According to the structure of formulas and the characteristics of numbers, flexible use of operation rules, laws, properties and some formulas can make some complex elementary arithmetic simple and difficult.
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Example 1 answer
Calculate 4.75-9.63+(8.25- 1.37)
In mental navigation, the brackets are removed first, so that 4.75 and 8.25 are added together to form a whole, and then the nature of subtraction: A-B-C = A-(B+C) is used to make the operation process simple. therefore
Original formula = 4.75+8.25-9.63- 1.37.
= 13-(9.63+ 1.37)
= 13- 1 1
=2
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Exercise 1
Calculate the following questions.
1.6.73-2 and 8/ 17+(3.27- 1 and 9/ 17) answers
2.7 5/9-(3.8+15/9)-1and 1/5 answers
3. 14. 15-(7 7/8-6 and 17/20)-2. 125 answer
4. 13 and 7/ 13-(4 and 1/4+3 and 7/ 13)-0.75 answers.
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Example 2 Answer
Calculate 333387 and 1/2×79+790×666 1 and 1/4.
Mental navigation can make use of the changing law of the product after the fraction is converted into decimal and the multiplication and division method to make the calculation simple. therefore
The original formula = 33387.5×79+790×666 1.25.
=33338.75×790+790×6666 1.25
=(33338.75+6666 1.25)×790
= 100000×790
=79000000
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Exercise 2
Calculate the following questions:
Answer 1. 3.5× 1 and1/4+125%+1and 1/2÷4/5.
2. Answer 975× 0.25+9 and 3/4× 76-9.75.
3.9 Answer 2/5×425+4.25÷ 1/60
4.0.9999× 0.7+0.1111× 2.7 answer.
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Example 3 Answer
Calculation: 36× 1.09+ 1.2×67.3.
On the surface, there is no simple algorithm for mental navigation. Careful observation of the characteristics of numbers shows that 36 = 1.2×30. With this transformation, the laws of multiplication and distribution can be applied. therefore
The original formula =1.2× 30×1.09+1.2× 67.3.
= 1.2×(30× 1.09+ 1.2×67.3)
= 1.2×(32.7+67.3)
= 1.2× 100
= 120
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Exercise 3
Calculation: a.
1.45×2.08+ 1.5×37.6
2.52× 1 1. 1+2.6×778
3.48× 1.08+ 1.2×56.8
4.72×2.09- 1.8×73.6
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Example 4 Answer
Calculation: 3 3/5×25 2/5+37.9× 6 2/5.
Although the sum of 3 3/5 and 6 2/5 is 10, another factor of their multiplication is different. So we can easily think of dividing 37.9 into 25.4 and 12.5. When 12.5×6.4 appears, we can regard 6.4 as 8×0.8 again, so the calculation is much simpler. therefore
The original formula = 3 3/5× 25 2/5+(25.4+12.5 )× 6.4.
= 3 3/5×25 2/5+25.4× 6.4+ 12.5× 6.4
=(3.6+6.4)×25.4+ 12.5×8×0.8
=254+80
=334
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Exercise 4
Calculate the following questions: a.
1.6.8× 16.8+ 19.3×3.2
2. 139× 137/ 138+ 137× 1/ 138
3.4.4×57.8+45.3×5.6
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Example 5 Answer
Calculate 81.5×15.8+81.5× 51.8+67.6×18.5.
Firstly, the common factor is extracted by grouping, and then the common factor is extracted for the second time, so the calculation is simple. therefore
The original formula = 81.5× (15.8+51.8)+67.6×18.5.
=8 1.5×67.6+67.6× 18.5
=(8 1.5+ 18.5)×67.6
= 100×67.6
=6760
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Exercise 5 A
1.53.5×35.3+53.5×43.2+78.5×46.5
2.235× 12. 1++235×42.2- 135×54.3
3.3.75×735-3/8×5730+ 16.2×62.5
Answer:
Exercise 1
1.6.73-2 and 8/ 17+(3.27- 1 and 9/ 17)
= (6.73+3.27)-(2 8/ 17+9/ 17)
= 6
2.7 5/9-(3.8+15/9)-1and 1/5
= (7 5/9-15/9)-(3.8+1and 1/5)
= 6-5
= 1
3. 14. 15-(7 7/8-6 and 17/20)-2. 125
=( 14. 15+6.85)-(7.875+2. 125)
= 2 1- 10
= 1 1
4. 13 and 7/ 13-(4 and 1/4+3 and 7/ 13)-0.75
= 13 and 7/ 13-3 and 7/ 13-(4.25+0.75)
= 10-5
= 5
Exercise 2
1.3.5× 1 and1/4+125%+1and 1/2÷4/5.
= (3.5+1+1.5) ×1and 1/4.
= 7.5
2.975× 0.25+9 and 3/4× 76-9.75
= 9.75×(25+76- 1)
= 975
3.9 2/5×425+4.25÷ 1/60
= 4.25×940+4.25÷60
= 4.25×(940+60)
= 4250
4.0.9999×0.7+0. 1 1 1 1×2.7
= 0.9999×(0.7+0.3)
= 0.9999
Exercise 3
1.45×2.08+ 1.5×37.6
= 1.5×62.4+ 1.5×37.6
= 1.5×(62.4+37.6)
= 150
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2.52× 1 1. 1+2.6×778
= 2.6×222+2.6×778
= 2.6×(222+778)
= 2600
3.48× 1.08+ 1.2×56.8
= 1.2× 43.2+ 1.2 with a difference of 56.8.
= 1.2×(43.2+56.8)
= 120
4.72×2.09- 1.8×73.6
= 1.8×83.6- 1.8×73.6
= 1.8×(83.6-73.6)
= 18
Exercise 4
1.6.8× 16.8+ 19.3×3.2
= 6.8× 16.8+ 16.8×3.2+2.5×3.2
= (6.8+3.2)× 16.8+2.5×4×0.8
= 168+8
= 176
2. 139× 137/ 138+ 137× 1/ 138
= 139× 137/ 138+ 1× 137/ 138
= ( 139+ 1)× 137/ 138
= 138× 137/ 138+2× 137/ 138
= 138 and 68/69
3.4.4×57.8+45.3×5.6
= 4.4×45.3+4.4× 12.5+45.3×5.6
= (4.4+5.6)×45.3+0.55×8× 12.5
= 453+55
= 508
Exercise 5
1.53.5×35.3+53.5×43.2+78.5×46.5
= 53.5×78.5+78.5×46.5
= (53.5+46.5)×78.5
= 7850
2.235× 12. 1++235×42.2- 135×54.3
= 235×54.3- 135×54.3
= (235- 135)×54.3
= 5430
3.3.75×735-3/8×5730+ 16.2×62.5
= 3.75×735-3.75×573+ 16.2×62.5
= 3.75× 162+ 16.2×62.5
= 162×(3.75+6.25)
= 1620
Hope to adopt (∩ _ ∩)