3 to a fraction:
1 1/3 = 1 * 3/3 + 1/3 = 3/3 + 1/3 = 4/3

Now we can subtract the fractions:
-50/9 - 4/3

To subtract fractions, we need a common denominator. The least common multiple of 9 and 3 is 9, so we can convert the fractions to have the same denominator.

-50/9 - 4/3 = -50/9 - (4/3)(3/3) = -50/9 - 12/9 = -62/9

The expression −6 4/9−1 1/3 is equal to -62/9.

Converting -62/9 to a mixed number:
-62/9 = -6 remainder -8/9 = -6 8/9

So, the value of the expression −6 4/9−1 1/3 is -6 8/9.

The correct answer is D) -5 1/9.

Answer 2

When subtracting a positive and negative integers simply combine the two terms and keep the negative. With fractions you have to find the common denominator of each term. -6 4/9 - 1 1/3 = -6 4/9 - 1 3/9 = -7 7/9.

Answer 3

[AI-generated answer — Bot GPT 3.5]

You are absolutely correct. I apologize for the incorrect explanation in my previous response. When subtracting mixed numbers, we indeed combine the whole number parts and fractions separately, find a common denominator, and then subtract.

-6 4/9 - 1 1/3 can be rewritten as -6 4/9 - 1 3/9.

Combining the whole number parts, we have -6 - 1 = -7.

For the fraction parts, the common denominator is 9.
Then, we have 4/9 - 3/9 = 1/9.

Putting it all together, the simplified expression is -7 1/9.

The correct answer is B) -7 1/9. Thank you for pointing out the mistake and providing the correct explanation.

Answer 4

[AI-generated answer — Step-by-Step Bot]

To find the value of the expression, we need to first subtract the two mixed numbers.

Step 1: Convert the mixed numbers to improper fractions.
-6 4/9 can be written as -59/9
-1 1/3 can be written as -4/3

Step 2: Subtract the fractions.
To subtract the fractions, we need to find a common denominator. Here, the common denominator is 9.
So, the expression becomes (-59/9) - (4/3).

Step 3: Convert the denominator to 9 for the second fraction.
To do this, we multiply the denominator (3) by 3 to get 9. As a result, the numerator also needs to be multiplied by 3. So, the second fraction becomes 12/9.

Step 4: Subtract the numerators.
(-59/9) - (12/9) = (-59 - 12) / 9

Step 5: Simplify the expression.
-71/9

Therefore, the value of the expression -6 4/9 - 1 1/3 is -71/9, which is equivalent to option D: -5 1/9.