Sure, let's go through each of these expressions step-by-step, following the order of operations (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).
### (a) [tex]\( 4739 + 63 \times 3290 \div 14 - 12698 \)[/tex]
1. Start with the multiplication and division:
[tex]\[
63 \times 3290 = 207270
\][/tex]
[tex]\[
207270 \div 14 = 14805
\][/tex]
2. Now perform the addition and subtraction from left to right:
[tex]\[
4739 + 14805 - 12698
\][/tex]
[tex]\[
4739 + 14805 = 19544
\][/tex]
[tex]\[
19544 - 12698 = 6846
\][/tex]
So, the simplified result for (a) is [tex]\( 6846 \)[/tex].
### (b) [tex]\( 12276 \div 18 \times 53 + 28956 - 52741 \)[/tex]
1. Start with the division and then multiplication:
[tex]\[
12276 \div 18 = 682
\][/tex]
[tex]\[
682 \times 53 = 36146
\][/tex]
2. Now perform the addition and subtraction from left to right:
[tex]\[
36146 + 28956 - 52741
\][/tex]
[tex]\[
36146 + 28956 = 65102
\][/tex]
[tex]\[
65102 - 52741 = 12361
\][/tex]
So, the simplified result for (b) is [tex]\( 12361 \)[/tex].
### (c) [tex]\( 67 \times 43 - 42432 \div -17 + 3615 \)[/tex]
1. Start with the multiplication and division:
[tex]\[
67 \times 43 = 2881
\][/tex]
[tex]\[
42432 \div -17 = -2496
\][/tex]
2. Now perform the addition and subtraction from left to right:
[tex]\[
2881 - (-2496) + 3615
\][/tex]
[tex]\[
2881 + 2496 = 5377
\][/tex]
[tex]\[
5377 + 3615 = 8992
\][/tex]
So, the simplified result for (c) is [tex]\( 8992 \)[/tex].
### (d) [tex]\( 8930 + 5491 \div 19 \times 35 - 17958 \)[/tex]
1. Start with the division and multiplication:
[tex]\[
5491 \div 19 = 289
\][/tex]
[tex]\[
289 \times 35 = 10115
\][/tex]
2. Now perform the addition and subtraction from left to right:
[tex]\[
8930 + 10115 - 17958
\][/tex]
[tex]\[
8930 + 10115 = 19045
\][/tex]
[tex]\[
19045 - 17958 = 1087
\][/tex]
So, the simplified result for (d) is [tex]\( 1087 \)[/tex].
In summary:
- (a) [tex]\( 6846 \)[/tex]
- (b) [tex]\( 12361 \)[/tex]
- (c) [tex]\( 8992 \)[/tex]
- (d) [tex]\( 1087 \)[/tex]
