Let’s work through each part of the worksheet step by step.
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Part 1: In the problem 67 × 88 = 5,896 name:
This is about identifying parts of a multiplication equation.
In any multiplication problem like A × B = C:
-
Multiplicand is the first number (the one being multiplied)
-
Multiplier is the second number (how many times you multiply)
-
Product is the result
So for 67 × 88 = 5,896:
a) The multiplicand =
67
b) The multiplier =
88
c) The product =
5,896
✔ Verified — this matches standard math terminology.
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Problem 1: 368 × 5 using partial products
We break 368 into 300 + 60 + 8, then multiply each by 5.
Step-by-step:
- 5 × 8 =
40
- 5 × 60 =
300
- 5 × 300 =
1,500
Now add them up:
40 + 300 = 340
340 + 1,500 =
1,840
Check: 368 × 5 = ?
300×5=1500, 60×5=300, 8×5=40 → total 1840
✔
Final answer for Problem 1:
1,840
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Problem 2: 63 × 78 using partial products
Break both numbers:
63 = 60 + 3
78 = 70 + 8
Partial products:
- 3 × 8 =
24
- 3 × 70 =
210
- 60 × 8 =
480
- 60 × 70 =
4,200
Add them:
24 + 210 = 234
234 + 480 = 714
714 + 4,200 =
4,914
Check with calculator or standard multiplication:
63 × 78 = ?
60×78 = 4680
3×78 = 234
Total = 4680 + 234 =
4,914 ✔
Final answer for Problem 2:
4,914
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Problem 3: 646 × 72 using partial products
Break 646 = 600 + 40 + 6
Break 72 = 70 + 2
Partial products:
First, multiply by 2:
- 2 × 6 =
12
- 2 × 40 =
80
- 2 × 600 =
1,200
Then multiply by 70:
- 70 × 6 =
420
- 70 × 40 =
2,800
- 70 × 600 =
42,000
Now add all six values:
Start small to big:
12 + 80 = 92
92 + 1,200 = 1,292
1,292 + 420 = 1,712
1,712 + 2,800 = 4,512
4,512 + 42,000 =
46,512
Check: 646 × 72
Alternative way:
646 × 70 = 45,220
646 × 2 = 1,292
Total = 45,220 + 1,292 =
46,512 ✔
Final answer for Problem 3:
46,512
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Problem 4: 8624 × 94 using partial products
Break 8624 = 8000 + 600 + 20 + 4
Break 94 = 90 + 4
Partial products:
Multiply by 4:
- 4 × 4 =
16
- 4 × 20 =
80
- 4 × 600 =
2,400
- 4 × 8000 =
32,000
Multiply by 90:
- 90 × 4 =
360
- 90 × 20 =
1,800
- 90 × 600 =
54,000
- 90 × 8000 =
720,000
Now list all 8 partial products:
From ×4: 16, 80, 2400, 32000
From ×90: 360, 1800, 54000, 720000
Add them in groups:
Group 1 (small ones):
16 + 80 = 96
96 + 360 = 456
456 + 1800 = 2,256
Group 2 (medium):
2,256 + 2,400 = 4,656
4,656 + 54,000 = 58,656
Group 3 (large):
58,656 + 32,000 = 90,656
90,656 + 720,000 =
810,656
Wait — let me double-check that addition carefully.
List all values again:
16
80
2,400
32,000
360
1,800
54,000
720,000
Add step by step:
Start from bottom:
720,000
+54,000 = 774,000
+32,000 = 806,000
+2,400 = 808,400
+1,800 = 810,200
+360 = 810,560
+80 = 810,640
+16 =
810,656
✔ Correct.
Check with alternative method:
8624 × 94 = 8624 × (100 - 6) = 8624×100 - 8624×6
= 862,400 - 51,744 = ?
862,400 - 50,000 = 812,400
812,400 - 1,744 = 810,656
✔
Final answer for Problem 4:
810,656
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All problems solved and verified.
Final Answer:
a) 67
b) 88
c) 5,896
1) 1,840
2) 4,914
3) 46,512
4) 810,656
Parent Tip: Review the logic above to help your child master the concept of multiply using partial products worksheet.
