Question

The total length of 3 pieces of rope is 3 1/2 feet. The first pieces of rope is 1 3/4 feet long. The second piece of rope is 7/8 feet long. What is the length of the third piece of rope?

Answer 1

Answer:

$\frac{7}{8}$  feet

Step-by-step explanation:

Total length of the 3 pieces of rope = $3\frac{1}{2}$ feet.

Length of the first piece of rope =$1\frac{3}{4}$ feet.

Length of the second piece of rope =$\frac{7}{8}$  feet.

Let the length of the third piece = x

$1\frac{3}{4}+ \frac{7}{8} + x =3\frac{1}{2}\\ \frac{7}{4}+ \frac{7}{8} + x =\frac{7}{2}$

Lets multiply all through by the LCM of 2, 4 and 8 which is 8

14+7+8x=28

21+8x=28

8x=28-21

8x=7

$x=\frac{7}{8}$  

The length of the third piece is $\frac{7}{8}$  feet

Answer 2

Answer: The length of the third piece of rope is 7/8 feet

Step-by-step explanation:

What is required here is basically the knowledge of addition and subtraction of fractions.

Now, if the three pieces of rope has a total measurement or combined length of 3 1/2feet; the first piece of rope us 1 3/4 feet long and the second piece is 7/8 feet long, to find the third piece, we will subtract the sum of the lengths of the first anf second pieces of rope and then subtract the result from the total length or the combined length of the three pieces.

Therefore, adding the lengths of the first and second pieces of rope :-

1 3/4 + 7/8

We change 1 3/4 to improper fraction

[(4×1)+3]/4 + 7/8

= 7/4 + 7/8

= (14+7)/8

= 21/8 feet

We then subtract 21/8 feet from the total length of the three pieces:

= 3 1/2 feet - 21/8 feet

Converting 3 1/2 feet gives 7/2

7/2 - 21/8

= (28 - 21)/8

= 7/8 feet

Therefore, the length of the third piece of rope is 7/8 feet.