Addition and subtraction

Two-step problems with addition and subtraction

Two-step problems with addition and subtraction

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Tutor: Toby


Two-step problems with addition and subtraction

​​In a nutshell

Addition and subtraction problems can involve more than one calculation. Given the context of a problem, it may be necessary to add in one step, then subtract in the next for example.

Addition and subtraction methods

With two-step problems, any addition and subtraction methods you already know are applicable. It is likely that you have come across two methods already: using mental arithmetic, perhaps involving number lines, and using the column method.

Example 1

Jean is buying new furniture. She chooses a chair that costs £15.99£15.99 and a desk that costs £49.99£49.99. On her way to pay, she sees a lamp for £9.50£9.50. If she buys all three items, how much does she have to pay?

You need to add these three values. This can be done in two step: start by adding the first two together:

1151.919+49.9965.98\begin {array} { c c c c c c} & \overset{1}1 & \overset{1}5 & . & \overset{1}9 & 9 \\+ & 4 & 9 & . & 9 & 9 \\ \hline & 6 & 5 & . & 9&8 \\ \hline\end {array}​​

Next you add the third number to the current total:

6151.98+9.5075.48\begin {array} { c c c c c c} & \overset{1}6 & \overset{1}5 & . & 9 & 8 \\+ & & 9 & . & 5 & 0 \\ \hline & 7 & 5 & . & 4&8 \\ \hline\end {array}​​

So the final total is £75.48£75.48. ​Note: If you have three numbers to add, the order in which you add them doesn't matter. Here you would get the same answer if you added 49.9949.99 and 9.509.50 first, then added 15.9915.99.

Take care with the order

With addition, the order doesn't matter, as seen above. More care and attention is required with when subtraction is involved. Observe:


If you try to add the one to the three, then subtract that total from the five, get the wrong answer. Instead you must read this problem from left to right:


More specifically, you must be aware that the 33 in this problem is not 33 at all, rather it is 3-3. Hence you can rewrite this problem as


This is because adding a negative number is the same as subtracting the positive number. Now you have an addition problem which can be done in any order, so long as you add 3-3 rather than 33.

Example 2



You can start by subtracting 2121 from 3636. This could be done mentally with two number lines. First subtract the one unit:

1333435363738\begin{array}{cccccccccccccc}&&&&&-1&&&&&&& \\& &&&&\curvearrowleft &&&\\33&&34&&\underline{35}&&\underline{36}&&37&&38 \\|&&|&&|&&|&&|&&| \\ \hline\end{array}​​

Next subtract the two tens:

1010551525354555\begin{array}{cccccccccccccc}&&&&&-10&&-10&&&&& \\& &&&&\curvearrowleft &&\curvearrowleft&& &&&&\\-5&&5&&\underline{15}&&25&&\underline{35}&&45&&55&& \\|&&|&&|&&|&&|&&|&&| \\ \hline\end{array}​​

You have 1515 so far. Now you can add the 1616. This can also be done mentally. Start by adding the six units:

+11+1+1+1+115161718192021\begin{array}{cccccccccccccc}&+1&&-1&&+1&&+1&&+1&&+1&&& \\& \curvearrowright&&\curvearrowright &&\curvearrowright &&\curvearrowright&&\curvearrowright &&\curvearrowright &&\\\underline{15}&&16&&17&&18&&19&&20&&\underline{21}&& \\|&&|&&|&&|&&|&&|&&| \\ \hline\end{array}​​

Now add the one ten:

+10911121314151\begin{array}{cccccccccccccc}&&&&&&&+10&&&&& \\& &&&& &&\curvearrowright&& &&&&\\-9&&1&&11&&\underline{21}&&\underline{31}&&41&&51&& \\|&&|&&|&&|&&|&&|&&| \\ \hline\end{array}​​



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