Mixed operations: Decimals | 5th Grade Math

Grade 5 Math – Mixed operations: Decimals
Complete Notes & Formulae
1. Add, Subtract, Multiply, and Divide Decimals
  • Line up decimals for addition and subtraction
  • Add/subtract as with whole numbers, then place the decimal in the answer
Addition:
\(\begin{align*} 3.45 + 2.67 &= 6.12 \\ \end{align*}\) Subtraction:
\(\begin{align*} 5.80 - 2.75 &= 3.05 \\ \end{align*}\)
  • For multiplication:
    • Ignore decimals, multiply as whole numbers
    • Count total decimal places in factors and place in the answer
Multiplication:
\(\begin{align*} 2.3 \times 1.2 &= 2.76 \quad \text{(2 decimal places total)} \\ \end{align*}\)
  • For division:
    • Move decimal point in divisor to make it a whole number, do the same for dividend
    • Divide as whole numbers, then place decimal in answer directly above dividend’s decimal
Division:
\(\begin{align*} 6.25 \div 2.5 &= 2.5 \\ \end{align*}\)
2. Add, Subtract, Multiply, Divide Decimals: Word Problems
Example: Sarah bought 3.5 kg apples at 4.2 AED per kg.
Calculation: \(3.5 \times 4.2 = 14.7\) AED
  • Identify operation required from the context (add/subtract/multiply/divide)
  • Use appropriate decimal operation
  • Check answer makes sense in the problem
Sample Multi-Step:
\( \text{Total cost} = (\text{Quantity}) \times (\text{Price per unit}) \)
3. Add, Subtract, Multiply, and Divide Decimals: Multi-Step Word Problems
Example: A recipe needs 2.5 L water. You already poured in 0.75 L. How much more is needed if each jug holds 0.25 L?
Step 1: \(2.5 - 0.75 = 1.75\) L left
Step 2: \(1.75 \div 0.25 = 7\) jugs needed
  • Solve each step one at a time
  • Use order of operations where needed \((\text{Parentheses} \rightarrow \text{Exponents} \rightarrow \text{Multiply/Divide} \rightarrow \text{Add/Subtract})
4. Equations with Mixed Operations: True or False
Example: Is \(2.5 + 3.1 = 5.6\)?
\(2.5 + 3.1 = 5.6\) True
Example: Is \(7.4 - 1.2 = 6.1\)?
\(7.4 - 1.2 = 6.2\) False
  • Apply correct calculation to check if statement is True or False
  • Check decimal place alignment and calculation steps