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Take each digit of the number (371) in reverse order (173), multiplying them successively by the digits 1, 3, 2, 6, 4, 5, repeating with this sequence of multipliers as long as necessary (1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, ...), and adding the products (1×1 + 7×3 + 3×2 = 1 + 21 + 6 = 28). The original number is divisible by 7 if and only if ...
For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2. If the initial term of an arithmetic progression is a 1 {\displaystyle a_{1}} and the common difference of successive members is d {\displaystyle d} , then the n {\displaystyle n} -th term of the sequence ( a n {\displaystyle a_{n ...
The difference of two squares can also be illustrated geometrically as the difference of two square areas in a plane. In the diagram, the shaded part represents the difference between the areas of the two squares, i.e. a 2 − b 2 {\displaystyle a^{2}-b^{2}} .
In terms of partition, 20 / 5 means the size of each of 5 parts into which a set of size 20 is divided. For example, 20 apples divide into five groups of four apples, meaning that "twenty divided by five is equal to four". This is denoted as 20 / 5 = 4, or 20 / 5 = 4. [2] In the example, 20 is the dividend, 5 is the divisor, and 4 is ...
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).
For example, a ratio of 3:2 is the same as 12:8. It is usual either to reduce terms to the lowest common denominator, or to express them in parts per hundred . If a mixture contains substances A, B, C and D in the ratio 5:9:4:2 then there are 5 parts of A for every 9 parts of B, 4 parts of C and 2 parts of D.
Furthermore, if b 1, b 2 are both coprime with a, then so is their product b 1 b 2 (i.e., modulo a it is a product of invertible elements, and therefore invertible); [6] this also follows from the first point by Euclid's lemma, which states that if a prime number p divides a product bc, then p divides at least one of the factors b, c.
The difference between explanations and arguments reflects a difference in the kind of question that arises. In the case of arguments, we start from a doubted fact, which we try to support by arguments. In the case of explanations, we start with an accepted fact, the question being why is this fact or what caused it.