longmult 15*12

{ "query": { "display": "long multiplication $$15\\cdot\\:12$$", "symbolab_question": "PRE_ALGEBRA#longmult 15\\cdot 12" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Long Arithmetics", "subTopic": "Long Multiplication", "default": "180", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$15\\cdot\\:12=180$$", "input": "15\\cdot\\:12", "steps": [ { "type": "step", "primary": "Line up the numbers", "result": "\\begin{matrix}\\:\\:&1&5\\\\\\times\\:&1&2\\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{5}\\\\\\times\\:&1&\\bold{2}\\end{matrix}" }, { "type": "step", "primary": "Mutliply the bold numbers: $$5\\cdot\\:2=10$$", "secondary": [ "Carry $$1$$ to the column on the left and write $$0$$ in the result line" ], "result": "\\frac{\\begin{matrix}\\:\\:&1&\\:\\:\\\\\\:\\:&1&\\bold{5}\\\\\\times\\:&1&\\bold{2}\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&0\\end{matrix}}" }, { "type": "step", "primary": "Add the carried number to the multiplication: $$1+1\\cdot\\:2=3$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\bold{1}&\\:\\:\\\\\\:\\:&\\bold{1}&5\\\\\\times\\:&1&\\bold{2}\\end{matrix}}{\\begin{matrix}\\:\\:&3&0\\end{matrix}}" }, { "type": "step", "primary": "Multiply the top number by the bolded digit of the bottom number", "result": "\\frac{\\begin{matrix}\\:\\:&\\bold{1}&\\bold{5}\\\\\\times\\:&\\bold{1}&2\\end{matrix}}{\\begin{matrix}\\:\\:&3&0\\end{matrix}}" }, { "type": "step", "primary": "Mutliply the bold numbers: $$5\\cdot\\:1=5$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&1&\\bold{5}\\\\\\:\\:&\\times\\:&\\bold{1}&2\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&3&0\\\\\\:\\:&\\:\\:&5&\\:\\:\\end{matrix}}" }, { "type": "step", "primary": "Mutliply the bold numbers: $$1\\cdot\\:1=1$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&\\bold{1}&5\\\\\\:\\:&\\times\\:&\\bold{1}&2\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&3&0\\\\\\:\\:&1&5&\\:\\:\\end{matrix}}" }, { "type": "step", "primary": "Add the rows to get the answer. For simplicity, fill in trailing zeros ", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&1&5\\\\\\:\\:&\\times\\:&1&2\\end{matrix}}{\\begin{matrix}\\:\\:&0&3&0\\\\\\:\\:&1&5&0\\end{matrix}}" }, { "type": "interim", "title": "$$30+150=180$$", "input": "\\begin{matrix}\\:\\:&0&3&0\\\\+&1&5&0\\end{matrix}", "steps": [ { "type": "step", "primary": "Add the digits of the bolded column: $$0+0=0$$", "result": "\\frac{\\begin{matrix}\\:\\:&0&3&\\bold{0}\\\\+&1&5&\\bold{0}\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\:\\:&\\:\\:&\\bold{0}\\end{matrix}}" }, { "type": "step", "primary": "Add the digits of the bolded column: $$3+5=8$$", "result": "\\frac{\\begin{matrix}\\:\\:&0&\\bold{3}&0\\\\+&1&\\bold{5}&0\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\:\\:&\\bold{8}&0\\end{matrix}}" }, { "type": "step", "primary": "Add the digits of the bolded column: $$0+1=1$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\bold{0}&3&0\\\\+&\\bold{1}&5&0\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\bold{1}&8&0\\end{matrix}}" }, { "type": "step", "result": "=180" } ], "meta": { "solvingClass": "StepsLongAddition", "interimType": "StepsLongAddition" } }, { "type": "step", "result": "=180" } ], "meta": { "solvingClass": "StepsLongMultiplication" } }, "meta": { "showVerify": true } }