Distributive Property (Expanding) With Area Model Problems

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#1 of 8: Mild

Distributive property (expanding) with area model

Use the area model to simplify the expression:`5(9 + 2j)`<selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><TableUIv2 data-props='{ "borderless": true, "transparent": true, "rows": [ [ { "value": "" }, { "value": "`9`" }, { "value": "`2j`" } ], [ { "value": "`5`", "styles": { "border_right": { "color": "black", "width": "2" } } }, { "value": "`?`", "colors": "black", "styles": { "border_top": { "color": "black", "width": "1.5" }, "border_right": { "color": "black", "width": "1.5" }, "border_bottom": { "color": "black", "width": "1.5" }, "height": "120", "width": "160" } }, { "value": "`?`", "colors": "black", "styles": { "border_top": { "color": "black", "width": "1.5" }, "border_right": { "color": "black", "width": "1.5" }, "border_bottom": { "color": "black", "width": "1.5" }, "height": "120", "width": "160" } } ] ]}'></TableUIv2 ></selectivedisplay>

#2 of 8: Mild

Distributive property (expanding) with area model

Use the area model to simplify the expression:`9(4x + 8)`<selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><TableUIv2 data-props='{ "borderless": true, "transparent": true, "rows": [ [ { "value": "" }, { "value": "`4x`" }, { "value": "`8`" } ], [ { "value": "`9`", "styles": { "border_right": { "color": "black", "width": "2" } } }, { "value": "`?`", "colors": "black", "styles": { "border_top": { "color": "black", "width": "1.5" }, "border_right": { "color": "black", "width": "1.5" }, "border_bottom": { "color": "black", "width": "1.5" }, "height": "120", "width": "160" } }, { "value": "`?`", "colors": "black", "styles": { "border_top": { "color": "black", "width": "1.5" }, "border_right": { "color": "black", "width": "1.5" }, "border_bottom": { "color": "black", "width": "1.5" }, "height": "120", "width": "160" } } ] ]}'></TableUIv2 ></selectivedisplay>

#3 of 8: Medium

Distributive property (expanding) with area model

Use the area model to simplify the expression:`3(10y + 14z)`<selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><TableUIv2 data-props='{ "borderless": true, "transparent": true, "rows": [ [ { "value": "" }, { "value": "`10y`" }, { "value": "`14z`" } ], [ { "value": "`3`", "styles": { "border_right": { "color": "black", "width": "2" } } }, { "value": "`?`", "colors": "black", "styles": { "border_top": { "color": "black", "width": "1.5" }, "border_right": { "color": "black", "width": "1.5" }, "border_bottom": { "color": "black", "width": "1.5" }, "height": "120", "width": "160" } }, { "value": "`?`", "colors": "black", "styles": { "border_top": { "color": "black", "width": "1.5" }, "border_right": { "color": "black", "width": "1.5" }, "border_bottom": { "color": "black", "width": "1.5" }, "height": "120", "width": "160" } } ] ]}'></TableUIv2 ></selectivedisplay>

#4 of 8: Medium

Distributive property (expanding) with area model

Use the area model to simplify the expression:`4.5 (2h + 20j)`<selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><TableUIv2 data-props='{ "borderless": true, "transparent": true, "rows": [ [ { "value": "" }, { "value": "`2h`" }, { "value": "`20j`" } ], [ { "value": "`4.5`", "styles": { "border_right": { "color": "black", "width": "2" } } }, { "value": "`?`", "colors": "black", "styles": { "border_top": { "color": "black", "width": "1.5" }, "border_right": { "color": "black", "width": "1.5" }, "border_bottom": { "color": "black", "width": "1.5" }, "height": "120", "width": "160" } }, { "value": "`?`", "colors": "black", "styles": { "border_top": { "color": "black", "width": "1.5" }, "border_right": { "color": "black", "width": "1.5" }, "border_bottom": { "color": "black", "width": "1.5" }, "height": "120", "width": "160" } } ] ]}'></TableUIv2 ></selectivedisplay>

