longmult 25*16

{ "query": { "display": "long multiplication $$25\\cdot\\:16$$", "symbolab_question": "PRE_ALGEBRA#longmult 25\\cdot 16" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Long Arithmetics", "subTopic": "Long Multiplication", "default": "400", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$25\\cdot\\:16=400$$", "input": "25\\cdot\\:16", "steps": [ { "type": "step", "primary": "Line up the numbers", "result": "\\begin{matrix}\\:\\:&2&5\\\\\\times\\:&1&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{5}\\\\\\times\\:&1&\\bold{6}\\end{matrix}" }, { "type": "step", "primary": "Mutliply the bold numbers: $$5\\cdot\\:6=30$$", "secondary": [ "Carry $$3$$ to the column on the left and write $$0$$ in the result line" ], "result": "\\frac{\\begin{matrix}\\:\\:&3&\\:\\:\\\\\\:\\:&2&\\bold{5}\\\\\\times\\:&1&\\bold{6}\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&0\\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}&5\\\\\\times\\:&\\:\\:&1&\\bold{6}\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&5&0\\end{matrix}}" }, { "type": "step", "primary": "Add the carried digit, $$1$$, to the result", "result": "\\frac{\\begin{matrix}\\:\\:&1&3&\\:\\:\\\\\\:\\:&\\:\\:&2&5\\\\\\times\\:&\\:\\:&1&6\\end{matrix}}{\\begin{matrix}\\:\\:&1&5&0\\end{matrix}}" }, { "type": "step", "primary": "Multiply the top number by the bolded digit of the bottom number", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&\\bold{2}&\\bold{5}\\\\\\:\\:&\\times\\:&\\bold{1}&6\\end{matrix}}{\\begin{matrix}\\:\\:&1&5&0\\end{matrix}}" }, { "type": "step", "primary": "Mutliply the bold numbers: $$5\\cdot\\:1=5$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&2&\\bold{5}\\\\\\:\\:&\\times\\:&\\bold{1}&6\\end{matrix}}{\\begin{matrix}\\:\\:&1&5&0\\\\\\:\\:&\\:\\:&5&\\:\\:\\end{matrix}}" }, { "type": "step", "primary": "Mutliply the bold numbers: $$2\\cdot\\:1=2$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&\\bold{2}&5\\\\\\:\\:&\\times\\:&\\bold{1}&6\\end{matrix}}{\\begin{matrix}\\:\\:&1&5&0\\\\\\:\\:&2&5&\\:\\:\\end{matrix}}" }, { "type": "step", "primary": "Add the rows to get the answer. For simplicity, fill in trailing zeros ", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&2&5\\\\\\:\\:&\\times\\:&1&6\\end{matrix}}{\\begin{matrix}\\:\\:&1&5&0\\\\\\:\\:&2&5&0\\end{matrix}}" }, { "type": "interim", "title": "$$150+250=400$$", "input": "\\begin{matrix}\\:\\:&1&5&0\\\\+&2&5&0\\end{matrix}", "steps": [ { "type": "step", "primary": "Add the digits of the bolded column: $$0+0=0$$", "result": "\\frac{\\begin{matrix}\\:\\:&1&5&\\bold{0}\\\\+&2&5&\\bold{0}\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\:\\:&\\:\\:&\\bold{0}\\end{matrix}}" }, { "type": "step", "primary": "Add the digits of the bolded column: $$5+5=10$$", "result": "\\frac{\\begin{matrix}\\:\\:&1&\\bold{5}&0\\\\+&2&\\bold{5}&0\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\:\\:&\\bold{\\:\\:}&0\\end{matrix}}" }, { "type": "step", "primary": "Carry $$1$$ to the column on the left and write $$0$$ in the bolded column", "result": "\\frac{\\begin{matrix}\\:\\:&1&\\bold{\\:\\:}&\\:\\:\\\\\\:\\:&1&\\bold{5}&0\\\\+&2&\\bold{5}&0\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\:\\:&\\bold{0}&0\\end{matrix}}" }, { "type": "step", "primary": "Add the digits of the bolded column: $$1+1+2=4$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\bold{1}&\\:\\:&\\:\\:\\\\\\:\\:&\\bold{1}&5&0\\\\+&\\bold{2}&5&0\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\bold{4}&0&0\\end{matrix}}" }, { "type": "step", "result": "=400" } ], "meta": { "solvingClass": "StepsLongAddition", "interimType": "StepsLongAddition" } }, { "type": "step", "result": "=400" } ], "meta": { "solvingClass": "StepsLongMultiplication" } }, "meta": { "showVerify": true } }