longsub-6.1+1.7

{ "query": { "display": "long subtraction $$-6.1+1.7$$", "symbolab_question": "PRE_ALGEBRA#longsub -6.1+1.7" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Long Arithmetics", "subTopic": "Long Subtraction", "default": "-4.4", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$1.7-6.1=-4.4$$", "input": "1.7-6.1", "steps": [ { "type": "step", "primary": "To subtract a larger number from a smaller one switch the order of the numbers. Negate the result by attaching a minus sign" }, { "type": "interim", "title": "$$6.1-1.7=4.4$$", "input": "6.1-1.7", "steps": [ { "type": "step", "primary": "Write the numbers one under the other, line up the decimal points.<br/>Add trailing zeroes so the numbers have the same length.", "result": "\\begin{matrix}\\:\\:&6&.&1\\\\-&1&.&7\\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}\\:\\:&6&.&\\bold{1}\\\\-&1&.&\\bold{7}\\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 $$6$$. The remainder is $$5$$", "result": "\\begin{matrix}\\:\\:&\\bold{5}&\\:\\:&10\\\\\\:\\:&\\bold{\\sout{6}}&.&1\\\\-&\\bold{1}&.&7\\end{matrix}" }, { "type": "step", "primary": "Add $$1$$ ten to $$1$$: $$10+1=11$$", "result": "\\begin{matrix}\\:\\:&5&\\:\\:&\\bold{11}\\\\\\:\\:&\\sout{6}&.&\\bold{\\sout{1}}\\\\-&1&.&\\bold{7}\\end{matrix}" }, { "type": "step", "primary": "In the bolded column, subtract the second digit from the first: $$11-7=4$$", "result": "\\frac{\\begin{matrix}\\:\\:&5&\\:\\:&\\bold{11}\\\\\\:\\:&\\sout{6}&.&\\bold{\\sout{1}}\\\\-&1&.&\\bold{7}\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\:\\:&\\:\\:&\\bold{4}\\end{matrix}}" }, { "type": "step", "primary": "Place the decimal point in the answer directly below the decimal points in the terms", "result": "\\frac{\\begin{matrix}\\:\\:&5&\\bold{\\:\\:}&11\\\\\\:\\:&\\sout{6}&\\bold{.}&\\sout{1}\\\\-&1&\\bold{.}&7\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\:\\:&\\bold{.}&4\\end{matrix}}" }, { "type": "step", "primary": "In the bolded column, subtract the second digit from the first: $$5-1=4$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\bold{5}&\\:\\:&11\\\\\\:\\:&\\bold{\\sout{6}}&.&\\sout{1}\\\\-&\\bold{1}&.&7\\end{matrix}}{\\begin{matrix}\\phantom{+}&\\bold{4}&.&4\\end{matrix}}" }, { "type": "step", "result": "=4.4" } ], "meta": { "solvingClass": "StepsLongSubtraction", "interimType": "StepsLongSubtraction" } }, { "type": "step", "primary": "Place a minus sign in front of the answer", "result": "=-4.4" } ], "meta": { "solvingClass": "StepsLongSubtraction" } }, "meta": { "showVerify": true } }