longmult 12*14

{ "query": { "display": "long multiplication $$12\\cdot\\:14$$", "symbolab_question": "PRE_ALGEBRA#longmult 12\\cdot 14" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Long Arithmetics", "subTopic": "Long Multiplication", "default": "168", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$12\\cdot\\:14=168$$", "input": "12\\cdot\\:14", "steps": [ { "type": "step", "primary": "Line up the numbers", "result": "\\begin{matrix}\\:\\:&1&2\\\\\\times\\:&1&4\\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{1}&\\bold{2}\\\\\\times\\:&1&\\bold{4}\\end{matrix}" }, { "type": "step", "primary": "Mutliply the bold numbers: $$2\\cdot\\:4=8$$", "result": "\\frac{\\begin{matrix}\\:\\:&1&\\bold{2}\\\\\\times\\:&1&\\bold{4}\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&8\\end{matrix}}" }, { "type": "step", "primary": "Mutliply the bold numbers: $$1\\cdot\\:4=4$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\bold{1}&2\\\\\\times\\:&1&\\bold{4}\\end{matrix}}{\\begin{matrix}\\:\\:&4&8\\end{matrix}}" }, { "type": "step", "primary": "Multiply the top number by the bolded digit of the bottom number", "result": "\\frac{\\begin{matrix}\\:\\:&\\bold{1}&\\bold{2}\\\\\\times\\:&\\bold{1}&4\\end{matrix}}{\\begin{matrix}\\:\\:&4&8\\end{matrix}}" }, { "type": "step", "primary": "Mutliply the bold numbers: $$2\\cdot\\:1=2$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&1&\\bold{2}\\\\\\:\\:&\\times\\:&\\bold{1}&4\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&4&8\\\\\\:\\:&\\:\\:&2&\\:\\:\\end{matrix}}" }, { "type": "step", "primary": "Mutliply the bold numbers: $$1\\cdot\\:1=1$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&\\bold{1}&2\\\\\\:\\:&\\times\\:&\\bold{1}&4\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&4&8\\\\\\:\\:&1&2&\\:\\:\\end{matrix}}" }, { "type": "step", "primary": "Add the rows to get the answer. For simplicity, fill in trailing zeros ", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&1&2\\\\\\:\\:&\\times\\:&1&4\\end{matrix}}{\\begin{matrix}\\:\\:&0&4&8\\\\\\:\\:&1&2&0\\end{matrix}}" }, { "type": "interim", "title": "$$48+120=168$$", "input": "\\begin{matrix}\\:\\:&0&4&8\\\\+&1&2&0\\end{matrix}", "steps": [ { "type": "step", "primary": "Add the digits of the bolded column: $$8+0=8$$", "result": "\\frac{\\begin{matrix}\\:\\:&0&4&\\bold{8}\\\\+&1&2&\\bold{0}\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\:\\:&\\:\\:&\\bold{8}\\end{matrix}}" }, { "type": "step", "primary": "Add the digits of the bolded column: $$4+2=6$$", "result": "\\frac{\\begin{matrix}\\:\\:&0&\\bold{4}&8\\\\+&1&\\bold{2}&0\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\:\\:&\\bold{6}&8\\end{matrix}}" }, { "type": "step", "primary": "Add the digits of the bolded column: $$0+1=1$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\bold{0}&4&8\\\\+&\\bold{1}&2&0\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\bold{1}&6&8\\end{matrix}}" }, { "type": "step", "result": "=168" } ], "meta": { "solvingClass": "StepsLongAddition", "interimType": "StepsLongAddition" } }, { "type": "step", "result": "=168" } ], "meta": { "solvingClass": "StepsLongMultiplication" } }, "meta": { "showVerify": true } }