Grades 5-6 Video Solutions 2024-2024_5-6

Video Transcription

Question 28. Dan plans to cut a rope into 12 equal pieces and marks the points where he needs to cut. Muhammad plans to cut the same rope into 16 equal pieces and marks the  points where he needs to cut. Then Maya cuts the rope at all the marked points. How many pieces does Maya get? Dan plans to cut the rope in 12 equal pieces. He will mark every  one-twelfth of the rope, giving us 11 marks. Muhammad plans to cut the rope into 16 pieces. So he will mark every one-sixteenth of the rope, giving us 15 more marks. Notice how  the greatest common factor of 12 and 16 is 4, and this means that Dan and Muhammad will mark at the exact same place every one-fourth of the rope. We can see this occur at the  circled locations. Since these marks are in the exact same location, each pair will only lead to one cut, so we need to subtract the three duplicate marks, giving us 23 marks  in total. We will have one more piece of rope than the number of marks, so we add 1 to 23 to get 24 pieces of rope.

Video Summary

Maya cuts the rope using the marks made by Dan and Muhammad. Dan's plan results in 11 marks, and Muhammad's results in 15 marks, totaling 26 marks. However, they share common marks every one-fourth of the rope, which occur three times due to the greatest common factor of 12 and 16 being 4. These overlapping marks mean Maya only makes 23 cuts. Since the number of pieces is one more than the number of cuts, Maya will end up with 24 pieces of rope.

Keywords

rope cutting

marks overlap

greatest common factor

Maya

24 pieces