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What does partitioning mean? Explain and illustrate your answer.


Use the Method of compensation to show how you can make the subtraction of 563 -79 easier


Use the vertical and horizontal algorithms to find the sum or difference of the following.

( Explain the "borrow and carry" concepts.)

a) 587 + 620

b) 749 - 568


Define the number and numeral and provide an example for each.


Test the following numbers for divisibility by 6,9 and 11.( Do not divide or fractorise)

a) 6 184 046

b) 21 589 434


The sum of two positive number is 14 and difference between their squares is 56. What is the sum of their squares?


use a standard algorithm to calculate 4 + 2/3 - 3/4

the 2/3 and the 3/4 are fractions.


a3x+5/ a3x-1

Andy and his friend Sam were walking along the road together. Andy had a big bag of marbles. Unfortunately the bottom of the bag split and all the marbles spilled out. Poor Andy!


• One third (13) of the marbles rolled down the slope too quickly for Andy to pick them up. One sixth (16) of all the marbles disappeared into the rain-water drain.

• Andy and Sam picked up all they could but half (12) of the marbles that remained nearby were picked up by other children who ran off with them.

• Andy counted all the marbles he and Sam had rescued.

• He gave one third (13) of these to Sam for helping him pick them up. Andy put his remaining marbles into his pocket. There were 14 of them.


a) How many marbles were there in Andy's bag before the bottom split?

b) What fraction of the total number that had been in the bag had he lost or given away?


What number is opposite 11