Adding two two-digit numbers

There are 22 chil­dren in one class and 33 in the next. A bat­ter scores 36 runs in one match and 43 in the next. A shop­keeper sells 53 pens on Mon­day and 76 on Tues­day. To find each total you add two two-digit num­bers. The plan is sim­ple: tens go with tens, and units go with units.

A num­ber like 56 is 5 tens and 6 units, so $56 = 50 + 6$. Keep that pic­ture in mind through the whole les­son.

Tens with tens#

Adding whole tens is sin­gle-digit adding with a zero on the end. Three tens and five tens make eight tens, so $30 + 50 = 80$.

Look at $40 + 70$. Four and seven make eleven, so four tens and seven tens make eleven tens, and eleven tens is 110. Tens can go past a hun­dred, just as 4 and 7 go past ten.

The pairs that make a hun­dred#

These are the tens part­ners again, grown ten times big­ger.

A whole ten plus a two-digit num­ber#

Only the tens change. Add the tens and carry the units across untouched.

Exam­ple 1#

Work out $50 + 94$.

$$\begin{aligned}50 + 94 &= (50 + 90) + 4 \\ &= 140 + 4 \\ &= 144\end{aligned}$$

Two-digit num­bers: tens with tens, units with units#

Split both num­bers. Add the tens together and the units together. Then put the two answers together.

Exam­ple 2#

Work out $22 + 33$.

$$\begin{aligned}22 + 33 &= (20 + 30) + (2 + 3) \\ &= 50 + 5 \\ &= 55\end{aligned}$$

A good habit is to under­line the tens dig­its of both num­bers and join the units dig­its with an arc. Then you can see which dig­its go together.

Exam­ple 3#

Work out $52 + 33$ the other way: add the tens on first, then the units.

$$\begin{aligned}52 + 33 &= (52 + 30) + 3 \\ &= 82 + 3 \\ &= 85\end{aligned}$$

Some chil­dren find this way eas­ier, because there is only one thing to hold in mind at a time.

Exam­ple 4#

Work out $53 + 76$.

$$\begin{aligned}53 + 76 &= (50 + 70) + (3 + 6) \\ &= 120 + 9 \\ &= 129\end{aligned}$$

The tens made 12 tens, which is 120. That is fine. The answer sim­ply goes past a hun­dred.

Exam­ple 5#

Work out $93 + 94$.

$$\begin{aligned}93 + 94 &= (90 + 90) + (3 + 4) \\ &= 180 + 7 \\ &= 187\end{aligned}$$

When the units spill over#

If the units add up to ten or more, they make a whole new ten of their own. Noth­ing has gone wrong. Just add that ten on too.

In the pic­ture there are 6 blue cubes and 8 orange cubes, 14 cubes in all. Ten of them make one more rod. That leaves 9 rods and 4 loose cubes, which is 94.

Exam­ple 6#

Work out $56 + 38$.

$$\begin{aligned}56 + 38 &= (50 + 30) + (6 + 8) \\ &= 80 + 14 \\ &= 94\end{aligned}$$

Or add the tens on first:

$$\begin{aligned}56 + 38 &= (56 + 30) + 8 \\ &= 86 + 8 \\ &= 94\end{aligned}$$

Exam­ple 7#

Work out $76 + 48$.

$$\begin{aligned}76 + 48 &= (70 + 40) + (6 + 8) \\ &= 110 + 14 \\ &= 124\end{aligned}$$

There is a shorter way for this one. Move 2 from the 76 across to the 48, so that 48 becomes the round num­ber 50.

$$76 + 48 = 74 + 50 = 124$$

The total does not change, because noth­ing left the sum. It only moved from one num­ber to the other.

Remem­ber. In an adding sum you may move an amount from one num­ber to the other. Move enough to make one of them round.

Exam­ple 8#

Class 2A col­lected 38 news­pa­pers and Class 2B col­lected 45. How many did they col­lect together?

$$\begin{aligned}38 + 45 &= (30 + 40) + (8 + 5) \\ &= 70 + 13 \\ &= 83\end{aligned}$$

They col­lected 83 news­pa­pers. A quick check: 38 is nearly 40, and $40 + 45 = 85$. The answer should be 2 less than that, which is 83.

Dou­bling#

To dou­ble a num­ber, add it to itself. Then dou­ble the answer, and dou­ble again. Every step is a sum you can already do.

Com­mon mis­takes#

• Adding a ten as if it were a unit. In $64 + 30$ the 3 is 3 tens, so the answer is 94, not 67.
• Los­ing the new ten. In $56 + 38$ the units make 14. Writ­ing only the 4 gives 84 instead of 94.
• Writ­ing 14 inside the answer. $80 + 14$ is 94, not 8014.
• Mov­ing an amount one way only. When you take 2 from one num­ber you must give the same 2 to the other.

Key terms#

• Tens digit: the left digit of a two-digit num­ber. In 56 it is 5, worth fifty.
• Units digit: the right digit. In 56 it is 6.
• Spill over: when the units add up to ten or more, ten of them become one new ten.
• Dou­ble: a num­ber added to itself, such as $36 + 36 = 72$.

Prac­tice#

1. $60 + 70$
2. $40 + 86$
3. $23 + 51$
4. $43 + 34$
5. $54 + 23$
6. $41 + 58$
7. $62 + 53$
8. $87 + 92$
9. $27 + 58$
10. $36 + 49$
11. $68 + 57$
12. Ravi reads 46 pages on Sat­ur­day and 38 pages on Sun­day. How many pages does he read alto­gether?

Answers#