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DECIMAL OPERATIONS • Decimal operations refer to the mathematical operations that can be performed with decimals: addition, subtraction, multiplication and division. • The process for adding, subtracting, multiplying and dividing decimals must be followed in order to achieve the correct answer. Decimals can be used in all operations and also with integers in all operations. Decimals can also be used in algebraic equations. • A typical situation of an equation with decimals is dollars and cents. How to use decimal operations: • The process of adding and subtracting decimals must be used in order to achieve the correct answer. When adding or subtracting decimals, the decimals are typically placed vertically. • To add or subtract, the decimal points must be lined up for all decimals being added or subtracted. Once the decimal points are lined up, the numbers are added or subtracted and then the decimal point is brought down into the answer. Examples: 23.825 16.325 + .067 - 2.9 23.892 13.425 • When dividing decimals by integers, the decimal point is brought up into the answer and then the numbers are divided. Example: _.__ .54 3.24 ÷ 6 → 6 )3.24 → 6 )3.24 → .54 30 ↓ 24 24 0 © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

• When dividing decimals by decimals or integers by decimals, the decimal point is sometimes moved, depending on the numbers being divided by. If 13.5 is divided by 1.5, the decimal point will need to be moved over in the divisor and dividend. This will affect where the decimal point is in the quotient or answer. If 14 is divided by 2.5, the decimal point again will have to be moved over in the divisor and dividend to make 2.5 a whole number, 25, and 14 to become 140. The decimal point is then moved into the answer and the numbers are divided. Example: ____ ___9. 13.5 ÷ 1.5 → 1.5 )13.5 → 15 )135. ← decimal moved 1 place 135 0 • Decimals can be used to solve algebraic equations the same as integers as long as the rules for adding, subtracting, multiplying and dividing are followed. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Try This! Add the following: 1.59 +. 002__________ 26.389 + 1.74_____________ .099 + 6.03 ______________ Subtract the following: 14.005 - 6.7_______ 3.72 - .086______ .0956 - .002_________ Divide the following: 16.75 ÷ 5_______ 3.9 ÷ 3_______ 240.075 ÷15 ______ 4.2 ÷ 2.1_______ 40.95 ÷ 9.1________ 255 ÷ 5.1________ 244 ÷ 30.5_________ Solve for x: x + 1.2 = 14.5_________ x - 22.65 = 5.07________ $3.99x = $59.85_________ 4.099 ÷ x = 59.85_______ © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.