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Distributive Property with area models

Learn and apply the distributive property of multiplication over addition with area models. Practice mental math skills, factor out GCF, and multiply binomials. Examples provided for easy understanding. Improve your math skills now!

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Distributive Property with area models

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  1. Distributive Property with area models

  2. Recall the distributive property of multiplication over addition . . . symbolically: a × (b + c) = a × b + a × c and pictorially (rectangular array area model): b c a a × b a × c

  3. An example: 6 x 13 using your mental math skills . . . symbolically: 6 × (10 + 3) = 6 × 10 + 6 × 3 and pictorially (rectangular array area model): 10 3 6 6 × 10 6 × 3

  4. Factoring out the gcf with distributive property

  5. 3x + 12 • Find the gcf of 3x and 12 • Divide each term by the gcf • Re-write using distributive property Answer: 3 (x + 4)

  6. Examples • 12y – 36 • 9z + 81 • 20j – 32 • 6h + 15k

  7. Example answers • 12 (x – 3) • 9 (z + 9) • 4 (5j - 8) • 3 (2h + 5k)

  8. 200 30 40 + 6 276 20 3 What about 12 x 23? Mental math skills? (10+2)(20+3) = 10×20 + 10×3 + 2×20 + 2×3 10 10 × 20 10 × 3 2 2 × 20 2×3

  9. c d And now for multiplying binomials (a+b)×(c+d) = a×(c+d) + b×(c+d) = a×c + a×d + b×c + b×d a a × c a × d b b × c b×d

  10. We note that the product of the two binomials has four terms – each of these is a partial product. We multiply each term of the first binomial by each term of the second binomial to get the four partial products. F + O + I + L ( a + b )( c + d ) = ac + ad + bc + bd Product of the FIRST terms of the binomials Product of the OUTSIDE terms of the binomials Product of the INSIDE terms of the binomials Product of the LAST terms of the binomials Because this product is composed of the First, Outside, Inside, and Last terms, this pattern is often referred to as FOIL method of multiplying two binomials. Note that each of these four partial products represents the area of one of the four rectangles making up the large rectangle.

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