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
[latex]\begin{array}{rr}&62\\\times&4\\\hline&8\end{array}[/latex]
Step 2: 4 × 6 tens = 24 tens = 2 hundreds and 4 tens
[latex]\begin{array}{rr}&62\\\times&4\\\hline&248\end{array}[/latex]
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.
- [latex]\begin{array}{rr}&72\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&81\\\times&5\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&21\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&80\\\times&6\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&73\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&71\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&40\\\times&7\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&90\\\times&9\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&82\\\times&4\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&40\\\times&5\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&92\\\times&4\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&83\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&90\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&71\\\times&9\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&53\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&30\\\times&6\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&81\\\times&7\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&61\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&70\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&41\\\times&6\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&90\\\times&5\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&60\\\times&9\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&92\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&81\\\times&4\\\hline\\\end{array}[/latex]
- 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 =
[latex]\begin{array}{rr}&523\\\times&3\\\hline&1569\end{array}[/latex]
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 =
[latex]\begin{array}{rr}&901\\\times&8\\\hline&7208\end{array}[/latex]
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.
- [latex]\begin{array}{rr}&601\\\times&7\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&423\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&641\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&922\\\times&4\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&820\\\times&4\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&211\\\times&5\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&803\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&542\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&813\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&610\\\times&4\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&901\\\times&6\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&711\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&720\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&910\\\times&5\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&801\\\times&6\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&932\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&731\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&701\\\times&5\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&521\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&632\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&720\\\times&4\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&942\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&710\\\times&9\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&601\\\times&8\\\hline\\\end{array}[/latex]
- 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
[latex]\begin{array}{rr}&68\\\times&7\\\hline\end{array}[/latex]
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.
[latex]\begin{array}{rrr}&_5\hspace{0.5em}\\&68\\\times&7\\\hline&6\end{array}[/latex]
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
[latex]\begin{array}{rrr}&_5\hspace{0.5em}\\&68\\\times&7\\\hline&476\end{array}[/latex]
Exercise 3
Find the product. Check your work using the answer key at the end of the exercise.
- [latex]\begin{array}{rr}&16\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&62\\\times&6\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&37\\\times&4\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&14\\\times&9\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&36\\\times&7\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&92\\\times&9\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&48\\\times&6\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&17\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&26\\\times&4\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&54\\\times&7\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&58\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&45\\\times&4\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&56\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&47\\\times&5\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&39\\\times&6\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&75\\\times&6\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&38\\\times&5\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&82\\\times&7\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&98\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&29\\\times&5\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&47\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&74\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&56\\\times&5\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&98\\\times&4\\\hline\\\end{array}[/latex]
- 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
[latex]4\times224=[/latex]
[latex]\begin{array}{rr}&224\\\times&4\\\hline\end{array}[/latex]
Step 1: 4 × 4 ones = 16 ones = 1 ten and 6 ones
Write the 6 ones in the product and carry the one ten.
[latex]\begin{array}{rr}&_1\hspace{0.5em}\\&224\\\times&4\\\hline&6\end{array}[/latex]
Step 2: 4 × 2 tens = 8 tens
8 tens + 1 ten we carried = 9 tens
[latex]\begin{array}{rr}&_1\hspace{0.5em}\\&224\\\times&4\\\hline&96\end{array}[/latex]
Step 3: 4 × 2 hundreds = 8 hundreds
[latex]\begin{array}{rr}&_1\hspace{0.5em}\\&224\\\times&4\\\hline&896\end{array}[/latex]
Example F
[latex]4\times456=[/latex]
[latex]\begin{array}{rr}&456\\\times&5\\\hline\end{array}[/latex]
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.
[latex]\begin{array}{rr}&_3\hspace{0.5em}\\&456\\\times&5\\\hline&0\end{array}[/latex]
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.
[latex]\begin{array}{rr}&_{2\text{ }3}\hspace{0.5em}\\&456\\\times&5\\\hline&80\end{array}[/latex]
Step 3: 5 × 4 hundreds = 20 hundreds + 2 hundreds = 22 hundreds = 2 thousands and 2 hundreds
[latex]\begin{array}{rr}&_{2\text{ }3}\hspace{0.5em}\\&456\\\times&5\\\hline&2280\end{array}[/latex]
Exercise 4
Find the products. Check your work using the answer key at the end of the exercise.
- [latex]\begin{array}{rr}&648\\\times&9\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&240\\\times&7\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&457\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&404\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&106\\\times&9\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&156\\\times&4\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&407\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&239\\\times&6\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&118\\\times&9\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&425\\\times&7\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&139\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&565\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&248\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&604\\\times&6\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&239\\\times&4\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&576\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&857\\\times&6\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&478\\\times&9\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&674\\\times&7\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&629\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&893\\\times&5\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&583\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&952\\\times&9\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&293\\\times&7\\\hline\\\end{array}[/latex]
- 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
[latex]\begin{array}{rr}&2408\\\times&9\\\hline\end{array}[/latex]
[latex]\begin{array}{rr}&_3\hspace{0.7em}_7\hspace{0.5em}\\&2408\\\times&9\\\hline&21672\end{array}[/latex]
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.
- [latex]\begin{array}{rr}&4103\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&6087\\\times&4\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&3280\\\times&6\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&7034\\\times&5\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&8456\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&4758\\\times&7\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&4735\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&5402\\\times&9\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&5394\\\times&4\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&2034\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&8652\\\times&5\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&6392\\\times&7\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&4187\\\times&6\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&1376\\\times&9\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&3297\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&9628\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&7689\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&5160\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&4256\\\times&7\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&5491\\\times&5\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&8032\\\times&9\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&8645\\\times&6\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&6453\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&8129\\\times&4\\\hline\\\end{array}[/latex]
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)
- [latex]\begin{array}{rr}&62\\\times&4\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&31\\\times&4\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&423\\\times&3\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&734\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&8342\\\times&2\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&5231\\\times&3\\\hline\\\end{array}[/latex]
B. Multiply these numbers. (4 marks)
- [latex]\begin{array}{rr}&44\\\times&7\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&69\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&207\\\times&9\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&184\\\times&6\\\hline\\\end{array}[/latex]
C. Find the products. (4 marks)
- [latex]\begin{array}{rr}&2834\\\times&5\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&4037\\\times&6\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&9241\\\times&8\\\hline\\\end{array}[/latex]
- [latex]\begin{array}{rr}&3652\\\times&4\\\hline\\\end{array}[/latex]
- Find the products.
- 248
- 124
- 1269
- 1468
- 16684
- 15693
- Multiply these numbers.
- 308
- 552
- 1863
- 1104
- Find the products.
- 14170
- 24222
- 73928
- 14608