# Multiply using expanded forms and distibutive law 45*7 56*7 145*2 415*6

neela | High School Teacher | (Level 3) Valedictorian

Posted on

By  distributive law of multiplication over addition iis fiven by:

a(b+c) = ab+bc. Or

(b+c)a = ba+ca .

Therefore 45*7 = (40+5)7

45*7 = 40*7+5*7

45*7= 280+35

45*7 = 315.

56*7 = (50+6)7

56*7= 50*7+6*7

56*7= 350+6*7

56*7= 392.

145*2 = (100+45)2

145*2= (100+45)2

145*2= 100*2+45*2

145*2= 200+(40+5)

145*2 = 200+40*2 +5*2

145*2 = 200+80+10

145*2 = 290.

415*6 = (400+15)6

415*6= 400*6+15*6

415*6= 2400+(10+5)6

415*6= 2400+10*6+5*6

415*6 = 2400+60+30

415*6 = 2490

william1941 | College Teacher | (Level 3) Valedictorian

Posted on

For the expressions given we have to expand and multiply, making use of the distributive law:

• 45*7 = (40+ 5)*( 10 -3)

= 400 + 50 - 120 -15

=315

• 56*7 = (60 - 4)*(10 -3)

= 600 -40 -180 +12

= 392

• 145*2 = (100 + 40 + 5)*(1+1)

=100+ 40 + 5+ 100 + 40 +5

=290

• 415*6 = (400 +10 +5)*(10-4)

= 4000 - 1600 +100 -40 + 50 -20

= 2490

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To multiply 45*7, we'll write the expanded form of 45:

45 = 40 + 5

We'll re-write the multiplication:

45*7 = (40+5)*7

We'll use the distributive law:

(40+5)*7 = 40*7 + 5*7

40*7 + 5*7 = 280 + 35

40*7 + 5*7 = 315

45*7 = 315

We'll do the same steps for the multiplication:

56*7

We'll write the expanded form of 56:

56 = (50+6)

We'll re-write the multiplication:

(50+6)*7

We'll use the distributive law:

(50+6)*7 = 50*7 + 6*7

(50+6)*7 = 350 + 42

(50+6)*7 = 392

56*7 = 392

We'll do the same steps for the multiplication:

145*2

We'll write the expanded form of 145:

145 = 100 + 40 + 5

We'll re-write the multiplication:

(100 + 40 + 5)*2

We'll use the distributive law:

(100 + 40 + 5)*2 = 100*2 + 40*2 + 5*2

(100 + 40 + 5)*2 = 200 + 80 + 10

(100 + 40 + 5)*2 = 290

145*2= 290

We'll write the expanded form of 415:

415 = 400 + 10 + 5

We'll re-write the multiplication:

(400 + 10 + 5)*6

We'll use the distributive law:

(400 + 10 + 5)*6 = 400*6 + 10*6 + 5*6

(400 + 10 + 5)*6 = 2400 + 60 + 30

(400 + 10 + 5)*6 = 2490

415*6 = 2490