Fast Multiplication Techniques

Multiplication appears constantly in QR: calculating total costs (quantity × price), finding areas (length × width), scaling recipes, and more. The on-screen calculator handles multiplication, but for many common multiplications, mental techniques are significantly faster. This lesson covers the most useful shortcuts.

---

Multiplying by 5, 50, and 500

These all exploit the relationship between 5 and 10.

Multiply by 5: ×10 then ÷2

Since 5 = 10 ÷ 2:

Calculation	×10	÷2	Answer
48 × 5	480	240	240
73 × 5	730	365	365
156 × 5	1,560	780	780

Multiply by 50: ×100 then ÷2

Since 50 = 100 ÷ 2:

Calculation	×100	÷2	Answer
36 × 50	3,600	1,800	1,800
84 × 50	8,400	4,200	4,200
125 × 50	12,500	6,250	6,250

Multiply by 500: ×1,000 then ÷2

Since 500 = 1,000 ÷ 2:

Calculation	×1,000	÷2	Answer
14 × 500	14,000	7,000	7,000
37 × 500	37,000	18,500	18,500

---

Multiplying by 25 and 125

Multiply by 25: ×100 then ÷4

Since 25 = 100 ÷ 4:

Calculation	×100	÷4	Answer
32 × 25	3,200	800	800
48 × 25	4,800	1,200	1,200
17 × 25	1,700	425	425

Tip: Dividing by 4 is the same as halving twice. So 1,700 ÷ 4 = 1,700 ÷ 2 ÷ 2 = 850 ÷ 2 = 425.

Multiply by 125: ×1,000 then ÷8

Since 125 = 1,000 ÷ 8:

Calculation	×1,000	÷8	Answer
24 × 125	24,000	3,000	3,000
64 × 125	64,000	8,000	8,000
15 × 125	15,000	1,875	1,875

Tip: Dividing by 8 is halving three times. So 15,000 ÷ 8 = 7,500 ÷ 4 = 3,750 ÷ 2 = 1,875.

---

The Doubling and Halving Method

If one factor is even, you can halve it and double the other to make the multiplication easier. You can repeat this as many times as helpful.

How It Works

The product does not change when you halve one factor and double the other (because a × b = (a÷2) × (b×2)).

Original	Halve × Double	Simplified	Answer
14 × 35	7 × 70	Easy	490
24 × 15	12 × 30	Easy	360
16 × 45	8 × 90	Easy	720
32 × 15	16 × 30 → 8 × 60	Easy	480

When to Use This

Doubling and halving is most useful when one number is a multiple of 2, 4, 8, or 16 and the other becomes a round number after doubling.

---

The Grid Method for 2-Digit × 2-Digit

When you cannot simplify a multiplication with the above shortcuts, the grid method (also called the box method or partial products method) breaks it into manageable pieces.

Method

Split each number into tens and ones, multiply each pair, then add.

Example: 34 × 27

×	30	4
20	600	80
7	210	28

Sum: 600 + 80 + 210 + 28 = 918

Step by step:

1. 30 × 20 = 600
2. 4 × 20 = 80
3. 30 × 7 = 210
4. 4 × 7 = 28
5. Total: 600 + 80 + 210 + 28 = 918

Example: 56 × 43

×	50	6
40	2,000	240
3	150	18

Sum: 2,000 + 240 + 150 + 18 = 2,408

Mental execution: You do not need to draw the grid. Think: "50 × 40 = 2,000; 6 × 40 = 240; 50 × 3 = 150; 6 × 3 = 18. Total: 2,000 + 240 + 150 + 18 = 2,408."

When to Use the Grid Method vs the Calculator