Topic A: Multiplying Larger Numbers

Wendy Tagami; Liz Girard

Topic A: Multiplying Larger Numbers

It is usually easier to multiply larger numbers if they are written underneath each other. The bottom number is called the multiplier.

To find the product of a one digit multiplier, use as many of these steps as you need to complete each multiplication question:

Step 1: Multiply the ones digit in the large number by the one-digit multiplier.
Step 2: Multiply the tens digit in the large number by the multiplier.
Step 3: Multiply the hundreds digit in the large number by the multiplier.
Step 4: Multiply the thousands digit in the large number by the multiplier.

Example A

62 × 4 =

Step 1: 4 × 2 ones = 8

$\begin{array}{rr}&62\\\times&4\\\hline&8\end{array}$

Step 2: 4 × 6 tens = 24 tens = 2 hundreds and 4 tens

$\begin{array}{rr}&62\\\times&4\\\hline&248\end{array}$

The product of 62 × 4 is 248.

Exercise 1

Find the product. Check your work using the answer key at the end of the exercise.

$\begin{array}{rr}&72\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&81\\\times&5\\\hline\\\end{array}$
$\begin{array}{rr}&21\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&80\\\times&6\\\hline\\\end{array}$
$\begin{array}{rr}&73\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&71\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&40\\\times&7\\\hline\\\end{array}$
$\begin{array}{rr}&90\\\times&9\\\hline\\\end{array}$
$\begin{array}{rr}&82\\\times&4\\\hline\\\end{array}$
$\begin{array}{rr}&40\\\times&5\\\hline\\\end{array}$
$\begin{array}{rr}&92\\\times&4\\\hline\\\end{array}$
$\begin{array}{rr}&83\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&90\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&71\\\times&9\\\hline\\\end{array}$
$\begin{array}{rr}&53\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&30\\\times&6\\\hline\\\end{array}$
$\begin{array}{rr}&81\\\times&7\\\hline\\\end{array}$
$\begin{array}{rr}&61\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&70\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&41\\\times&6\\\hline\\\end{array}$
$\begin{array}{rr}&90\\\times&5\\\hline\\\end{array}$
$\begin{array}{rr}&60\\\times&9\\\hline\\\end{array}$
$\begin{array}{rr}&92\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&81\\\times&4\\\hline\\\end{array}$

Answers to Exercise 1

144
405
168
480
219
213
280
810
328
200
368
249
720
639
106
180
567
122
560
246
450
540
276
324

Example B

523 × 3 =

$\begin{array}{rr}&523\\\times&3\\\hline&1569\end{array}$

Step 1: 3 × 3 ones = 9 ones

Step 2: 3 × 2 tens = 6 tens

Step 3: 3 × 5 hundreds = 15 hundreds = 1 thousand and 5 hundreds

The product of 523 × 3 is 1569.

Example C

901 × 8 =

$\begin{array}{rr}&901\\\times&8\\\hline&7208\end{array}$

Step 1: 8 × 1 one = 8 ones

Step 2: 8 × 0 tens = 0 tens

Step 3: 8 × 9 hundreds = 72 hundreds = 7 thousands and 2 hundreds

The product of 901 × 8 is 7208.

Exercise 2

Find the product. Check your work using the answer key at the end of the exercise.

$\begin{array}{rr}&601\\\times&7\\\hline\\\end{array}$
$\begin{array}{rr}&423\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&641\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&922\\\times&4\\\hline\\\end{array}$
$\begin{array}{rr}&820\\\times&4\\\hline\\\end{array}$
$\begin{array}{rr}&211\\\times&5\\\hline\\\end{array}$
$\begin{array}{rr}&803\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&542\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&813\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&610\\\times&4\\\hline\\\end{array}$
$\begin{array}{rr}&901\\\times&6\\\hline\\\end{array}$
$\begin{array}{rr}&711\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&720\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&910\\\times&5\\\hline\\\end{array}$
$\begin{array}{rr}&801\\\times&6\\\hline\\\end{array}$
$\begin{array}{rr}&932\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&731\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&701\\\times&5\\\hline\\\end{array}$
$\begin{array}{rr}&521\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&632\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&720\\\times&4\\\hline\\\end{array}$
$\begin{array}{rr}&942\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&710\\\times&9\\\hline\\\end{array}$
$\begin{array}{rr}&601\\\times&8\\\hline\\\end{array}$

Answers to Exercise 2

4207
1269
1282
3688
3280
1055
1606
1084
2439
2440
5406
5688
2160
4550
4806
2796
1462
3505
1042
1896
2880
1884
6390
4808

Renaming and Carrying

In the times tables, the products are often two digit numbers. You must rename and carry. The amount you carry is added onto the product of the next column.

Example D

$\begin{array}{rr}&68\\\times&7\\\hline\end{array}$

Step 1: Multiply the ones by the multiplier.

