Erik has a set of number cards from 1 to 20.
He picks four different cards.
Exactly three of his cards are multiples of 5.
Exactly three of his cards are even numbers.
All four of the numbers add up to less than 40.
What cards could Erik pick?
Answers
Answer:
Multiplication and division of whole numbers throw up many surprising things. This module encourages multiplicative thinking about numbers, and introduces ideas that are essential skills in fractions and algebra.
The ideas of this module are presented in purely arithmetical form, and no algebra is used except in some remarks that look forward to later work. The only numbers in the module are whole numbers, apart from the final paragraphs, where fractions are used so that the fifth index law can be presented in a more satisfactory form.
Students first meet the distinction between odd numbers and even numbers in early primary school, but it is useful everywhere in mathematics. Even numbers are multiples of 2, and more generally, multiples arise throughout mathematics and everyday life. The mass of a stack of bricks is a multiple of the mass of one brick. The number of pages in a packet of notebooks is a multiple of the number of pages in one notebook.
The factors of a number can be displayed using rectangular arrays. Some numbers, such as 30, can arise in many different ways as a product,
30 = 1 × 30 = 2 × 15 = 3 × 10 = 5 × 6 = 2 × 3 × 5,