Unit 2: Adding and Subtracting Decimals
Topic B: Subtracting Decimals
Line Up the Decimals
To subtract decimals you must subtract each digit from the digit of the same place value.
- Subtract thousandths from thousandths.
- Subtract hundredths from hundredths.
- Subtract tenths from tenths.
The best way to do this is to line up your decimals.
How to Subtract Decimals
The same techniques that you used in adding decimals are helpful when you subtract decimals.
- Rewrite the problem. Write the first number. Put the amount you are subtracting underneath so the decimal points are in a straight column.
[latex]\begin{array}{rrl}0.468&-&0.3=\\ \uparrow &&\uparrow \\ \text{starting number}&&\text{subtracting this much}\end{array}[/latex]
[latex]\begin{array}{ll}&0.468\\-&0.3\\ \hline\end{array}[/latex] - Put zeros at the end of the decimals so that all the decimals in the question have the same number of decimal places.
[latex]0.468-0.3=\begin{array}[t]{ll}&0.468\\-&0.3\mathbf{00}\\ \hline\end{array}[/latex] - Subtract the numbers, keeping the decimal point in the answer directly beneath the other decimal points.
[latex]\begin{array}{ll}&0.468\\-&0.300\\ \hline &\phantom{0}\mathbf{.}\end{array}[/latex]
Example A
[latex]2.536-0.59=[/latex]
- Rewrite the problem, lining up the decimals:
[latex]\begin{array}{ll}&2.536\\- &0.59\\ \hline \end{array}[/latex] - Add zeros so that there are the same number of decimal places for each.
[latex]\begin{array}{ll}&2.536\\- &0.59\mathbf{0}\\ \hline \end{array}[/latex] - Subtract the numbers. You will need to borrow.
[latex]\begin{array}{ll}&\tiny{\,1\;4\,1}\\&2.536\\- &0.590\\ \hline &1.946 \end{array}[/latex]
Vocabulary Review.
Write the definition.
[latex]8-5 = 3[/latex] ← Difference
Difference:
Exercise 1
Subtract to find the differences.
- [latex]\begin{array}[t]{ll}&2.75\\-&0.68\\ \hline&2.07\end{array}[/latex]
- [latex]\begin{array}[t]{ll}&9.64\\-&7.15\\ \hline&2.49\end{array}[/latex]
- [latex]\begin{array}[t]{ll}&3.85\\-&1.75 \\ \hline\\ \end{array}[/latex]
- [latex]\begin{array}[t]{ll}&1.17\\-&0.92 \\ \hline\\ \end{array}[/latex]
- [latex]\begin{array}[t]{ll}&27.3\\-&18.9 \\ \hline\\ \end{array}[/latex]
- [latex]\begin{array}[t]{ll}&0.732\\-&0.651 \\ \hline\\ \end{array}[/latex]
- [latex]\begin{array}[t]{ll}&0.362\\-&0.177 \\ \hline\\ \end{array}[/latex]
- [latex]\begin{array}[t]{ll}&6.85\\-&1.28 \\ \hline\\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&18.5\\-&7.9 \\ \hline\\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&98.6\\-&45.8 \\ \hline\\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&5.276\\-&3.298 \\ \hline\\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&5.251\\-&2.738 \\ \hline\\ \end{array}[/latex]
Answers to Exercise 1
- 2.07
- 2.49
- 2.10
- 0.25
- 8.4
- 0.081
- 0.185
- 5.57
- 10.6
- 52.8
- 1.978
- 2.513
Subtracting a Decimal from a Whole Number
Follow these steps to subtract a decimal from a whole number:
- Put a decimal point after the whole number.
16. − 0.4 = - Rewrite the problem.