show the work for these problems 4 2/3-1 1/6 = and 10 1/2-6 2/5=

4 2/3-1 1/6= 4/6-1/6= (3 3/6) 10 1/2-6 2/5= 5/10-4/10= (4 1/10)

4 2/3-1 1/6

= 14/3 - 7/6
= 28/6 - 7/6
= 21/6
= 7/2 or 3 1/2

Your second has the correct answer, but is nonsense in between
10 1/2-6 2/5
= 21/2 - 32/5 , ( LCD = 10 )
= 105/10 - 64/10
= 41/10 or 4 1/10

PS, I always consider an "improper" fraction in lowest terms a better fraction than the mixed fraction.
A mixed fraction in most cases is not usable and has to be converted into an improper fraction anyway.
I hope that someday they will come up with a better name for "improper" fraction, maybe something like "good fraction"

Sure! I can help you with these problems and show you the step-by-step work.

Let's start with the problem:
4 2/3 - 1 1/6

Step 1: Convert the mixed numbers into improper fractions.

To convert 4 2/3 into an improper fraction:
Multiply the whole number (4) by the denominator (3) and add the numerator (2):
4 * 3 + 2 = 12 + 2 = 14
So, 4 2/3 as an improper fraction is 14/3.

To convert 1 1/6 into an improper fraction:
Multiply the whole number (1) by the denominator (6) and add the numerator (1):
1 * 6 + 1 = 6 + 1 = 7
So, 1 1/6 as an improper fraction is 7/6.

Step 2: Find a common denominator.

To subtract fractions, we need a common denominator. In this case, the denominators are 3 and 6, which have a common multiple of 6.

Step 3: Rewrite the fractions with the common denominator.

14/3 - 7/6

Since the common denominator is 6, we need to adjust the numerators accordingly:
14/3 = (14 * 2)/(3 * 2) = 28/6
7/6 remains unchanged.

Now, we have:
28/6 - 7/6

Step 4: Subtract the fractions.

When the denominators are the same, we simply subtract the numerators:
28/6 - 7/6 = (28 - 7)/6 = 21/6

Step 5: Simplify the fraction (if necessary).

21/6 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:
21/6 = (21 ÷ 3)/(6 ÷ 3) = 7/2

So, the answer to 4 2/3 - 1 1/6 is 7/2 or 3 1/2.

Now, let's move on to the next problem:
10 1/2 - 6 2/5

We'll follow the same steps as above.

Step 1: Convert the mixed numbers into improper fractions.

10 1/2 as an improper fraction is: 10 * 2 + 1 = 20 + 1 = 21/2
6 2/5 as an improper fraction is: 6 * 5 + 2 = 30 + 2 = 32/5

Step 2: Find a common denominator.

The denominators are already different, so we need to find a common multiple. In this case, the least common multiple (LCM) of 2 and 5 is 10.

Step 3: Rewrite the fractions with the common denominator.

21/2 = (21 * 5)/(2 * 5) = 105/10
32/5 remains unchanged.

Now, we have:
105/10 - 32/5

Step 4: Subtract the fractions.

105/10 - 32/5 = (105 - (32 * 2))/(10) = (105 - 64)/10 = 41/10

Step 5: Simplify the fraction (if necessary).

41/10 cannot be simplified further.

So, the answer to 10 1/2 - 6 2/5 is 4 1/10 or 4.1.

I hope that helps! Let me know if you have any other questions.

what are your answers?

I will tell you if they are right or wrong.