Үржүүлэх нь ижил нэр томьёоны нийлбэрээр илэрхийлж болох математикийн үйлдэл юм.

Агуулга

Үржүүлэх ерөнхий зарчим

Жишээ нь a ⋅ b ("a удаа b" гэж уншина) нь бид нөхцлүүдийг нэгтгэдэг гэсэн үг юм a, тоо нь тэнцүү байна b. Үржүүлгийн үр дүнг бүтээгдэхүүн гэж нэрлэдэг.

Үржүүлэх хүснэгтийг хэрхэн хурдан, хялбар сурах вэ

жишээ:

  • 2 ⋅ 6 = 2 + 2 + 2 + 2 + 2 + 2 = 12

    (зургаа дахин хоёр)

  • 5 ⋅ 4 = 5 + 5 + 5 + 5 = 20

    (дөрөв дахин тав)

  • 3 ⋅ 8 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 24

    (наймыг гурав дахин)

Бидний мэдэж байгаагаар хүчин зүйлсийн байршлын өөрчлөлтөөс харахад бүтээгдэхүүн өөрчлөгддөггүй. Дээрх жишээнүүдийн хувьд дараах байдалтай байна.

  • 6 ⋅ 2 = 6 + 6 = 12

    (хоёр удаа зургаа)

  • 4 ⋅ 5 = 4 + 4 + 4 + 4 + 4 = 20

    (таван дахин дөрөв)

  • 8 ⋅ 3 = 8 + 8 + 8 = 24

    (гурав дахин найм)

Практик ашиг тус

Үржүүлгийн ачаар та ижил төрлийн зүйлийн нийт тоог мэдэгдэхүйц бууруулж чадна гэх мэт. Жишээлбэл, хэрэв бид 7 багцтай, тус бүр нь 5 үзэг агуулдаг бол эдгээрийг үржүүлснээр нийт үзэгний тоог олно. хоёр тоо:

5 ⋅ 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35

(таван үзэг долоон удаа)

0 -аар үржүүлэх

Үр дүн нь үргэлж тэг байдаг.

  • 0 ⋅ 0 = 0
  • 1 ⋅ 0 = 0 ⋅ 1 = 0
  • 2 ⋅ 0 = 0 ⋅ 2 = 0 + 0 = 0
  • 3 ⋅ 0 = 0 ⋅ 3 = 0 + 0 + 0 = 0
  • 4 ⋅ 0 = 0 ⋅ 4 = 0 + 0 + 0 + 0 = 0
  • 5 ⋅ 0 = 0 ⋅ 5 = 0 + 0 + 0 + 0 + 0 = 0
  • 6 ⋅ 0 = 0 ⋅ 6 = 0 + 0 + 0 + 0 + 0 + 0 = 0
  • 7 ⋅ 0 = 0 ⋅ 7 = 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0
  • 8 ⋅ 0 = 0 ⋅ 8 = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0
  • 9 ⋅ 0 = 0 ⋅ 9 = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0
  • 10 ⋅ 0 = 0 ⋅ 10 = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0

1 -аар үржүүлэх

Бүтээгдэхүүн нь нэгээс өөр үржүүлэгчтэй тэнцүү байна.

  • 1 ⋅ 1 = 1
  • 2 ⋅ 1 = 2 ⋅ 1 = 2
  • 3 ⋅ 1 = 3 ⋅ 1 = 3
  • 4 ⋅ 1 = 4 ⋅ 1 = 4
  • 5 ⋅ 1 = 5 ⋅ 1 = 5
  • 6 ⋅ 1 = 6 ⋅ 1 = 6
  • 7 ⋅ 1 = 7 ⋅ 1 = 7
  • 8 ⋅ 1 = 8 ⋅ 1 = 8
  • 9 ⋅ 1 = 9 ⋅ 1 = 9
  • 10 ⋅ 1 = 10 ⋅ 1 = 10

2 -аар үржүүлэх

Эхний хүчин зүйлийг өөртөө нэмнэ үү.

  • 1 ⋅ 2 = 1 + 1 = 2
  • 2 ⋅ 2 = 2 + 2 = 4
  • 3 ⋅ 2 = 3 + 3 = 6
  • 4 ⋅ 2 = 4 + 4 = 8
  • 5 ⋅ 2 = 5 + 5 = 10
  • 6 ⋅ 2 = 6 + 6 = 12
  • 7 ⋅ 2 = 7 + 7 = 14
  • 8 ⋅ 2 = 8 + 8 = 16
  • 9 ⋅ 2 = 9 + 9 = 18
  • 10 ⋅ 2 = 10 + 10 = 20

3 -аар үржүүлэх

Бид эхний хүчин зүйлийг 2-оор үржүүлж, үр дүнд нь нэмнэ.

