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Decimal Math Operations for Beginners: Addition, Subtraction, Multiplication, Division

Learn to add, subtract, multiply, and divide decimal numbers. Understand using estimation and order of operations. Practice problem-solving scenarios.

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Decimal Math Operations for Beginners: Addition, Subtraction, Multiplication, Division

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  1. Chapter 2 Operations on Decimal Numbers

  2. What You Will Learn: • To add and subtract decimal numbers • To multiply decimal numbers • To divide decimal numbers • To use the order of operations (BEDMAS) to perform calculations with decimal numbers • To use estimation to check your answers

  3. 2.1 – Adding and Subtracting Decimals • Before actually performing addition and subtraction of decimal values, we need to work on estimating • Estimation provides us with a ‘ballpark’ figure so we can check our answer

  4. Example: • Ashley and Marshall live in Winnipeg. They are traveling to Jasper. The actual distances are given below: • Ashley estimates that the total trip distance is about 1700 km, while Marshall estimates the distance as 1400 km

  5. Estimate your own value for the trip distance • Feel free to estimate as closely to the value as you feel comfortable, but you should be able to perform the calculation in your head! • My Answer:

  6. Estimation Methods • There are two main estimation methods • Front-end estimation uses only the first number in each value and rounds the remaining values to zero • Relative-size estimation looks at the leading and second digits to round the values before estimating

  7. Ex: Estimate 81.95 + 12.50 + 29.30 • Front-End: • Relative Size:

  8. Ex: Placing Decimals Using Estimation • Place the decimals in each of these answers using estimation (do not calculate them) • 423.6 - 107.2 = 3 1 6 4 0 • 7.85 + 2.06 + 4.123 = 1 4 0 3 3

  9. Adding and Subtracting Decimals • We use column addition and subtraction to add and subtract decimals • The reason for this is so that we can align the decimal places

  10. Ex: Add the following • 3.2 + 6.8 • 4.51 + 1.76 • 9.1 + 5.04

  11. Ex: Subtract the following • 8.57 – 3.12 • 4.07 – 2.64 • 10.3 – 7.06

  12. Problem Solving • Leslie has $5.50. She purchases some gum for $1.29 and an iced tea for $1.79. How much money does Leslie have left?

  13. 2.2 – Multiplying Decimals • When multiplying decimals, estimation can again be used to check our answer • Ex: Chris finds 5 books at a cost of $1.65 each. He has $9.00 in change. Can he afford to buy these books?

  14. Multiplying Decimals • The process of multiplying decimals is no different from multiplying any other two numbers • The number of decimal places in the final answer depends on the number of decimal places that you start with

  15. Ex: Multiply the following • 1.5 × 3 • 7.5 × 1.2 • 3.6 × 4.0

  16. Problem Solving: • Karl is preparing apple pies for a family reunion. He will need 4.5 pounds of apples to make the pies. Apples cost $1.29 / lb. What will the total cost of the apples be?

  17. 2.3 – Dividing Decimals • Dividing decimal numbers is slightly more difficult than multiplication • Often it is a good idea to estimate the answer before working on the question

  18. Ex: Estimate the following to determine where to place the decimal • 15.4 ÷ 3.6 = 4 2 7 7 7 8 • 4.4 ÷ 0.42 = 1 0 4 7 6 1 9

  19. Division of Decimals • To divide using decimals, it is easiest to remove the decimals completely from the dividend and divisor • We can then use estimation to place the decimal when we are finished

  20. Ex: Divide the following • 1.36 ÷ 0.34 • 57.9 ÷ 3

  21. Problem Solving • Juice boxes have a volume of 0.25 L. How many juice boxes will contain the same amount of juice as a 1.89 L bottle?

  22. 2.4 – Order of Operations • In mathematics, there are many operations • Rules have been developed to determine the order in which operations are performed if there are several different types together

  23. BEDMAS • BEDMAS is an acronym that is used to help you to keep in mind what order operations must be completed in • B: • E: • D: • M: • A: • S:

  24. Examples: • 5.3 × 1.2 + 4.5 • (3.6 + 4.6) ÷ 2.4 + 5

  25. Problem Solving • The Edwards family filled up their van with 72.4 L of gas at a cost of 121.9 ¢ / L. They also bought 4 drinks at a cost of $1.69 each and 2 ice-cream bars at a cost of $1.39 each. What is the total cost of their purchase?

  26. Problem Solving • Murphy walks the same distance on each of 4 days for a total of 5.2 km. Then Murphy walks 2.1 km on the fifth day. What distance did Murphy travel on days 4 and 5 together?

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