longmult 36*36

{ "query": { "display": "long multiplication $$36\\cdot\\:36$$", "symbolab_question": "PRE_ALGEBRA#longmult 36\\cdot 36" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Long Arithmetics", "subTopic": "Long Multiplication", "default": "1296", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$36\\cdot\\:36=1296$$", "input": "36\\cdot\\:36", "steps": [ { "type": "step", "primary": "Line up the numbers", "result": "\\begin{matrix}\\:\\:&3&6\\\\\\times\\:&3&6\\end{matrix}" }, { "type": "step", "primary": "Multiply the top number by the bottom number one digit at a time starting with the ones digit (from right to left)" }, { "type": "step", "primary": "Multiply the top number by the bolded digit of the bottom number", "result": "\\begin{matrix}\\:\\:&\\bold{3}&\\bold{6}\\\\\\times\\:&3&\\bold{6}\\end{matrix}" }, { "type": "step", "primary": "Mutliply the bold numbers: $$6\\cdot\\:6=36$$", "secondary": [ "Carry $$3$$ to the column on the left and write $$6$$ in the result line" ], "result": "\\frac{\\begin{matrix}\\:\\:&3&\\:\\:\\\\\\:\\:&3&\\bold{6}\\\\\\times\\:&3&\\bold{6}\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&6\\end{matrix}}" }, { "type": "step", "primary": "Add the carried number to the multiplication: $$3+3\\cdot\\:6=21$$", "secondary": [ "Carry $$2$$ to the column on the left and write $$1$$ in the result line" ], "result": "\\frac{\\begin{matrix}\\:\\:&2&\\bold{3}&\\:\\:\\\\\\:\\:&\\:\\:&\\bold{3}&6\\\\\\times\\:&\\:\\:&3&\\bold{6}\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&1&6\\end{matrix}}" }, { "type": "step", "primary": "Add the carried digit, $$2$$, to the result", "result": "\\frac{\\begin{matrix}\\:\\:&2&3&\\:\\:\\\\\\:\\:&\\:\\:&3&6\\\\\\times\\:&\\:\\:&3&6\\end{matrix}}{\\begin{matrix}\\:\\:&2&1&6\\end{matrix}}" }, { "type": "step", "primary": "Multiply the top number by the bolded digit of the bottom number", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&\\bold{3}&\\bold{6}\\\\\\:\\:&\\times\\:&\\bold{3}&6\\end{matrix}}{\\begin{matrix}\\:\\:&2&1&6\\end{matrix}}" }, { "type": "step", "primary": "Mutliply the bold numbers: $$6\\cdot\\:3=18$$", "secondary": [ "Carry $$1$$ to the column on the left and write $$8$$ in the result line" ], "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&1&\\:\\:\\\\\\:\\:&\\:\\:&3&\\bold{6}\\\\\\:\\:&\\times\\:&\\bold{3}&6\\end{matrix}}{\\begin{matrix}\\:\\:&2&1&6\\\\\\:\\:&\\:\\:&8&\\:\\:\\end{matrix}}" }, { "type": "step", "primary": "Add the carried number to the multiplication: $$1+3\\cdot\\:3=10$$", "secondary": [ "Carry $$1$$ to the column on the left and write $$0$$ in the result line" ], "result": "\\frac{\\begin{matrix}\\:\\:&1&\\bold{1}&\\:\\:\\\\\\:\\:&\\:\\:&\\bold{3}&6\\\\\\times\\:&\\:\\:&\\bold{3}&6\\end{matrix}}{\\begin{matrix}\\:\\:&2&1&6\\\\\\:\\:&0&8&\\:\\:\\end{matrix}}" }, { "type": "step", "primary": "Add the carried digit, $$1$$, to the result", "result": "\\frac{\\begin{matrix}\\:\\:&1&1&\\:\\:\\\\\\:\\:&\\:\\:&3&6\\\\\\times\\:&\\:\\:&3&6\\end{matrix}}{\\begin{matrix}\\:\\:&2&1&6\\\\1&0&8&\\:\\:\\end{matrix}}" }, { "type": "step", "primary": "Add the rows to get the answer. For simplicity, fill in trailing zeros ", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&3&6\\\\\\:\\:&\\times\\:&3&6\\end{matrix}}{\\begin{matrix}0&2&1&6\\\\1&0&8&0\\end{matrix}}" }, { "type": "interim", "title": "$$216+1080=1296$$", "input": "\\begin{matrix}\\:\\:&0&2&1&6\\\\+&1&0&8&0\\end{matrix}", "steps": [ { "type": "step", "primary": "Add the digits of the bolded column: $$6+0=6$$", "result": "\\frac{\\begin{matrix}\\:\\:&0&2&1&\\bold{6}\\\\+&1&0&8&\\bold{0}\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\:\\:&\\:\\:&\\:\\:&\\bold{6}\\end{matrix}}" }, { "type": "step", "primary": "Add the digits of the bolded column: $$1+8=9$$", "result": "\\frac{\\begin{matrix}\\:\\:&0&2&\\bold{1}&6\\\\+&1&0&\\bold{8}&0\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\:\\:&\\:\\:&\\bold{9}&6\\end{matrix}}" }, { "type": "step", "primary": "Add the digits of the bolded column: $$2+0=2$$", "result": "\\frac{\\begin{matrix}\\:\\:&0&\\bold{2}&1&6\\\\+&1&\\bold{0}&8&0\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\:\\:&\\bold{2}&9&6\\end{matrix}}" }, { "type": "step", "primary": "Add the digits of the bolded column: $$0+1=1$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\bold{0}&2&1&6\\\\+&\\bold{1}&0&8&0\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\bold{1}&2&9&6\\end{matrix}}" }, { "type": "step", "result": "=1296" } ], "meta": { "solvingClass": "StepsLongAddition", "interimType": "StepsLongAddition" } }, { "type": "step", "result": "=1296" } ], "meta": { "solvingClass": "StepsLongMultiplication" } }, "meta": { "showVerify": true } }