  • 1 ⋅ 3 = (1 ⋅ 2) + 1 = 2 + 1 = 3
  • 2 ⋅ 3 = (2 ⋅ 2) + 2 = 4 + 2 = 6
  • 3 ⋅ 3 = (3 ⋅ 2) + 3 = 6 + 3 = 9
  • 4 ⋅ 3 = (4 ⋅ 2) + 4 = 8 + 4 = 12
  • 5 ⋅ 3 = (5 ⋅ 2) + 5 = 10 + 5 = 15
  • 6 ⋅ 3 = (6 ⋅ 2) + 6 = 12 + 6 = 18
  • 7 ⋅ 3 = (7 ⋅ 2) + 7 = 14 + 7 = 21
  • 8 ⋅ 3 = (8 ⋅ 2) + 8 = 16 + 8 = 24
  • 9 ⋅ 3 = (9 ⋅ 2) + 9 = 18 + 9 = 27
  • 10 ⋅ 3 = (10 ⋅ 2) + 10 = 20 + 10 = 30

4 -аар үржүүлэх

Бид хоёр дахин нэмэгдсэн эхний хүчин зүйл дээр ижил хэмжээг нэмнэ.

  • 1 ⋅ 4 = (1 ⋅ 2) + (1 ⋅ 2) = 2 + 2 = 4
  • 2 ⋅ 4 = (2 ⋅ 2) + (2 ⋅ 2) = 4 + 4 = 8
  • 3 ⋅ 4 = (3 ⋅ 2) + (3 ⋅ 2) = 6 + 6 = 12
  • 4 ⋅ 4 = (4 ⋅ 2) + (4 ⋅ 2) = 8 + 8 = 16
  • 5 ⋅ 4 = (5 ⋅ 2) + (5 ⋅ 2) = 10 + 10 = 20
  • 6 ⋅ 4 = (6 ⋅ 2) + (6 ⋅ 2) = 12 + 12 = 24
  • 7 ⋅ 4 = (7 ⋅ 2) + (7 ⋅ 2) = 14 + 14 = 28
  • 8 ⋅ 4 = (8 ⋅ 2) + (8 ⋅ 2) = 16 + 16 = 32
  • 9 ⋅ 4 = (9 ⋅ 2) + (9 ⋅ 2) = 18 + 18 = 36
  • 10 ⋅ 4 = (10 ⋅ 2) + (10 ⋅ 2) = 20 + 20 = 40

5 -аар үржүүлэх

Хэрэв нөгөө үржүүлэгч нь тэгш тоо байвал үр дүн нь тэг, сондгой бол 5 тоогоор төгсөнө.

  • 1 ⋅ 5 = 5 ⋅ 1 = 5
  • 2 ⋅ 5 = 5 ⋅ 2 = 5 + 5 = 10
  • 3 ⋅ 5 = 5 ⋅ 3 = (5 ⋅ 2) + 5 = 15
  • 4 ⋅ 5 = 5 ⋅ 4 = (5 ⋅ 2) + (5 ⋅ 2) = 20
  • 5 ⋅ 5 = 5 + 5 + 5 + 5 + 5 = 25
  • 6 ⋅ 5 = 5 ⋅ 6 = (5 ⋅ 5) + 5 = 30
  • 7 ⋅ 5 = 5 ⋅ 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35
  • 8 ⋅ 5 = 5 ⋅ 8 = (5 ⋅ 4) + (5 ⋅ 4) = 40
  • 9 ⋅ 5 = 5 ⋅ 9 = (5 ⋅ 10) – 5 = 45
  • 10 ⋅ 5 = 5 ⋅ 10 = 50

6 -аар үржүүлэх

Бид эхний хүчин зүйлийг 5-аар үржүүлж, үр дүнг нь нэмнэ.

  • 1 ⋅ 6 = (1 ⋅ 5) + 1 = 5 + 1 = 6
  • 2 ⋅ 6 = (2 ⋅ 5) + 2 = 10 + 2 = 12
  • 3 ⋅ 6 = (3 ⋅ 5) + 3 = 15 + 3 = 18
  • 4 ⋅ 6 = (4 ⋅ 5) + 4 = 20 + 4 = 24
  • 5 ⋅ 6 = (5 ⋅ 5) + 5 = 25 + 5 = 30
  • 6 ⋅ 6 = (6 ⋅ 5) + 6 = 30 + 6 = 36
  • 7 ⋅ 6 = (7 ⋅ 5) + 7 = 35 + 7 = 42
  • 8 ⋅ 6 = (8 ⋅ 5) + 8 = 40 + 8 = 48
  • 9 ⋅ 6 = (9 ⋅ 5) + 9 = 45 + 9 = 54
  • 10 ⋅ 6 = (10 ⋅ 5) + 10 = 50 + 10 = 60

7 -аар үржүүлэх

7-оор үржүүлэх хялбаршуулсан алгоритм байхгүй тул бид бусад хүчин зүйлд хамаарах аргуудыг ашигладаг.

