Problem 60 - Elementary Algebra

Question

Simplify. $$ 310+512-16 $$

Step-by-Step Solution

Answer

806

Step 1: Simplify Addition

Start by adding the numbers 310 and 512. \[ 310 + 512 = 822 \] After performing the addition, we get 822.

Step 2: Simplify Subtraction

Next, subtract 16 from the sum obtained in Step 1.\[ 822 - 16 = 806 \] After performing this subtraction, we get the final simplified result, which is 806.

Key Concepts

Addition

When simplifying expressions with addition, you're combining numbers to find their total. In our exercise, the numbers 310 and 512 are added together. This operation is straightforward: gather the numbers and sum them. Adding numbers involves lining up their digits according to place value and adding column by column.

• Start with the units place: 0 + 2 = 2.
• Proceed to the tens: 1 + 1 = 2.
• Finally, handle the hundreds: 3 + 5 = 8.

Combining these, 310 + 512 equals 822. Addition is the process of moving numbers forward, increasing their total value. It is one of the fundamental operations in arithmetic, helping to combine quantities or values.

Subtraction

Subtraction is the operation used to find the difference between numbers, essentially removing a part from a total. In the given problem, we need to subtract 16 from 822, which was obtained from the addition step. To perform subtraction, align numbers according to their place values like addition.

• Start from the units: 2 - 6 cannot be done without borrowing. So, borrow 1 ten from the tens digit of 2, which becomes 1.
• Now perform subtraction: 12 (after borrowing) - 6 = 6.
• In the tens column, since we borrowed, subtract: 1 (new tens digit) - 1 = 0.
• Finally, in the hundreds column, subtract: 8 - 0 = 8.

This gives the final result of 806. Subtraction reduces the total value and helps compare differences between numbers or quantities.

Simplification

Simplification is the process of breaking down a mathematical expression to its simplest form. In the context of our exercise, it involves conducting operations like addition and subtraction step-by-step. Start by tackling one operation at a time.

• First, perform addition or subtraction in the order they appear when facing basic arithmetic problems without brackets.
• Check your calculations carefully at each step to ensure accuracy.
• The goal is to reduce the expression to a simple, single number where no further operations are possible.

Through simplification, we made the expression 310+512-16 into a more manageable and concise form, which is 806. It’s about making complex calculations easier and more understandable, providing clear and precise results.