Question

3.4 use the distributive property to multiply two - digit numbers
learning target: use the distributive property to multiply.
use the distributive property to find the product.

1. 43×18 =
2. 35×57 =
3. 81×76 =

3.5 use partial products to multiply two - digit numbers
learning target: use place value and partial products to multiply.
find the product. check whether your answer is reasonable.

1. estimate:

18
×22

1. estimate:

73
×46

1. estimate:

39
×84
find the missing digits. then find the product.
15.
□2
×□5
1 0
5 0
6 0
+3 0 0
□
16.
□1
×□4
4
2 0 0
4 0
+2,0 0 0
□

Explanation:

Step1: Solve 43×18 using distributive property

We can write 18 as 10 + 8. Then 43×18=43×(10 + 8). By the distributive property a×(b + c)=a×b+a×c, so 43×(10 + 8)=43×10+43×8. 43×10 = 430 and 43×8=344. Then 430+344 = 774.

Step2: Solve 35×57 using distributive property

Write 57 as 50+7. Then 35×57=35×(50 + 7)=35×50+35×7. 35×50 = 1750 and 35×7 = 245. So 1750+245=1995.

Step3: Solve 81×76 using distributive property

Write 76 as 70+6. Then 81×76=81×(70 + 6)=81×70+81×6. 81×70=5670 and 81×6 = 486. So 5670+486=6156.

Step4: Estimate 18×22

Round 18 to 20 and 22 to 20. Then 20×20 = 400.

Step5: Estimate 73×46

Round 73 to 70 and 46 to 50. Then 70×50=3500.

Step6: Estimate 39×84

Round 39 to 40 and 84 to 80. Then 40×80 = 3200.

Step7: Solve 15

From the multiplication 2×5 = 10. The first - digit of the first factor multiplied by 5 gives 50, so the first - digit of the first factor is 1. The first - digit of the second factor multiplied by 2 gives 60, so the first - digit of the second factor is 3. The product is 12×35=420.

Step8: Solve 16

From 1×4 = 4. The first - digit of the first factor multiplied by 4 gives 200, so the first - digit of the first factor is 5. The first - digit of the second factor multiplied by 1 gives 40, so the first - digit of the second factor is 4. The product is 51×44=2244.

Answer:

1. 774
2. 1995
3. 6156
4. 400
5. 3500
6. 3200
7. The missing digits are 1 and 3, product is 420
8. The missing digits are 5 and 4, product is 2244