1. 15+4×3÷16
A. Parentheses come first.
There are no parentheses
B. Exponents come second
There are no exponents
C. Multiplications and divisions come third, as they appear
going left to right.
The first of these going left to right is 4×3, so we replace
4×3 by 12 and copy everything else over just as it is:
15+12÷16
A. Parentheses come first.
There are no parentheses
B. Exponents come second
There are no exponents
C. Multiplications and divisions come third, as they appear
going left to right.
The first (only) of these going left to right is 12÷16 , so
we replace 12÷16 by 
reduced to 
and copy
everything else over just as it is:
15+
There is only this operation of addition remaining, so
the answer is gotten my getting the LCD:
or 
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2. 8×10÷5+7
A. Parentheses come first.
There are no parentheses
B. Exponents come second
There are no exponents
C. Multiplications and divisions come third, as they appear
going left to right.
The first of these going left to right is 8×10, so we replace
8×10 by 80 and copy everything else over just as it is:
80÷5+7
A. Parentheses come first.
There are no parentheses
B. Exponents come second
There are no exponents
C. Multiplications and divisions come third, as they appear
going left to right.
The first (the one one) of these going left to right is 80÷5,
so we replace 80÷5 by 16 and copy everything else over just as it is:
16+7
There is only this operation of addition remaining, and 16+7 = 23
Answer: 23
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3. 42+16÷8×5
A. Parentheses come first.
There are no parentheses
B. Exponents come second
There are no exponents
C. Multiplications and divisions come third, as they appear
going left to right.
The first of these going left to right is 16÷8, so we replace
16÷8 by 2 and copy everything else over just as it is:
42+2×5
A. Parentheses come first.
There are no parentheses
B. Exponents come second
There are no exponents
C. Multiplications and divisions come third, as they appear
going left to right.
The first (only one) of these going left to right is 16÷8, so
we replace 2×5 by 10 and copy everything else over just as it is:
42+10
There is only this operation of addition remaining, and 42+10 = 52
Answer: 52
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4. (2×6)÷4+8
A. Parentheses come first.
The parentheses (2×6) contain the operation 2×6,
so we replace the (2×6) by 12 and copy everything else over
12÷4+8
A. Parentheses come first.
There are no parentheses
B. Exponents come second
There are no exponents
C. Multiplications and divisions come third, as they appear
going left to right.
The first (only one) of these going left to right is 4×3, so
we replace 12÷4 by 3 and copy everything else over just as
it is:
3+8
That's just 11.
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5. 4×9-[(12-5)÷7]
A. Parentheses come first.
Innermost parentheses come first.
The innermost parentheses is (12-5),and
it contains 12-5 so we replace (12-5) by 7
and copy everything else over:
4×9-[7÷7]
A. Parentheses come first.
The parentheses [7÷7] contains 7÷7 which is 1,
so we replace [7÷7] by 1 and copy everything
else over:
4×9-1
A. Parentheses come first.
There are no parentheses
B. Exponents come second
There are no exponents
C. Multiplications and divisions come third, as they appear
going left to right.
The first (only one) of these going left to right is 4×9,
so we replace 4×9 by 36 and copy everything else over just
as it is:
36-1
That's just 35.
Edwin
