---
title: "Addition with Carrying"
book: "Primary & Middle School Mathematics"
subject: math
language: en
chapter: 8
exercises: 10
source: https://one-course.com/books/math/1/en/chapter/8-addition-with-carrying
---

# Chapter 8 — Addition with Carrying

When the units of a [sum](https://one-course.com/books/math/1/en/chapter/2-addition-first-steps#def-g1-addition-def) pass nine, ten of them bundle into a new ten — and that little bundle, moved to the next column, is the famous *carry*. This chapter explains the carry with sticks, then trains the written method.

## 8.1 Why we carry

**Example 8.1 (Bundling ten units).**

$27 + 15$: put the units together, $7 + 5 = 12$ units. But ten units make a ten! Bundle ten of them: that leaves $2$ loose units and one new ten to carry. Now the tens: $2 + 1 + 1 = 4$ tens. So $27 + 15 = 42$.

![The carry is a bundle: ten loose units become one ten, moved to the tens column.](https://one-course.com/images/onecourse/chapters/math-1/g2-addition/fig-3a255fe678d1.svg)

*The carry is a bundle: ten loose units become one ten, moved to the tens column.*

## 8.2 The written method

**Method 8.2 (Column addition).**

1. Write the numbers one under the other, units under units, tens under tens;
2. add the units; if the answer passes $9$ , write the units digit and carry a small $1$ above the tens;
3. add the tens (with the carry), then the hundreds;
4. check with an estimate: round each number and add roughly.

**Example 8.3.**

Compute $268 + 156$:

$$
\begin{array}{r}
{\scriptstyle 1}\ {\scriptstyle 1}\ \phantom{0} \\[-3pt]
2\,6\,8 \\
+\ 1\,5\,6 \\
\hline
4\,2\,4
\end{array}
$$

Units: $8 + 6 = 14$: write $4$, carry $1$. Tens: $6 + 5 + 1 = 12$: write $2$, carry $1$. Hundreds: $2 + 1 + 1 = 4$. Estimate check: about $270 + 160 = 430$, close to $424$. ✓

## 8.3 Adding in your head

**Example 8.4 (Make a ten).**

For small [sums](https://one-course.com/books/math/1/en/chapter/2-addition-first-steps#def-g1-addition-def), jump to a round number first:

$$
48 + 6 = 48 + 2 + 4 = 50 + 4 = 54 .
$$

Add tens and units separately: $35 + 23 = (30 + 20) + (5 + 3) = 50 + 8 = 58$. And a near-hundred trick: $99 + 46 = 100 + 46 - 1 = 145$.

**Example 8.5 (A little problem).**

“The library has $185$ books; $57$ new ones arrive. How many books now?” Adding: $185 + 57 = 242$ (units $5 + 7 = 12$, carry …). The library has $242$ books.

## 8.4 Exercises

**Exercise 8.1 ★.**

Compute (no carry needed): $34 + 25$; $126 + 43$; $507 + 82$.

**Solution of Exercise 8.1.**

$34 + 25 = 59$; $126 + 43 = 169$; $507 + 82 = 589$.

**Exercise 8.2 ★.**

Compute with a carry: $47 + 8$; $56 + 27$; $65 + 19$.

**Solution of Exercise 8.2.**

$47 + 8 = 55$; $56 + 27 = 83$; $65 + 19 = 84$.

**Exercise 8.3 ★.**

Compute in columns: $268 + 145$; $374 + 158$; $429 + 293$.

**Solution of Exercise 8.3.**

$268 + 145 = 413$; $374 + 158 = 532$; $429 + 293 = 722$.

**Exercise 8.4 ★.**

Compute in your head by making a ten: $38 + 5$; $67 + 6$; $54 + 8$.

**Solution of Exercise 8.4.**

$38 + 5 = 38 + 2 + 3 = 43$; $67 + 6 = 67 + 3 + 3 = 73$; $54 + 8 = 54 + 6 + 2 = 62$.

**Exercise 8.5 ★.**

Compute by adding tens and units separately: $42 + 36$; $53 + 24$; $61 + 28$.

**Solution of Exercise 8.5.**

$42 + 36 = 70 + 8 = 78$; $53 + 24 = 70 + 7 = 77$; $61 + 28 = 80 + 9 = 89$.

**Exercise 8.6 ★.**

Estimate first (round to the nearest ten or hundred), then compute exactly: $58 + 34$; $296 + 187$.

**Solution of Exercise 8.6.**

$58 + 34$: estimate $60 + 30 = 90$; exactly $92$. $296 + 187$: estimate $300 + 200 = 500$; exactly $483$.

**Exercise 8.7 ★.**

“Ana has $128$ marbles, Tom has $95$. How many together?” Write the addition and the answer sentence.

**Solution of Exercise 8.7.**

$128 + 95 = 223$. Together they have $223$ marbles.

**Exercise 8.8 ★.**

Complete the units hole: $3\,?\, + 27 = 64$ (find the missing units digit of the first number).

**Solution of Exercise 8.8.**

The first number plus $27$ is $64$, so it is $64 - 27 = 37$: the missing units digit is $7$ (the number is $37$).

**Exercise 8.9 ★.**

Two classes go to the show: $27$ and $28$ children, plus $6$ grown-ups. How many people in all? (Add the two classes first.)

**Solution of Exercise 8.9.**

Children: $27 + 28 = 55$; with the grown-ups, $55 + 6 = 61$ people.

**Exercise 8.10 ★★.**

Find three numbers on the list $27$, $33$, $40$, $65$ that add up to $100$. (Look for two whose units are ten friends first.)

**Solution of Exercise 8.10.**

$27$ and $33$ have units $7$ and $3$ (ten friends): $27 + 33 = 60$, then $60 + 40 = 100$. The three numbers are $27$, $33$ and $40$.