Problem 25 - Algebra 1

Question

Evaluate the expression. $$6 \div 3+2 \cdot 7$$

Step-by-Step Solution

Answer

The evaluated result of the expression is 16.

Step 1: Apply Division

First, perform the division operation according to the order of operations. So, divide 6 by 3, resulting in 2.

Step 2: Apply Multiplication

Next, perform the multiplication operation. Multiply 2 by 7, resulting in 14.

Step 3: Apply Addition

Lastly, perform the addition operation. Add 2 (the result from the division in step 1) and 14 (the result from the multiplication in step 2), resulting in 16.

Key Concepts

Division: Breaking Down Numbers

Division is about splitting something into equal parts. When you see a division sign, like in the expression \(6 \div 3\), it means "how many times does 3 fit into 6". The answer is 2 because if you divide 6 by 3, you get two groups of 3.

Think of division as sharing. If you have 6 cookies and 3 people, each person gets 2 cookies. Division tells you how the number is shared among equal groups.

When solving expressions, division is one of the first operations to complete because of the order of operations rule (PEMDAS/BODMAS). So always check your expression for any division to handle it early.

Multiplication: Doubling and Beyond

Multiplication is like adding a number to itself several times. In the expression, 2 is multiplied by 7. This is like saying, “I want 2 added together 7 times,” which equals 14.

It's a way to quickly find totals of groups. If you have 2 boxes and each box has 7 apples, you simply multiply to find out you have 14 apples in total.

In terms of operations order, multiplication takes priority after division. This means, once you've handled any division, move on to multiplication before adding or subtracting in your expression.

An easy trick is to think of multiplication as grouping or arranging these numbers in rows or columns to quickly find the total without repeatedly adding. It’s efficient and saves time.

Addition: Putting It All Together

Addition joins numbers together to find a sum. In this final step, after solving division and multiplication, you're left with numbers to add. In our expression, you add the 2 from the division (\(6 \div 3\) gives 2) and 14 from the multiplication (\(2 \times 7\) gives 14). So, 2 plus 14 equals 16.

Addition is about combining, like stacking building blocks. It’s fundamental and often the last step in multi-operation problems.

After completing the higher-priority operations (division and multiplication) first, addition pulls everything together to give you the final answer. It is straightforward but crucial, as skipping any addition step or doing it out of order affects the total sum and changes the result significantly.