7 × 8 ones = 56 ones = 5 tens + 6 ones

Write the 6 ones in the product.

Carry the 5 tens to the tens column and make a note of it for yourself. You might write it above the tens column.

$\begin{array}{rrr}&_5\hspace{0.5em}\\&68\\\times&7\\\hline&6\end{array}$

Step 2: Multiply the tens by the multiplier.

7 × 6 tens = 42 tens

Now add on the 5 tens that you carried.

42 tens + 5 tens = 47 tens = 4 hundreds and 7 tens

$\begin{array}{rrr}&_5\hspace{0.5em}\\&68\\\times&7\\\hline&476\end{array}$

Exercise 3

Find the product. Check your work using the answer key at the end of the exercise.

$\begin{array}{rr}&16\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&62\\\times&6\\\hline\\\end{array}$
$\begin{array}{rr}&37\\\times&4\\\hline\\\end{array}$
$\begin{array}{rr}&14\\\times&9\\\hline\\\end{array}$
$\begin{array}{rr}&36\\\times&7\\\hline\\\end{array}$
$\begin{array}{rr}&92\\\times&9\\\hline\\\end{array}$
$\begin{array}{rr}&48\\\times&6\\\hline\\\end{array}$
$\begin{array}{rr}&17\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&26\\\times&4\\\hline\\\end{array}$
$\begin{array}{rr}&54\\\times&7\\\hline\\\end{array}$
$\begin{array}{rr}&58\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&45\\\times&4\\\hline\\\end{array}$
$\begin{array}{rr}&56\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&47\\\times&5\\\hline\\\end{array}$
$\begin{array}{rr}&39\\\times&6\\\hline\\\end{array}$
$\begin{array}{rr}&75\\\times&6\\\hline\\\end{array}$
$\begin{array}{rr}&38\\\times&5\\\hline\\\end{array}$
$\begin{array}{rr}&82\\\times&7\\\hline\\\end{array}$
$\begin{array}{rr}&98\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&29\\\times&5\\\hline\\\end{array}$
$\begin{array}{rr}&47\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&74\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&56\\\times&5\\\hline\\\end{array}$
$\begin{array}{rr}&98\\\times&4\\\hline\\\end{array}$

Answers to Exercise 3

128
372
148
126
252
828
288
34
104
378
464
180
168
235
234
450
190
574
294
145
141
592
280
392

Example E

$4\times224=$

$\begin{array}{rr}&224\\\times&4\\\hline\end{array}$

Step 1: 4 × 4 ones = 16 ones = 1 ten and 6 ones

Write the 6 ones in the product and carry the one ten.

$\begin{array}{rr}&_1\hspace{0.5em}\\&224\\\times&4\\\hline&6\end{array}$

Step 2: 4 × 2 tens = 8 tens

8 tens + 1 ten we carried = 9 tens

$\begin{array}{rr}&_1\hspace{0.5em}\\&224\\\times&4\\\hline&96\end{array}$

Step 3: 4 × 2 hundreds = 8 hundreds

$\begin{array}{rr}&_1\hspace{0.5em}\\&224\\\times&4\\\hline&896\end{array}$

Example F

$4\times456=$

$\begin{array}{rr}&456\\\times&5\\\hline\end{array}$

Step 1: 5 × 6 ones = 30 ones = 3 ten and 0 ones

The 0 must be written to hold the ones place. Carry the 3 tens.

$\begin{array}{rr}&_3\hspace{0.5em}\\&456\\\times&5\\\hline&0\end{array}$

Step 2: 5 × 5 tens = 25 tens

25 tens + 3 tens = 28 tens = 2 hundreds and 8 tens

Write the 8 tens in the product. Carry the 2 hundreds.

$\begin{array}{rr}&_{2\text{ }3}\hspace{0.5em}\\&456\\\times&5\\\hline&80\end{array}$

Step 3: 5 × 4 hundreds = 20 hundreds + 2 hundreds = 22 hundreds = 2 thousands and 2 hundreds

$\begin{array}{rr}&_{2\text{ }3}\hspace{0.5em}\\&456\\\times&5\\\hline&2280\end{array}$

Exercise 4

Find the products. Check your work using the answer key at the end of the exercise.

