Example: Divide 3 loaves between 5 people First, divide two of the loaves into thirds..... each person gets one-third wach, with one third left over 1/3 Then divide the left-over third from the second loaf into fifths So, each person gets: 1/5 and the third loaf into fifths each person gets a slice (one fifteenth) 1/15 each person gets one-fifth each I ITT TI 12 3 4 5 6 7 8 Example: 924 TIIT = 9 2 If a collection of balls are arranged in rows of 3, there is one ball left over 000 9 If arranged in rows of 5, there are two balls left over If arranged in rows of 7, there are three balls left ove The Chinese Remainder Theorem proves that the smallest number of balls must be 52 The Egyptians used the approximated process to work on the area of a circle as shown in the picture. 1.4 Show the representation of the fractions on the second row. (2) 1.5 Show the algorithm/abstract strategy to justify the 3/5 found as the answer. (3) The table on the left shows the Chinese numbering system. 1.6 Write down the number 7 429 using these symbols. (2) In this picture, there are 52 balls, - when 52 is divided in 3, there are 17 rows and 1 ball remained (52 ÷ 3 = 17 remainder 1) - when 52 is divided in 5, there are 10 rows and 2 balls remained (52 +5 = 10 remainder 2) - when 52 is divided in 7, there are 17 rows and 1 ball remained (52 ÷ 7 = 7 remainder 3) 1.7 When 72 is divided by 8, - how many rows will there be? (1) (1) - how many balls remain? - Write the representation of the second illustration as multiplication. Be mindful of the representation of the rows and the column as you write the multiplication representation. (1)
