Operations with Real Numbers

How do I compare numbers in different forms?

To compare numbers in different forms, change the numbers to the same form and then compare them.

For example, what inequality symbol correctly fills in the blank  __ 1.67?

To solve, first change  to 1.5. Then compare 1.5 and 1.67. 

How do I order numbers in different forms?

To order numbers in different forms, write all numbers in the same form, and then place them in the correct order.

For example, place , 213%, ,  in order from least to greatest.

First convert all the numbers to the same form.

The order is , , 2.13, 2.33. Change the numbers back to their original form to get , , 213%, .

What are the standard algorithms for operations with whole numbers?

What are the standard algorithms for operations with whole numbers?

An algorithm is a finite set of instructions for accomplishing some task when given a problem in its initial states.

We will study four algorithms for operations with whole numbers:

(1) addition,
(2) subtraction,
(3) multiplication, and
(4) division.

Addition

Add numbers from right to left, carrying as needed.

For example,

Subtraction

Subtract from right to left borrowing as needed.

For example,

Multiplication

Multiply from right to left, carrying as needed. Insert a place holder, which will be the number zero, for the second row of multiplication. Add the numbers to arrive at the answer.

For example,

Division

Determine the number of times the divisor goes into the dividend. Subtract the result. Carry down the next digit. Determine the number of times the divisor goes into the dividend. Subtract the result.

For example,

If a remainder exists, create a fraction using the remainder as the numerator and the divisor as the denominator.