#5 of 8: Medium

Distributive property (expanding) with area model

Use the area model to simplify the expression:`2.5(12y + 2z) `<selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><TableUIv2 data-props='{ "borderless": true, "transparent": true, "rows": [ [ { "value": "" }, { "value": "`12y`" }, { "value": "`2z`" } ], [ { "value": "`2.5`", "styles": { "border_right": { "color": "black", "width": "2" } } }, { "value": "`?`", "colors": "black", "styles": { "border_top": { "color": "black", "width": "1.5" }, "border_right": { "color": "black", "width": "1.5" }, "border_bottom": { "color": "black", "width": "1.5" }, "height": "120", "width": "160" } }, { "value": "`?`", "colors": "black", "styles": { "border_top": { "color": "black", "width": "1.5" }, "border_right": { "color": "black", "width": "1.5" }, "border_bottom": { "color": "black", "width": "1.5" }, "height": "120", "width": "160" } } ] ]}'></TableUIv2 ></selectivedisplay>

#6 of 8: Spicy

Distributive property (expanding) with area model

Use the area model to simplify the expression:`1/5 (30j + 25)`<selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><TableUIv2 data-props='{ "borderless": true, "transparent": true, "rows": [ [ { "value": "" }, { "value": "`30j`" }, { "value": "`25`" } ], [ { "value": "`1/5`", "styles": { "border_right": { "color": "black", "width": "2" } } }, { "value": "`?`", "colors": "black", "styles": { "border_top": { "color": "black", "width": "1.5" }, "border_right": { "color": "black", "width": "1.5" }, "border_bottom": { "color": "black", "width": "1.5" }, "height": "120", "width": "160" } }, { "value": "`?`", "colors": "black", "styles": { "border_top": { "color": "black", "width": "1.5" }, "border_right": { "color": "black", "width": "1.5" }, "border_bottom": { "color": "black", "width": "1.5" }, "height": "120", "width": "160" } } ] ]}'></TableUIv2 ></selectivedisplay>

#7 of 8: Spicy

Distributive property (expanding) with area model

Use the area model to simplify the expression:`1.5 (5x + 6)`<selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><TableUIv2 data-props='{ "borderless": true, "transparent": true, "rows": [ [ { "value": "" }, { "value": "`5x`" }, { "value": "`6`" } ], [ { "value": "`1.5`", "styles": { "border_right": { "color": "black", "width": "2" } } }, { "value": "`?`", "colors": "black", "styles": { "border_top": { "color": "black", "width": "1.5" }, "border_right": { "color": "black", "width": "1.5" }, "border_bottom": { "color": "black", "width": "1.5" }, "height": "120", "width": "160" } }, { "value": "`?`", "colors": "black", "styles": { "border_top": { "color": "black", "width": "1.5" }, "border_right": { "color": "black", "width": "1.5" }, "border_bottom": { "color": "black", "width": "1.5" }, "height": "120", "width": "160" } } ] ]}'></TableUIv2 ></selectivedisplay>

#8 of 8: Spicy

Distributive property (expanding) with area model

Use the area model to simplify the expression:`0.5 (8x + 22)`<selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><TableUIv2 data-props='{ "borderless": true, "transparent": true, "rows": [ [ { "value": "" }, { "value": "`8x`" }, { "value": "`22`" } ], [ { "value": "`0.5`", "styles": { "border_right": { "color": "black", "width": "2" } } }, { "value": "`?`", "colors": "black", "styles": { "border_top": { "color": "black", "width": "1.5" }, "border_right": { "color": "black", "width": "1.5" }, "border_bottom": { "color": "black", "width": "1.5" }, "height": "120", "width": "160" } }, { "value": "`?`", "colors": "black", "styles": { "border_top": { "color": "black", "width": "1.5" }, "border_right": { "color": "black", "width": "1.5" }, "border_bottom": { "color": "black", "width": "1.5" }, "height": "120", "width": "160" } } ] ]}'></TableUIv2 ></selectivedisplay>

Distributive property applies in a situation when a number is multiplied with the difference or the sum of two or more terms. This mathematical property helps us in solving complex equations from different domains of the subject. This property applies to the difference or the sum of two or more terms.

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Grade 6

Expressions, Equations, And Inequalities

6.EE.A.3