longmult 26*26

{ "query": { "display": "long multiplication $$26\\cdot\\:26$$", "symbolab_question": "PRE_ALGEBRA#longmult 26\\cdot 26" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Long Arithmetics", "subTopic": "Long Multiplication", "default": "676", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$26\\cdot\\:26=676$$", "input": "26\\cdot\\:26", "steps": [ { "type": "step", "primary": "Line up the numbers", "result": "\\begin{matrix}\\:\\:&2&6\\\\\\times\\:&2&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{2}&\\bold{6}\\\\\\times\\:&2&\\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&\\:\\:\\\\\\:\\:&2&\\bold{6}\\\\\\times\\:&2&\\bold{6}\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&6\\end{matrix}}" }, { "type": "step", "primary": "Add the carried number to the multiplication: $$3+2\\cdot\\:6=15$$", "secondary": [ "Carry $$1$$ to the column on the left and write $$5$$ in the result line" ], "result": "\\frac{\\begin{matrix}\\:\\:&1&\\bold{3}&\\:\\:\\\\\\:\\:&\\:\\:&\\bold{2}&6\\\\\\times\\:&\\:\\:&2&\\bold{6}\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&5&6\\end{matrix}}" }, { "type": "step", "primary": "Add the carried digit, $$1$$, to the result", "result": "\\frac{\\begin{matrix}\\:\\:&1&3&\\:\\:\\\\\\:\\:&\\:\\:&2&6\\\\\\times\\:&\\:\\:&2&6\\end{matrix}}{\\begin{matrix}\\:\\:&1&5&6\\end{matrix}}" }, { "type": "step", "primary": "Multiply the top number by the bolded digit of the bottom number", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&\\bold{2}&\\bold{6}\\\\\\:\\:&\\times\\:&\\bold{2}&6\\end{matrix}}{\\begin{matrix}\\:\\:&1&5&6\\end{matrix}}" }, { "type": "step", "primary": "Mutliply the bold numbers: $$6\\cdot\\:2=12$$", "secondary": [ "Carry $$1$$ to the column on the left and write $$2$$ in the result line" ], "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&1&\\:\\:\\\\\\:\\:&\\:\\:&2&\\bold{6}\\\\\\:\\:&\\times\\:&\\bold{2}&6\\end{matrix}}{\\begin{matrix}\\:\\:&1&5&6\\\\\\:\\:&\\:\\:&2&\\:\\:\\end{matrix}}" }, { "type": "step", "primary": "Add the carried number to the multiplication: $$1+2\\cdot\\:2=5$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&\\bold{1}&\\:\\:\\\\\\:\\:&\\:\\:&\\bold{2}&6\\\\\\:\\:&\\times\\:&\\bold{2}&6\\end{matrix}}{\\begin{matrix}\\:\\:&1&5&6\\\\\\:\\:&5&2&\\:\\:\\end{matrix}}" }, { "type": "step", "primary": "Add the rows to get the answer. For simplicity, fill in trailing zeros ", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&2&6\\\\\\:\\:&\\times\\:&2&6\\end{matrix}}{\\begin{matrix}\\:\\:&1&5&6\\\\\\:\\:&5&2&0\\end{matrix}}" }, { "type": "interim", "title": "$$156+520=676$$", "input": "\\begin{matrix}\\:\\:&1&5&6\\\\+&5&2&0\\end{matrix}", "steps": [ { "type": "step", "primary": "Add the digits of the bolded column: $$6+0=6$$", "result": "\\frac{\\begin{matrix}\\:\\:&1&5&\\bold{6}\\\\+&5&2&\\bold{0}\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\:\\:&\\:\\:&\\bold{6}\\end{matrix}}" }, { "type": "step", "primary": "Add the digits of the bolded column: $$5+2=7$$", "result": "\\frac{\\begin{matrix}\\:\\:&1&\\bold{5}&6\\\\+&5&\\bold{2}&0\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\:\\:&\\bold{7}&6\\end{matrix}}" }, { "type": "step", "primary": "Add the digits of the bolded column: $$1+5=6$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\bold{1}&5&6\\\\+&\\bold{5}&2&0\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\bold{6}&7&6\\end{matrix}}" }, { "type": "step", "result": "=676" } ], "meta": { "solvingClass": "StepsLongAddition", "interimType": "StepsLongAddition" } }, { "type": "step", "result": "=676" } ], "meta": { "solvingClass": "StepsLongMultiplication" } }, "meta": { "showVerify": true } }