A board is 6 1/2 feet long. You cut off a 1 3/4 foot piece and a 2 2/3 foot piece. How much of the original board is left?

To find out how much of the original board is left after cutting off two pieces, you first need to calculate the total length of the two pieces that were cut off.

The length of the first piece is 1 3/4 feet, which can be written as 7/4 feet. Similarly, the length of the second piece is 2 2/3 feet, which can be written as 8/3 feet.

To find the total length of the two pieces, you can add these two fractions:

7/4 feet + 8/3 feet

Before adding fractions, you need a common denominator. In this case, the least common denominator (LCD) of 4 and 3 is 12.

Multiplying both the numerator and the denominator of 7/4 by 3, you get 21/12.
Multiplying both the numerator and the denominator of 8/3 by 4, you get 32/12.

Now you can add the two fractions:

21/12 feet + 32/12 feet

To add fractions with the same denominator, you simply add their numerators:

(21 + 32) / 12 = 53/12 feet

So, the total length of the two pieces that were cut off is 53/12 feet.

To find out how much of the original board is left, subtract the length of the two pieces from the original length of the board:

6 1/2 feet - 53/12 feet

Before subtracting fractions, you need to find a common denominator. Again, the least common denominator (LCD) of 2 and 12 is 12.

Multiplying both the numerator and the denominator of 6 1/2 by 2, you get 13/2 feet.
Multiplying both the numerator and the denominator of 53/12 by 1, you get 53/12 feet (since it already has the LCD).

Now you can subtract the two fractions:

(13/2) feet - (53/12) feet

To subtract fractions with the same denominator, you simply subtract their numerators:

(13 - 53) / 12 = -40/12 feet

Since the numerator is negative, it means that the length left after cutting off the two pieces is a negative value. In reality, you cannot have a negative length, so this result does not make sense.

Therefore, after subtracting the length of the two pieces from the original length of the board, you are left with no board remaining.

5 18/12 - 1 9/12 - 2 8/12 = _____