# What real number is less than -1?

Many options - e.g. -2

"Real number" means all the numbers we know, including positive and negative numbers.

The only numbers that are not included are "imaginary numbers" - numbers that have an imaginary part i (used only i physics or high mathematics).

### The only number that is one less than a square?

Every non-negative real number is a square (every number if in the complex field) so every real number greater than or equal to -1 is one less than a square. Even if you restrict yourself to perfect squares, of the form n2, then n2 - 1 = (n-1)*(n+1) is one less than a square. There are infinitely many such numbers.

### What is before one half?

Real - or even rational - numbers are infinitely dense. What this means is that there is no real number immediately before any other since it is always possible to find another number which is better qualified to claim that position. For example, 1/5 is less than 1/2 but is it "before"? No, because (1/5 + 1/2)/2 = 7/20 is also less than 1/2 and is nearer. Is it "before"? No, because (7/20 + 1/2)/2…

### Can you multiply a bigger number to get a smaller number?

If you multiply a number by a number greater than 1, you get a result that's greater than the first number. Example: 8 x 2 = 16; 16 is greater than 8. If you multiply a number by a number less than 1, you get a result that's less than the first number. Example 1: 8 x 0.5 = 4, which is less than 8. Example 2: 8 x (-1) = -8, which is also…

### Why in a multipling decimal problem is the answer smaller the products?

If you multiply a number less than 1 by another number less than 1, then the product is less than either of the original numbers. The reason is that a number less than 1 represents a piece of 1 whole thing. Multiplying two numbers less than 1 represents taking a piece of a piece, and when you do that, you wind up with less than either one of the original pieces.

### What is the answer for Multiply or divide two quantities by the same number?

It is either two quantities that are larger or smaller than the ones that you started with, depending on whether the number that you multiplied or divided by was greater than or less than 1. Multiply by a number greater than 1 : both larger. Multiply by a number less than 1 : both smaller. Divide by a number greater than 1 : both smaller. Divide by a number less than 1 : both larger.

### Is the product of a fraction less than 1 and a whole number greater than less than the whole number?

### When you multiply two rational numbers will you always get a number that is smaller than the two factors?

No. A rational number is ANY number that can be represented as one integer over a second integer (which cannot be zero). There is no requirement that the top integer is less than the bottom integer (an improper fraction is still a rational number - all integers are rational numbers as they can be represented as an improper fraction with a 1 as the denominator). Only if both rational numbers are less than 1 will…

### What is the largest number that should be added to -3 to get a sum less than -1?

There is no solution if the question asks for 'less than -1'. Suppose a is the largest number. Then we have -3+a<-1, so a<2. But then I can take the number x:=(a+2)/2. This number is still less than 2 (it is in the middle of 2 and a on the number line) and so -3+x<-1. But x>a, which contradicts a being the largest number satisfying the required property. If it's 'less than or equal to…

### Is it possible to get an infinite root of a number?

Generally, no. But one of the infinite roots of 1 is 1. Otherwise one of the roots would be nearly 1. Just a whisker smaller than 1 if it was the root of a number between 0 and 1, and just a whisker larger if the number was greater than 1. If the number was less than 0, then the roots would vary from the real to the complex numbers.