  • 1 ⋅ 7 = 7 ⋅ 1 = 7
  • 2 ⋅ 7 = 7 ⋅ 2 = 7 + 7 = 14
  • 3 ⋅ 7 = 7 ⋅ 3 = (7 ⋅ 2) + 7 = 21
  • 4 ⋅ 7 = 7 ⋅ 4 = (7 ⋅ 2) + (7 ⋅ 2) = 28
  • 5 ⋅ 7 = 7 ⋅ 5 = 7 + 7 + 7 + 7 + 7 = 35
  • 6 ⋅ 7 = 7 ⋅ 6 = (7 ⋅ 5) + 7 = 42
  • 7 ⋅ 7 = 7 + 7 + 7 + 7 + 7 + 7 + 7 = 49
  • 8 ⋅ 7 = 7 ⋅ 8 = (7 ⋅ 4) + (7 ⋅ 4) = 56
  • 9 ⋅ 7 = 7 ⋅ 9 = (7 ⋅ 10) – 7 = 63
  • 10 ⋅ 7 = 70

8 -аар үржүүлэх

Бид эхний хүчин зүйлийг 4-ээр үржүүлж, үр дүнд нь ижил дүнг нэмнэ.

  • 1 ⋅ 8 = (1 ⋅ 4) + (1 ⋅ 4) = 8
  • 2 ⋅ 8 = (2 ⋅ 4) + (2 ⋅ 4) = 16
  • 3 ⋅ 8 = (3 ⋅ 4) + (3 ⋅ 4) = 24
  • 4 ⋅ 8 = (4 ⋅ 4) + (4 ⋅ 4) = 32
  • 5 ⋅ 8 = (5 ⋅ 4) + (5 ⋅ 4) = 40
  • 6 ⋅ 8 = (6 ⋅ 4) + (6 ⋅ 4) = 48
  • 7 ⋅ 8 = (7 ⋅ 4) + (7 ⋅ 4) = 56
  • 8 ⋅ 8 = (8 ⋅ 4) + (8 ⋅ 4) = 64
  • 9 ⋅ 8 = (9 ⋅ 4) + (9 ⋅ 4) = 72
  • 10 ⋅ 8 = (10 ⋅ 4) + (10 ⋅ 4) = 80

9 -аар үржүүлэх

Бид эхний хүчин зүйлийг 10-аар үржүүлж, дараа нь олж авсан үр дүнгээс хасна.

  • 1 ⋅ 9 = (1 ⋅ 10) – 1 = 10 – 1 = 9
  • 2 ⋅ 9 = (2 ⋅ 10) – 2 = 20 – 2 = 18
  • 3 ⋅ 9 = (3 ⋅ 10) – 3 = 30 – 3 = 27
  • 4 ⋅ 9 = (4 ⋅ 10) – 4 = 40 – 4 = 36
  • 5 ⋅ 9 = (5 ⋅ 10) – 5 = 50 – 5 = 45
  • 6 ⋅ 9 = (6 ⋅ 10) – 6 = 60 – 6 = 54
  • 7 ⋅ 9 = (7 ⋅ 10) – 7 = 70 – 7 = 63
  • 8 ⋅ 9 = (8 ⋅ 10) – 8 = 80 – 8 = 72
  • 9 ⋅ 9 = (9 ⋅ 10) – 9 = 90 – 9 = 81
  • 10 ⋅ 9 = (10 ⋅ 10) – 10 = 100 – 10 = 90

10 -аар үржүүлэх

Нөгөө үржүүлэгчийн төгсгөлд тэг нэмнэ.

  • 1 ⋅ 10 = 10 ⋅ 1 = 10
  • 2 ⋅ 10 = 10 ⋅ 2 = 20
  • 3 ⋅ 10 = 10 ⋅ 3 = 30
  • 4 ⋅ 10 = 10 ⋅ 4 = 40
  • 5 ⋅ 10 = 10 ⋅ 5 = 50
  • 6 ⋅ 10 = 10 ⋅ 6 = 60
  • 7 ⋅ 10 = 10 ⋅ 7 = 70
  • 8 ⋅ 10 = 10 ⋅ 8 = 80
  • 9 ⋅ 10 = 10 ⋅ 9 = 90
  • 10 ⋅ 10 = 10 ⋅ 10 = 100

хариу үлдээх