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Evaluate expressions with decimals

Evaluating expressions with decimals means finding the numerical value of a numerical or algebraic expression by substituting given decimal values for variables, applying parentheses and order of operations, and accurately performing decimal addition, subtraction, multiplication, and division using place-value reasoning. The learner interprets the expression’s structure rather than calculating strictly left to right, and connects the result to formulas and later work with proportional relationships; this scope is limited to finite decimals and whole-number exponents, not symbolic simplification or more advanced number systems.

Detailed Explanation: Evaluate expressions with decimals

To evaluate an expression with decimals:

  1. Substitute the given decimal values for the variables.
  2. Follow the order of operations:
    • Parentheses
    • Exponents
    • Multiplication and division
    • Addition and subtraction
  3. Line up decimal points when adding or subtracting. For multiplication, multiply as whole numbers, then count the decimal places in the factors.

Example: Evaluate

3.4+2(x−y)23.4+2(x-y)^2

when x=1.2x=1.2 and y=0.5y=0.5.

Step 1: Substitute the values.

3.4+2(1.2−0.5)23.4+2(1.2-0.5)^2

Step 2: Evaluate inside the parentheses.

Line up the decimal points:

1.2−0.5=0.71.2-0.5=0.7

Now the expression is

3.4+2(0.7)23.4+2(0.7)^2

Step 3: Evaluate the exponent.

An exponent of 22 means multiply the number by itself:

(0.7)2=0.7⋅0.7=0.49(0.7)^2=0.7\cdot0.7=0.49

So the expression becomes

3.4+2(0.49)3.4+2(0.49)

Step 4: Multiply.

2⋅0.49=0.982\cdot0.49=0.98

Now we have

3.4+0.983.4+0.98

Step 5: Add, lining up the decimal points.

3.40+0.984.38\begin{array}{r} 3.40\\ + 0.98\\ \hline 4.38 \end{array}

Therefore,

4.38\boxed{4.38}

Do not calculate strictly from left to right. Always use the order of operations so that parentheses and exponents are handled first.

Learn by doing: Evaluate expressions with decimals

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    Multiplication - Decimal Tenths

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