We'll begin by refreshing the following conditions that are respected. In remainder problems, when an integer n is divided by a nonzero integer d: n must be an integer, d must be a non-zero integer, d ? 0 the quotient must be an integer, the remainder must be a non-negative integer, i.e. remainder ? 0 When you divide 19 (n) by 5 (d), you get a quotient of 3 and a remainder of 4.   The remainder, as you would know, is the amount left over after division. The remainder is also defined as...

When an integer n is divided by a nonzero integer d, the quotient refers to the integer part of the result. For instance, when 300 (n) is divided by 15 (d), the result is 20. The quotient is 20 and the remainder is 0. Also written as 300 ÷ 15 = "20 Remainder 0" or "20 R 0" On mathematics, n is also known as the dividend but the question never uses the term dividend. Let's do another example: 300 ÷ 7 = 42.8571. Here, n = 300 and d = 7. The integer part of the result is 42. Hence 42 is the...

Multiples of any number are formed by multiplying that number by an integer. For example, you want to find the multiples of 6. You can do that by multiplying 6 by other integers. 6 × 1 = 6; 6 × 2 = 12; 6 × 3 = 18; 6 × 4 = 24; 6 × 0 = 0; 6 × -2 = -12.... So the multiples of 6 are 0, ±6, ±12, ±18, ±24....etc. Similarly, the multiples of -6 are the same as the multiples of 6. -6 × 1 = -6; -6 × 2 = -12; -6 × 3 = -18; -6 × 0 = 0; -6 × -1 = 6, -6 × -2 = 12,.... So the multiples of -6 are 0, ±6, ±12,...

We already know that 15 is divisible by 3 because the result of 15 ÷ 3 is an integer. Similarly, 15 is divisible by several other integers. 15 is divisible by 1, 3, 5, and 15. And 15 is also divisible by -1, -3, -5, and -15. In total, 15 is divisible by 8 integers: 1, -1, 3, -3, 5, -5, 15, and -15. All of these 8 integers (1, 3, 5, 15, -1. -3, -5, -15) are called factors of 15. On the questions, just like the term divisible, the term factor is never used when there is a non-integer involved....

The default meaning of the term divisible means that the result of dividing two integers is an integer. For example, 15 is divisible by 3, because 15 ÷ 3 = 5 (an integer) -14 is divisible by 2, because -14 ÷ 2 = -7 (an integer) -28 is divisible by -14 because -28 ÷ -14 = 2 (an integer) 100 is divisible by -50 because 100 ÷ (-50) = -2 (an integer) 9 is not divisible by 2 because 9 ÷ 2 is 4.5 (not an integer) The term divisible is never used when there is a non-integer involved. For example, 1.5...

Let's begin with a quick question. Which of the following are digits? 0 7 9 21 145.9 200 ?9 -100   A digit is any integer from 0 to 9. 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are the ten digits. Digits are used to make numbers. In the earlier question: 21 is a two-digit number made up of the digits "2" and "1". 145.9 is a 4-digit number made up of the digits "1", "4", "5", and "9". 200 is a 3-digit number made up of the digits "2" and "0". -9 is a 1-digit number made up the digit "9". and...

Let's begin with an easy question. Is -3 greater than -7? Yes No Solution: -3 is greater than -7. Let's discuss how!   Writing numbers down on a Number Line makes it easy to tell which numbers are greater or lesser. A number on the left is less than a number on the right.   Same as saying: A number on the right is greater than a number on the left.   For example: 5 is less than 8 "or" 8 is greater than 5 -1 is less than 1 "or" 1 is greater than -1 Similarly, -7 is less than -3...

The absolute value of a number means how far that number is from zero on the number line. Questions also uses terms like "magnitude" or "modulus" to represent the absolute value of a number.     "6" is 6 away from zero,and "?6" is also 6 away from zero. So the absolute value of 6 is 6,and the absolute value of ?6 is also 6 This is the same as saying....   The magnitude of 6 is 6 The modulus of 6 is 6 The magnitude of ?6 is also 6 The modulus of ?6 is also 6   More...

Positive: any number that is greater than zero.  For example, 0.5, 3/4, 5, 190, 908.9 It may also be written with a "+" in front, like +5. The word "positive" can be shortened to "+ve". Negative: any number that is smaller than zero.  For example, -0.25, -7/8, -1, -10.75, -1000 A negative number is always written with a minus sign in front. The word "negative" can be shortened to "−ve".   Zero is neutral - neither positive nor...