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Given: 42 × 15

Steps: - Divide the number by 2 42 ÷ 2 = 21

- Double the number ending with 5 15 × 2 = 30

- Multiply the quotient and the product 21 × 30 = 630 ↓ Final Answer

Examples:

1. Given: 88 × 25

- 88 ÷ 2 = 44

- 25 × 2 = 50

- 44 × 50 = 2 200 → Final Answer

2. Given: 78 × 65

- 78 ÷ 2 = 39

- 65 × 2 = 130

- 39 × 130 = 5 070 → Final Answer

3. Given: 24 × 35

- 28 ÷ 2 = 14

- 35 × 2 = 70

- 14 × 70 = 980 → Final Answer

● Multiplying any Number with 5

Given: 48 × 5

Steps: - Divide the number by 2 48 ÷ 2 = 24

- Multiply the quotient by 10 or simply add zero 24 × 10 = 240 ↓ Final Answer

Examples:

1. Given: 68 × 5

- 68 ÷ 2 = 34

- 34 × 10 = 340 → Final Answer

2. Given: 116 × 5

- 116 ÷ 2 = 58

- 58 × 10 = 580 → Final Answer

3. Given: 434 × 5

- 434 ÷ 2 = 217

- 217 × 10 = 2 170 → Final Answer

● Multiplying Numbers with Common First Digits

Given: 21 × 23

Steps: - Multiply the uncommon digits 1 × 3 = 3

· Add the uncommon digits 1 + 3 = 4

- Multiply the sum with the common digit 4 × 2 = 8

- Multiply the common first digits 2 × 2 = 4

- Combine the products 4 8 3 → Final Answer

Examples:

1. Given: 23 × 25

- 3 × 5 = 15 - · 3 + 5 = 8

- 8 × 2 = 16

- 2 × 2 = 4

- 1 1 + 4 6 5 5 7 5 → Final Answer

2. Given: 46 × 49

- 6 × 9 = 54 - · 6 + 9 = 15

- 15 × 4 = 60

- 4 × 4 = 16

- 1 6 5 + 6 0 4 2 2 5 4 → Final Answer

3. Given: 35 × 38

- 5 × 8 = 40 - · 5 + 8 = 13

- 13 × 2 = 26

- 2 × 2 = 4

- 2 4 + 4 6 0 7 0 0 → Final Answer

● Multiplying Numbers with Common Last digits

Given: 34 × 54

Steps: - Multiply the common last digits 4 × 4 = 16

- Add the uncommon digits 3 + 5 = 8

- Multiply the sum with the common digit 8 × 4 = 32

- Multiply the uncommon digits 3 × 5 = 15

- Add the products: 1 3 1 + 5 2 6 1 8 3 6 → Final Answer

Examples:

1. Given: 16 × 76

- 6 × 6 = 36

- 1 + 7 = 8

- 8 × 6 = 48

- 1 × 7 = 7

- 4 3 + 7 8 6 1 2 1 6 → Final Answer

2. Given: 27 × 37

- 7 × 7 = 49

- 2 + 3 = 5

- 5 × 7 = 35

- 2 × 3 = 6

- 3 4 + 6 5 9 9 9 9 → Final Answer

3. Given: 65 × 85

- 5 × 5 = 25

- 6 + 8 = 14

- 14 × 5 = 70

- 6 × 8 = 48

- 4 7 2 + 8 0 5 5 5 2 5 → Final Answer

● Difference of Two Square Numbers

Given: 16² - 25²

Steps: - Get the sum of the two base numbers 25 + 16 = 41

- Difference of the two base numbers 25 – 16 = 9

- Multiply the sum and difference 41 × 9 = 369 ↓ Final Answer

Examples:

1. Given: 17² - 20²

- 20 + 17 = 37

- 20 – 17 = 3

- 37 × 3 = 111 → Final Answer

2. Given: 58² - 69²

- 69 + 58 = 127

- 69 – 58 = 11

- 127 × 11 = 1397 → Final Answer

3. Given: 45² - 51²

- 51 + 45 = 96

- 51 – 45 = 6

- 96 × 6 = 576 → Final Answer

SHORTCUTS

IN

MATHEMATICAL

CALCULATIONS

(Project in Number Theory 8)

Phoebe Kyle Nadine B. Malig-on

8 – Archimedes

Mdme. Marichu S. Gajardo (subject teacher)…...

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