Answer:
B: 610; A: 202,000
D: 253; C: 2,007,000
Step-by-step explanation:
These are all expressions that can be calculated as is, or that can be simplified a little bit by taking advantage of the distributive property and other properties of addition and multiplication. The idea is to look for numbers that show up more than once, and rearrange the expression so they only show up once.
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<h3>B = (597 -176) +(13 +176)</h3>
This is a straight addition problem. The two "176" values have opposite signs, so cancel when they are added. Using the associative and commutative properties of addition, we can rearrange this to ...
597 +13 +(-176 +176)
= 597 +13
This can further be rearranged to ...
= (597 +3) +(13 -3)
= 600 +10
= 610
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<h3>A = 2020×173 -2020×73</h3>
The factor 2020 can be put outside parentheses using the distributive property:
= 2020(173 -73)
= 2020×100
= 202,000
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<h3>D 17×15 -15 +13</h3>
The value 15 is repeated. Terms using it can be combined using the distributive property.
= 15(17 -1) +13
= 15(16) +13
= 240 +13
= 253
Another way to look at this one is to use the factoring of the difference of squares.
= (16 +1)(16 -1) +(-15 +13)
= 16² -1² +(-2)
= 256 -3
= 253
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<h3>C 2019×890 -(12000 -2019×110)</h3>
Again, we can focus on rearranging so 2019 only needs to show up once.
= 2019(890 +110) -12000
= 2019×1000 -12×1000
= (2019 -12)×1000
= 2,007,000
