Distributive property: find the missing factor

Learning Objectives Identify the factors and products in a distributive property equation. Decompose a two-digit number into tens and ones to apply the distributive property. Solve for a missing factor in an equation like 8 x 45 = (8 x 40) + (8 x __). Solve for a missing factor in an equation like (7 x 20) + (7 x 3) = 7 x __. Explain how the distributive property helps solve multi-digit multiplication problems. Verify their answer by calculating the value of both sides of the equation. Imagine you need to pack 7 boxes, and each box holds 23 shiny marbles. How can you find the total number of marbles without a calculator? 🤔 Let's find out! Today, we'll learn a cool math trick called the distributive property. It helps us break down big multiplication problems into...

TermDefinitionExample Distributive PropertyA math rule that lets you multiply a number by a group of numbers added together. You 'distribute' or share the multiplication with each number in the group.4 x 12 can be broken down into 4 x (10 + 2), which is the same as (4 x 10) + (4 x 2). FactorA number that is multiplied by another number.In 5 x 8 = 40, the numbers 5 and 8 are the factors. ProductThe answer you get when you multiply numbers together.In 5 x 8 = 40, the number 40 is the product. DecomposeTo break a number down into its smaller parts, like tens and ones.Decomposing the number 57 gives you 50 + 7. Parentheses ( )Symbols used in math to group numbers together. You always do the work inside the parentheses first.In 2 x (3 + 4), you first add 3 + 4 to get 7. EquationA mat...

The Distributive Property Formula a \times (b + c) = (a \times b) + (a \times c) This rule shows that multiplying a number 'a' by a sum (b + c) is the same as multiplying 'a' by 'b' and 'a' by 'c' separately, and then adding those products together. Finding the Missing Part of the Sum If a \times N = (a \times b) + (a \times c), then N = b + c When you see a problem broken down, the two numbers being multiplied by the same factor ('b' and 'c') must add up to the original larger factor ('N').