Unit 4 Resources & Lessons
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Part 1: Fraction Operations
Objective: To add, subtract, multiply, and divide fractions, including those with unlike denominators.
Key Concepts
Adding/Subtracting (Unlike Denominators): Find the Least Common Denominator (LCD), rewrite fractions, then add or subtract numerators.
\( \frac{1}{3} + \frac{2}{5} \rightarrow \frac{1 \cdot 5}{3 \cdot 5} + \frac{2 \cdot 3}{5 \cdot 3} \rightarrow \frac{5}{15} + \frac{6}{15} = \frac{11}{15} \)
Multiplying: Multiply the numerators, then multiply the denominators. Simplify if possible.
\( \frac{2}{3} \times \frac{1}{4} = \frac{2 \cdot 1}{3 \cdot 4} = \frac{2}{12} = \frac{1}{6} \)
Dividing: Keep the first fraction, change division to multiplication, and flip the second fraction (use the reciprocal).
\( \frac{3}{4} \div \frac{1}{2} \rightarrow \frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = \frac{3}{2} \)
Part 2: Decimal Operations
Objective: To add, subtract, multiply, and divide decimals accurately.
Key Concepts
Adding/Subtracting: Line up the decimal points vertically. Add zeros as placeholders if needed.
12.50 + 3.45 ------- 15.95
Multiplying: Multiply as if they are whole numbers. Count the total decimal places in the factors to place the decimal in the product.
\( 2.5 \times 1.3 \rightarrow 25 \times 13 = 325 \rightarrow 3.25 \) (2 total decimal places)
Dividing: Move the decimal in the divisor to make it a whole number. Move the decimal in the dividend the same number of places.
\( 15.5 \div 0.5 \rightarrow 155 \div 5 = 31 \)