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Decimal Subtraction
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Foundational skills
Subtract tenths mentally (no exchange)
\[ 0.8 – 0.3 = 0.5 \]
Subtract one tenth value from another with no exchange required.
Subtract tenths from 1
\[ 1 – 0.4 = 0.6 \]
Subtract tenths from 1 whole.
Subtract hundredths mentally
\[ 0.08 – 0.03 = 0.05 \]
Subtract one hundredth value from another.
Subtracting decimals (same decimal places)
Subtract two 1dp decimals (no exchange)
\[ 7.8 – 3.2 = 4.6 \]
Subtract two decimals with one decimal place where no exchange is required.
Subtract two 1dp decimals (exchange from ones)
\[ 7.3 – 3.8 = 3.5 \]
Subtract two decimals with one decimal place where exchange from ones is required.
Subtract two 1dp decimals (exchange from tens)
\[ 12.3 – 7.8 = 4.5 \]
Subtract two decimals where exchange propagates from tens.
Subtract two 2dp decimals (no exchange)
\[ 8.75 – 3.23 = 5.52 \]
Subtract two decimals with two decimal places where no exchange is required.
Subtract two 2dp decimals (exchange from tenths)
\[ 8.52 – 3.27 = 5.25 \]
Subtract two decimals with two decimal places where exchange from tenths is required.
Subtract two 2dp decimals (multiple exchanges)
\[ 8.23 – 3.78 = 4.45 \]
Subtract two decimals with two decimal places requiring multiple exchanges.
Subtract two 3dp decimals
\[ 5.876 – 2.321 = 3.555 \]
Subtract two decimals with three decimal places.
Subtracting decimals (different decimal places)
Subtract 2dp from 1dp
\[ 8.7 – 3.25 = 5.45 \]
Subtract a 2dp decimal from a 1dp decimal.
Subtract 3dp from 1dp
\[ 7.5 – 2.123 = 5.377 \]
Subtract a 3dp decimal from a 1dp decimal.
Subtract 3dp from 2dp
\[ 7.58 – 2.125 = 5.455 \]
Subtract a 3dp decimal from a 2dp decimal.
Subtract 1dp from 2dp
\[ 8.75 – 3.2 = 5.55 \]
Subtract a 1dp decimal from a 2dp decimal.
Subtracting from whole numbers
Subtract 1dp decimal from whole number
\[ 8 – 3.4 = 4.6 \]
Subtract a decimal from a whole number.
Subtract 2dp decimal from whole number
\[ 8 – 3.45 = 4.55 \]
Subtract a 2dp decimal from a whole number.
Subtract 3dp decimal from whole number
\[ 5 – 0.234 = 4.766 \]
Subtract a 3dp decimal from a whole number.
Subtract decimal from 1
\[ 1 – 0.37 = 0.63 \]
Subtract a 2dp decimal from 1.
Subtract decimal from 10
\[ 10 – 3.7 = 6.3 \]
Subtract a 1dp decimal from 10.
Column method
Set up column subtraction with decimals
\[ 45.67 – 3.2 \rightarrow \text{columns} \]
Set up a decimal subtraction in column format with decimal points aligned.
Complete column subtraction (2dp no exchange)
\[ 8.75 – 3.23 = 5.52 \]
Use the column method to subtract two 2dp decimals without exchange.
Complete column subtraction (2dp with exchange)
\[ 8.52 – 3.27 = 5.25 \]
Use the column method to subtract two 2dp decimals with exchange.
Complete column subtraction (different dp)
\[ 12.5 – 3.27 = 9.23 \]
Use the column method to subtract decimals with different decimal places.
Complete column subtraction (from whole)
\[ 8 – 3.45 = 4.55 \]
Use the column method to subtract a decimal from a whole number.
Subtraction across zero tenths
Subtract creating zero in tenths
\[ 5.53 – 2.51 = 3.02 \]
Subtract where the answer has zero in the tenths place.
Subtract with zeros in subtrahend
\[ 8.7 – 3.05 = 5.65 \]
Subtract a decimal that contains zero in the tenths place.
Subtraction giving answer less than 1
Subtract to get decimal answer less than 1
\[ 2.3 – 1.8 = 0.5 \]
Subtract decimals where the answer is less than 1.
Special cases
Subtract from decimal ending in zero
\[ 8.50 – 3.27 = 5.23 \]
Subtract from a decimal that ends in zero.
Subtract giving whole number answer
\[ 8.5 – 3.5 = 5 \]
Subtract decimals where the answer is a whole number.
Subtract with repeated borrowing
\[ 10.01 – 3.45 = 6.56 \]
Subtract where borrowing cascades across multiple columns.
Subtract small decimals (both less than 1)
\[ 0.85 – 0.32 = 0.53 \]
Subtract two decimals that are both less than 1.
Find the difference between two decimals
\[ \text{Difference: } 8.5, 3.2 \]
Find the difference between two decimals (phrased as ‘difference’).
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