Question

A long stick was broken into 3 smaller sticks. The first stick is 4 1/3 cm long. The second stick is 1 3/4 cm shorter than the first one. The third stick is 6 1/2 cm long. What was the length of the long stick before it was broken into 3 smaller sticks?

A. 18 cm
B. 20 cm
C. 22 cm
D. 24 cm

Answer 1

The length of the long stick before it was broken into 3 smaller sticks is 161/12 cm.

Step-by-step explanation:

To find the length of the long stick before it was broken into 3 smaller sticks, we need to add up the lengths of the three smaller sticks. The first stick is 4 1/3 cm long, the second stick is 1 3/4 cm shorter than the first one, and the third stick is 6 1/2 cm long.

To find the length of the second stick, we need to subtract 1 3/4 cm from 4 1/3 cm. To do this, we convert both fractions to a common denominator. 1 3/4 is equal to 7/4, and 4 1/3 is equal to 13/3. Subtracting 7/4 from 13/3 gives us 13/3 - 7/4 = 52/12 - 21/12 = 31/12.

Now we can add up the lengths of all three sticks. 4 1/3 cm + 31/12 cm + 6 1/2 cm = 13/3 cm + 31/12 cm + 13/2 cm. To add these fractions, we need to convert them to a common denominator. The least common denominator of 3, 12, and 2 is 12. Converting the fractions to this denominator, we get 52/12 cm + 31/12 cm + 78/12 cm = 161/12 cm.

Therefore, the length of the long stick before it was broken into 3 smaller sticks is 161/12 cm.