longsub 180-48

{ "query": { "display": "long subtraction $$180-48$$", "symbolab_question": "PRE_ALGEBRA#longsub 180-48" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Long Arithmetics", "subTopic": "Long Subtraction", "default": "132", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$180-48=132$$", "input": "180-48", "steps": [ { "type": "step", "primary": "Line up the numbers", "result": "\\begin{matrix}\\:\\:&1&8&0\\\\-&0&4&8\\end{matrix}" }, { "type": "step", "primary": "Subtract each column of digits, starting from the right and working left<br/>If the digit being subtracted is larger than the digit above it, 'borrow' a digit from the next column to the left." }, { "type": "step", "primary": "In the bolded column, subtract the second digit from the first", "result": "\\begin{matrix}\\:\\:&1&8&\\bold{0}\\\\-&0&4&\\bold{8}\\end{matrix}" }, { "type": "step", "primary": "The bottom number is larger than the upper number. Try to'borrow' a digit from the left." }, { "type": "step", "primary": "Borrow $$1$$ from $$8$$. The remainder is $$7$$", "result": "\\begin{matrix}\\:\\:&\\:\\:&\\bold{7}&10\\\\\\:\\:&1&\\bold{\\sout{8}}&0\\\\-&0&\\bold{4}&8\\end{matrix}" }, { "type": "step", "primary": "Add $$1$$ ten to $$0$$: $$10+0=10$$", "result": "\\begin{matrix}\\:\\:&\\:\\:&7&\\bold{10}\\\\\\:\\:&1&\\sout{8}&\\bold{\\sout{0}}\\\\-&0&4&\\bold{8}\\end{matrix}" }, { "type": "step", "primary": "In the bolded column, subtract the second digit from the first: $$10-8=2$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&7&\\bold{10}\\\\\\:\\:&1&\\sout{8}&\\bold{\\sout{0}}\\\\-&0&4&\\bold{8}\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\:\\:&\\:\\:&\\bold{2}\\end{matrix}}" }, { "type": "step", "primary": "In the bolded column, subtract the second digit from the first: $$7-4=3$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&\\bold{7}&10\\\\\\:\\:&1&\\bold{\\sout{8}}&\\sout{0}\\\\-&0&\\bold{4}&8\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\:\\:&\\bold{3}&2\\end{matrix}}" }, { "type": "step", "primary": "In the bolded column, subtract the second digit from the first: $$1-0=1$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\bold{\\:\\:}&7&10\\\\\\:\\:&\\bold{1}&\\sout{8}&\\sout{0}\\\\-&\\bold{0}&4&8\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\bold{1}&3&2\\end{matrix}}" }, { "type": "step", "result": "=132" } ], "meta": { "solvingClass": "StepsLongSubtraction" } }, "meta": { "showVerify": true } }