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Using the distributive property, find the following products:

a) [tex]\( 937 \times 105 \)[/tex]

b) [tex]\( 346 \times 1007 \)[/tex]

c) [tex]\( 947 \times 96 \)[/tex]

d) [tex]\( 996 \times 267 \)[/tex]

Sagot :

GinnyAnswer
Sure! Let's solve each part using the distributive property.

### (a) [tex]\( 937 \times 105 \)[/tex]

We can express 105 as [tex]\( 100 + 5 \)[/tex]. Then, we use the distributive property:
[tex]\[ 937 \times 105 = 937 \times (100 + 5) \][/tex]
This can be broken down as:
[tex]\[ 937 \times 105 = 937 \times 100 + 937 \times 5 \][/tex]

Now, calculating each term:
[tex]\[ 937 \times 100 = 93700 \][/tex]
[tex]\[ 937 \times 5 = 4685 \][/tex]

Adding these together:
[tex]\[ 93700 + 4685 = 98385 \][/tex]

So,
[tex]\[ 937 \times 105 = 98385 \][/tex]

### (b) [tex]\( 346 \times 1007 \)[/tex]

We can express 1007 as [tex]\( 1000 + 7 \)[/tex]. Then, we use the distributive property:
[tex]\[ 346 \times 1007 = 346 \times (1000 + 7) \][/tex]
This can be broken down as:
[tex]\[ 346 \times 1007 = 346 \times 1000 + 346 \times 7 \][/tex]

Now, calculating each term:
[tex]\[ 346 \times 1000 = 346000 \][/tex]
[tex]\[ 346 \times 7 = 2422 \][/tex]

Adding these together:
[tex]\[ 346000 + 2422 = 348422 \][/tex]

So,
[tex]\[ 346 \times 1007 = 348422 \][/tex]

### (c) [tex]\( 947 \times 96 \)[/tex]

We can express 96 as [tex]\( 100 - 4 \)[/tex]. Then, we use the distributive property:
[tex]\[ 947 \times 96 = 947 \times (100 - 4) \][/tex]
This can be broken down as:
[tex]\[ 947 \times 96 = 947 \times 100 - 947 \times 4 \][/tex]

Now, calculating each term:
[tex]\[ 947 \times 100 = 94700 \][/tex]
[tex]\[ 947 \times 4 = 3788 \][/tex]

Subtracting these:
[tex]\[ 94700 - 3788 = 90912 \][/tex]

So,
[tex]\[ 947 \times 96 = 90912 \][/tex]

### (d) [tex]\( 996 \times 267 \)[/tex]

We can express 267 as [tex]\( 200 + 60 + 7 \)[/tex]. Then, we use the distributive property:
[tex]\[ 996 \times 267 = 996 \times (200 + 60 + 7) \][/tex]
This can be broken down as:
[tex]\[ 996 \times 267 = 996 \times 200 + 996 \times 60 + 996 \times 7 \][/tex]

Now, calculating each term:
[tex]\[ 996 \times 200 = 199200 \][/tex]
[tex]\[ 996 \times 60 = 59760 \][/tex]
[tex]\[ 996 \times 7 = 6972 \][/tex]

Adding these together:
[tex]\[ 199200 + 59760 + 6972 = 265932 \][/tex]

So,
[tex]\[ 996 \times 267 = 265932 \][/tex]

Summarizing all the results:
(a) [tex]\( 937 \times 105 = 98385 \)[/tex]
(b) [tex]\( 346 \times 1007 = 348422 \)[/tex]
(c) [tex]\( 947 \times 96 = 90912 \)[/tex]
(d) [tex]\( 996 \times 267 = 265932 \)[/tex]
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