Multiplication and division structures
 

Self-assessment questions

Give two problems associated with the multiplication 29 x 12, one using the idea of ’29 lots of 12’ and the other using ’12 lots of 29’.

Make up a problem using the repeated aggregation structure and the word per, in the context of shopping, corresponding to the multiplication, 12 x 25.

A box of yoghurts consists of 4 rows of 6 cartons arranged in a rectangular array. How would you use this as an example to illustrate the commutative property of multiplication?

The real car is 300 cm long and the model car is 15 cm long: how many times longer is the real car? (That is, what is the scale factor?) What is the calculation to be entered on a calculator to answer this? Of what division structure is this an example?

A sack of apples weighing 25 kilograms costs €12: what is the price per kilogram-weight of apples? What is the calculation to be entered on a calculator to answer this? Of what structure of division is this an example?

How many CDs costing €12.50 each can I afford to buy with €100? What is the calculation to be entered on a calculator to answer this? Of what division structure is this an example?

How many months do I need to save up €300 if I save €12 a month? What is the calculation to be entered on a calculator to answer this? Of what division structure is this an example?

Make up a problem that corresponds to the division, 60 + 4, using the equal-sharing structure in the context of shopping.

Make up a problem that corresponds to the division, 60 + 4, using the inverse-of-multiplication structure, incorporating the idea of repeated subtraction from a given quantity, in the context of shopping.

Make up a problem using the ratio structure in the context of salaries. Use a calculator to answer your own problem.