Joey has two pieces of wood. One is 120 inches and the other one is 210 inches long. He wants to cut both the pieces into smaller parts so that all these parts are of the same length. i) If he wants the smallest pieces to be as long as possible without having any leftover, how long should each piece be?
Ans:
ii) How many smaller pieces of wood will he have in total?
Ans:

A. 30 inches

B. 11 pieces

Step-by-step explanation:

Piece 1 = 120 inches

Piece 2 = 210 inches

1. He wants the smallest pieces to be as long as possible without having any leftover, how long should each piece be?

Find the highest common factor of 120 and 210

120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

210: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210.

The highest common factor of 120 and 210 = 30

Therefore, the smallest and longest pieces should be cut into 30 inches each

B. Total Smaller pieces of wood = piece 1 / 30 + piece 2 / 30

= 120/30 + 210/30

= 4 + 7

= 11 pieces