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P3 Addition and Subtraction

Writing four-digit addition and subtraction algorithms with carries and exchanges, then calculating two-digit sums and differences mentally.

⏱ 5 min · 🎯 4 things to master

Written working is a map: align equal places, record each carry, and show every exchange. Mental working is a different tool for small numbers, so keep it short and explain the partition or compensation you used.

Parents: ask your child to predict the size and number of carries first, then let them reveal one column at a time.

By the end you will be able to add and subtract numbers up to four digits in aligned columns and mentally add or subtract two 2-digit numbers.

Written addition: align every place

Place the ones under ones, tens under tens, hundreds under hundreds and thousands under thousands. In 2,786 + 1,547, a carry moves left after each column that makes 10 or more.

🤔 Predict first: Before 2,786 + 1,547, what should you expect?

Written addition: carry by place

Predict first: How many carries will 2,786 + 1,547 make?

Add 2,786 and 1,547

carry1112786+15474333\begin{array}{r r r r r}\text{carry}&1&1&1&\\&2&7&8&6\\+&1&5&4&7\\\hline&4&3&3&3\\\end{array}
ones: 6+7=13⇒ write 3, carry 1\text{ones: }6+7=13\Rightarrow\text{ write 3, carry 1}
tens: 8+4+1=13⇒ write 3, carry 1\text{tens: }8+4+1=13\Rightarrow\text{ write 3, carry 1}
hundreds: 7+5+1=13⇒ write 3, carry 1\text{hundreds: }7+5+1=13\Rightarrow\text{ write 3, carry 1}
thousands: 2+1+1=4\text{thousands: }2+1+1=4
2,786+1,547=4,3332,786+1,547=4,333

The carries are written above the next column so every place stays aligned.

Written subtraction: exchange through zeroes

Subtraction also starts at the ones. When a top digit is too small, exchange one unit from the next place. In 4,002 − 1,785, both the hundreds and tens begin at zero, so the exchange travels left before it reaches the ones.

Exchange through 4,002

regrouped39912−17852217\begin{array}{r r r r r}\text{regrouped}&3&9&9&12\\-&1&7&8&5\\\hline&2&2&1&7\\\end{array}
4 thousands→3 thousands+10 hundreds4\text{ thousands}\rightarrow3\text{ thousands}+10\text{ hundreds}
10 hundreds→9 hundreds+10 tens10\text{ hundreds}\rightarrow9\text{ hundreds}+10\text{ tens}
10 tens+2 ones→9 tens+12 ones10\text{ tens}+2\text{ ones}\rightarrow9\text{ tens}+12\text{ ones}
minuend columns: 3∣9∣9∣12\text{minuend columns: }3\mid9\mid9\mid12
ones: 12−5=7;tens: 9−8=1;hundreds: 9−7=2;thousands: 3−1=2\text{ones: }12-5=7;\quad\text{tens: }9-8=1;\quad\text{hundreds: }9-7=2;\quad\text{thousands: }3-1=2
4,002−1,785=2,2174,002-1,785=2,217

Written subtraction: exchange through zeroes

Predict first: How many exchanges does 4,002 − 1,785 need before the ones can be subtracted?

Mental addition and subtraction of two-digit numbers

For 58 + 27, partition 27 into 20 and 7: 58 + 20 = 78, then 78 + 7 = 85. For 67 − 29, subtract 30 and add 1 back: (67 − 30) + 1 = 38. These are mental methods, so they are separate from a four-digit written layout.

Two mental methods

58+27=58+20+7=78+7=8558+27=58+20+7=78+7=85
67−29=(67−30)+1=37+1=3867-29=(67-30)+1=37+1=38
85−27=58and38+29=6785-27=58\quad\text{and}\quad38+29=67

🤔 Predict first: What is 67 − 29? Predict a result just below 40, then choose the mental method.

Practise with worked steps

Practice 1. Calculate 2,786 + 1,547 in aligned columns and record every carry.

Show all addition carries

Column addition

carry1112786+15474333\begin{array}{r r r r r}\text{carry}&1&1&1&\\&2&7&8&6\\+&1&5&4&7\\\hline&4&3&3&3\\\end{array}
ones: 6+7=13⇒3, carry 1\text{ones: }6+7=13\Rightarrow3\text{, carry }1
tens: 8+4+1=13⇒3, carry 1\text{tens: }8+4+1=13\Rightarrow3\text{, carry }1
hundreds: 7+5+1=13⇒3, carry 1\text{hundreds: }7+5+1=13\Rightarrow3\text{, carry }1
thousands: 2+1+1=4\text{thousands: }2+1+1=4
2,786+1,547=4,3332,786+1,547=4,333

Practice 2. Calculate 4,002 − 1,785 and show the exchanges through both zero places.

Show the zero-crossing solution

Column subtraction

regrouped39912−17852217\begin{array}{r r r r r}\text{regrouped}&3&9&9&12\\-&1&7&8&5\\\hline&2&2&1&7\\\end{array}
4,002→3 thousands,9 hundreds,9 tens,12 ones4,002\rightarrow3\text{ thousands},9\text{ hundreds},9\text{ tens},12\text{ ones}
12−5=7;9−8=1;9−7=2;3−1=212-5=7;\quad9-8=1;\quad9-7=2;\quad3-1=2
4,002−1,785=2,2174,002-1,785=2,217

Practice 3. Mentally calculate 58 + 27, then use subtraction as an inverse check.

Show the partition and inverse check

Partition, then check

58+20+7=8558+20+7=85
85−27=5885-27=58

Watch out — easily mixed up

Follow the operation path

Review P3 whole numbers when place values are causing the error. For table-based multiplication and division, continue to P3 multiplication and division.

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

  1. A museum has 3,468 visitors in the morning and 2,105 in the afternoon. How many visitors come that day?

  2. A library has 7,000 books and lends out 3,456. How many books remain?

  3. What is 46 + 38 mentally?

  4. Which addition equation checks 4,002 − 1,785 = 2,217?

  5. What is 67 − 29 mentally?

  6. After regrouping 4,002 for 4,002 − 1,785, what are the minuend values in the thousands, hundreds, tens and ones columns?