Problem 92 - Elementary Algebra

Question

Add or subtract and reduce to lowest terms. $$ 23+35-29 $$

Step-by-Step Solution

Answer

29

Step 1: Simplify Addition

Start by adding the two numbers: 23 and 35. Calculate: \( 23 + 35 = 58 \).

Step 2: Subtract the Next Number

Now subtract the third number, 29, from the result of the addition. Calculate: \( 58 - 29 = 29 \).

Step 3: Check the Result

Since 29 is a whole number, it's already in the lowest terms. There's no need for further simplification.

Key Concepts

Addition

Addition is one of the basic operations of arithmetic. It involves combining two or more numbers to find their total sum. In our example, we began by adding 23 to 35.

Here's how you can think about addition:

• Add the digits in the same place value, starting from the rightmost digit, which is the ones place.
• Remember to carry over any extra value that exceeds 9 to the next higher place value.

For instance, 23 (which is 2 tens and 3 ones) and 35 (which is 3 tens and 5 ones) added together gives us a total of 58. There is no carrying over in this case. Addition lets us find how much more we have when quantities are brought together.

Subtraction

Subtraction is the process of finding the difference between numbers. It's essentially the opposite of addition. In the example, we subtracted 29 from the sum obtained from the previous addition step, 58.

Here's a breakdown to help understand subtraction:

• Begin by looking at the numbers from right to left, starting with the ones place.
• If the top digit is smaller than the bottom digit, "borrow" from the next left place value.

In this example, there was no need to borrow because 8 is greater than 9. Subtraction gives us the remaining value when a quantity is removed from another.

Simplification

Simplification involves making an expression or number more straightforward, usually by expressing it in its simplest terms. However, in our example of handling the expression 23 + 35 - 29, the end result was 29, which is already in its simplest form as it's a whole number.

When dealing with more complex numbers, the idea of simplification can mean:

• Reducing fractions to their lowest terms, by dividing both the numerator and the denominator by their greatest common divisor.
• Simplifying algebraic expressions by combining like terms or using basic arithmetic operations.

In essence, simplification aims to make mathematical expressions as concise and comprehensible as possible.