Which expression correctly applies the distributive property where a number multiplies a sum?

Which expression correctly applies the distributive property where a number multiplies a sum?

• A. 6 × (2 + 4) = 6 × 2 + 6 × 4
• B. 6 × (2 + 4) = 12 × (2 + 4)
• C. (6 × 2) + 4 = 6 × (2 + 4)
• D. 6 × 2 + 4 = 6 × (2 + 4)

Answer: (A)

Distributing a factor over a sum means you multiply that outside number by each addend inside the parentheses and then add the results. For 6 × (2 + 4), you apply the outside 6 to both 2 and 4, giving 6 × 2 + 6 × 4. This shows exactly how the outside factor spreads to each part of the sum, and the two sides are equal: 6 × (2 + 4) equals 36, and 6 × 2 + 6 × 4 equals 12 + 24, which also equals 36. The idea is that you can rewrite a product with a sum inside the parentheses as the sum of two products. Expressions that try to replace the outside factor with something else (like turning 6 × (2 + 4) into 12 × (2 + 4)) or that omit multiplying one of the addends by the outside factor no longer reflect the distributive property, so they don’t match the original value.

Distributing a factor over a sum means you multiply that outside number by each addend inside the parentheses and then add the results. For 6 × (2 + 4), you apply the outside 6 to both 2 and 4, giving 6 × 2 + 6 × 4. This shows exactly how the outside factor spreads to each part of the sum, and the two sides are equal: 6 × (2 + 4) equals 36, and 6 × 2 + 6 × 4 equals 12 + 24, which also equals 36.

The idea is that you can rewrite a product with a sum inside the parentheses as the sum of two products. Expressions that try to replace the outside factor with something else (like turning 6 × (2 + 4) into 12 × (2 + 4)) or that omit multiplying one of the addends by the outside factor no longer reflect the distributive property, so they don’t match the original value.