$\begin{array}{rr}&648\\\times&9\\\hline\\\end{array}$
$\begin{array}{rr}&240\\\times&7\\\hline\\\end{array}$
$\begin{array}{rr}&457\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&404\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&106\\\times&9\\\hline\\\end{array}$
$\begin{array}{rr}&156\\\times&4\\\hline\\\end{array}$
$\begin{array}{rr}&407\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&239\\\times&6\\\hline\\\end{array}$
$\begin{array}{rr}&118\\\times&9\\\hline\\\end{array}$
$\begin{array}{rr}&425\\\times&7\\\hline\\\end{array}$
$\begin{array}{rr}&139\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&565\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&248\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&604\\\times&6\\\hline\\\end{array}$
$\begin{array}{rr}&239\\\times&4\\\hline\\\end{array}$
$\begin{array}{rr}&576\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&857\\\times&6\\\hline\\\end{array}$
$\begin{array}{rr}&478\\\times&9\\\hline\\\end{array}$
$\begin{array}{rr}&674\\\times&7\\\hline\\\end{array}$
$\begin{array}{rr}&629\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&893\\\times&5\\\hline\\\end{array}$
$\begin{array}{rr}&583\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&952\\\times&9\\\hline\\\end{array}$
$\begin{array}{rr}&293\\\times&7\\\hline\\\end{array}$

Answers to Exercise 4

5832
1680
3656
808
954
624
3256
1434
1062
2975
1112
1130
744
3624
956
1728
5142
4302
4718
5032
4465
4664
8568
2051

Example G

$\begin{array}{rr}&2408\\\times&9\\\hline\end{array}$

$\begin{array}{rr}&_3\hspace{0.7em}_7\hspace{0.5em}\\&2408\\\times&9\\\hline&21672\end{array}$

Step 1: 9 × 8 ones = 72 ones = 7 tens and 2 ones

Step 2: 9 × 0 = 0 tens. 0 tens + 7 tens = 7 tens

Step 3: 9 × 4 hundreds = 36 hundreds = 3 thousands and 6 hundreds

Step 4: 9 × 2 thousands = 18 thousands. 18 thousands + 3 thousands = 21 thousands

Exercise 5

Find the products. Check your work using the answer key at the end of the exercise.

$\begin{array}{rr}&4103\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&6087\\\times&4\\\hline\\\end{array}$
$\begin{array}{rr}&3280\\\times&6\\\hline\\\end{array}$
$\begin{array}{rr}&7034\\\times&5\\\hline\\\end{array}$
$\begin{array}{rr}&8456\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&4758\\\times&7\\\hline\\\end{array}$
$\begin{array}{rr}&4735\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&5402\\\times&9\\\hline\\\end{array}$
$\begin{array}{rr}&5394\\\times&4\\\hline\\\end{array}$
$\begin{array}{rr}&2034\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&8652\\\times&5\\\hline\\\end{array}$
$\begin{array}{rr}&6392\\\times&7\\\hline\\\end{array}$
$\begin{array}{rr}&4187\\\times&6\\\hline\\\end{array}$
$\begin{array}{rr}&1376\\\times&9\\\hline\\\end{array}$
$\begin{array}{rr}&3297\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&9628\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&7689\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&5160\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&4256\\\times&7\\\hline\\\end{array}$
$\begin{array}{rr}&5491\\\times&5\\\hline\\\end{array}$
$\begin{array}{rr}&8032\\\times&9\\\hline\\\end{array}$
$\begin{array}{rr}&8645\\\times&6\\\hline\\\end{array}$
$\begin{array}{rr}&6453\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&8129\\\times&4\\\hline\\\end{array}$

Answers to Exercise 5

32824
24348
19680
35170
16912
33306
14205
48618
21576
16272
43260
44744
25122
12384
6594
28884
61512
15480
29792
27455
72288
51870
12906
32516

Topic A: Self-Test

Mark /14 Aim 11/14

A. Find the products. (6 marks)

$\begin{array}{rr}&62\\\times&4\\\hline\\\end{array}$
$\begin{array}{rr}&31\\\times&4\\\hline\\\end{array}$
$\begin{array}{rr}&423\\\times&3\\\hline\\\end{array}$
$\begin{array}{rr}&734\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&8342\\\times&2\\\hline\\\end{array}$
$\begin{array}{rr}&5231\\\times&3\\\hline\\\end{array}$

B. Multiply these numbers. (4 marks)

$\begin{array}{rr}&44\\\times&7\\\hline\\\end{array}$
$\begin{array}{rr}&69\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&207\\\times&9\\\hline\\\end{array}$
$\begin{array}{rr}&184\\\times&6\\\hline\\\end{array}$

C. Find the products. (4 marks)

$\begin{array}{rr}&2834\\\times&5\\\hline\\\end{array}$
$\begin{array}{rr}&4037\\\times&6\\\hline\\\end{array}$
$\begin{array}{rr}&9241\\\times&8\\\hline\\\end{array}$
$\begin{array}{rr}&3652\\\times&4\\\hline\\\end{array}$

Answers to Topic A Self-Test

Find the products.
1. 248
2. 124
3. 1269
4. 1468
5. 16684
6. 15693
Multiply these numbers.
1. 308
2. 552
3. 1863
4. 1104
Find the products.
1. 14170
2. 24222
3. 73928
4. 14608

License

Icon for the Creative Commons Attribution 4.0 International License