Question

instructions: elves like to represent their toy - making with number problems, so they get everything done in the correct order. use the order of operations to complete the questions below.
$3×(10×2)÷5$ $8 + 3 + 3×6$ $5×10-(6 - 3)$
$12÷(6 + 4 - 8)$ $4+(3 - 3)^3$ $(15 - 9)÷(9 - 3)$
$(4^2 - 2)×7$ $8×14÷(6 - 4)$ $8(5×3 - 9)$
$30÷(8-(7 - 4))$ $10÷((8 - 7)×2)$ $(16×2)÷(9 - 5)$
$10 - 12÷4 - 4$ $3 + 30÷10×2$ $2(5×8 - 2)$
$30÷(3 + 2)×8$ $(1 + 5)(8 - 7)$ $(20 - 10)÷(1 + 4)$
$(3 + 4 + 9)×2$ $8÷(4^2 - 8)$

Explanation:

Let's solve the first problem \( 3\times(10\times2)\div5 \) step by step.

Step1: Solve the innermost parentheses

First, calculate the expression inside the parentheses: \( 10\times2 = 20 \)

Step2: Perform multiplication

Now, multiply 3 by the result from Step 1: \( 3\times20 = 60 \)

Step3: Perform division

Finally, divide the result from Step 2 by 5: \( 60\div5 = 12 \)

Let's solve the second problem \( 8 + 3 + 3\times6 \)

Step1: Perform multiplication

First, calculate the multiplication: \( 3\times6 = 18 \)

Step2: Perform addition

Now, add the numbers: \( 8 + 3 + 18 = 11 + 18 = 29 \)

Let's solve the third problem \( 5\times10-(6 - 3) \)

Step1: Solve the parentheses

First, calculate the expression inside the parentheses: \( 6 - 3 = 3 \)

Step2: Perform multiplication

Now, multiply 5 by 10: \( 5\times10 = 50 \)

Step3: Perform subtraction

Finally, subtract the result from Step 1 from the result from Step 2: \( 50 - 3 = 47 \)

Let's solve the fourth problem \( 12\div(6 + 4 - 8) \)

Step1: Solve the parentheses

First, calculate the expression inside the parentheses: \( 6 + 4 - 8 = 10 - 8 = 2 \)

Step2: Perform division

Now, divide 12 by the result from Step 1: \( 12\div2 = 6 \)

Let's solve the fifth problem \( 4+(3 - 3)^{3} \)

Step1: Solve the parentheses

First, calculate the expression inside the parentheses: \( 3 - 3 = 0 \)

Step2: Calculate the exponent

Now, calculate the exponent: \( 0^{3} = 0 \)

Step3: Perform addition

Finally, add 4 and the result from Step 2: \( 4 + 0 = 4 \)

Let's solve the sixth problem \( (15 - 9)\div(9 - 3) \)

Step1: Solve the parentheses

First, calculate the expressions inside the parentheses: \( 15 - 9 = 6 \) and \( 9 - 3 = 6 \)

Step2: Perform division

Now, divide the results: \( 6\div6 = 1 \)

Let's solve the seventh problem \( (4^{2}-2)\times7 \)

Step1: Calculate the exponent

First, calculate the exponent: \( 4^{2} = 16 \)

Step2: Solve the parentheses

Now, calculate the expression inside the parentheses: \( 16 - 2 = 14 \)

Step3: Perform multiplication

Finally, multiply the result from Step 2 by 7: \( 14\times7 = 98 \)

Let's solve the eighth problem \( 8\times14\div(6 - 4) \)

Step1: Solve the parentheses

First, calculate the expression inside the parentheses: \( 6 - 4 = 2 \)

Step2: Perform multiplication

Now, multiply 8 and 14: \( 8\times14 = 112 \)

Step3: Perform division

Finally, divide the result from Step 2 by the result from Step 1: \( 112\div2 = 56 \)

Let's solve the ninth problem \( 8(5\times3 - 9) \)

Step1: Solve the parentheses

First, calculate the expression inside the parentheses: \( 5\times3 - 9 = 15 - 9 = 6 \)

Step2: Perform multiplication

Now, multiply 8 by the result from Step 1: \( 8\times6 = 48 \)

Let's solve the tenth problem \( 30\div(8-(7 - 4)) \)

Step1: Solve the innermost parentheses

First, calculate the innermost parentheses: \( 7 - 4 = 3 \)

Step2: Solve the outer parentheses

Now, calculate the outer parentheses: \( 8 - 3 = 5 \)

Step3: Perform division

Finally, divide 30 by the result from Step 2: \( 30\div5 = 6 \)

Let's solve the eleventh problem \( 10\div((8 - 7)\times2) \)

Step1: Solve the innermost parentheses

First, calculate the innermost parentheses: \( 8 - 7 = 1 \)

Step2: Solve the outer parentheses

Now, calculate the outer parentheses: \( 1\times2 = 2 \)

Step3: Perform division

Finally, divide 10 by the result from Step 2: \( 10\div2 = 5 \)

Let's solve the twelfth problem \( (16\times2)\div(9 - 5) \)

Step1: Solve the parentheses

First, calculate the expressions inside the parentheses: \( 16\times2 = 32 \) and \( 9 - 5 = 4 \)

Step2: Perform division

Now, divide the results: \( 32\div4 = 8 \)

Let's solve the thirteenth problem \( 10 - 12\div4 - 4 \)

Step1: Perform division

First, calculate the division: \( 12\div4 = 3 \)

Step2: Perform subtraction

Now, subtract from left to right: \( 10 - 3 - 4 = 7 - 4 = 3 \)

Let's solve the fourteenth problem \( 3 + 30\div10\times2 \)

Step1: Perform division

First, calculate the division: \( 30\div10 = 3 \)

Step2: Perform multiplication

Now, calculate the multiplication: \( 3\times2 = 6 \)

Step3: Perform addition

Finally, add 3 and the result from Step 2: \( 3 + 6 = 9 \)

Let's solve the fifteenth problem \( 2(5\times8 - 2) \)

Step1: Solve the parentheses

First, calculate the expression inside the parentheses: \( 5\times8 - 2 = 40 - 2 = 38 \)

Step2: Perform multiplication

Now, multiply 2 by the result from Step 1: \( 2\times38 = 76 \)

Let's solve the sixteenth problem \( 30\div(3 + 2)\times8 \)

Step1: Solve the parentheses

First, calculate the expression inside the parentheses: \( 3 + 2 = 5 \)

Step2: Perform division

Now, divide 30 by the result from Step 1: \( 30\div5 = 6 \)

Step3: Perform multiplication

Finally, multiply the result from Step 2 by 8: \( 6\times8 = 48 \)

Let's solve the seventeenth problem \( (1 + 5)(8 - 7) \)

Step1: Solve the parentheses

First, calculate the expressions inside the parentheses: \( 1 + 5 = 6 \) and \( 8 - 7 = 1 \)

Step2: Perform multiplication

Now, multiply the results: \( 6\times1 = 6 \)

Let's solve the eighteenth problem \( (20 - 10)\div(1 + 4) \)

Step1: Solve the parentheses

First, calculate the expressions inside the parentheses: \( 20 - 10 = 10 \) and \( 1 + 4 = 5 \)

Step2: Perform division

Now, divide the results: \( 10\div5 = 2 \)

Let's solve the nineteenth problem \( (3 + 4 + 9)\times2 \)

Step1: Solve the parentheses

First, calculate the expression inside the parentheses: \( 3 + 4 + 9 = 16 \)

Step2: Perform multiplication

Now, multiply the result from Step 1 by 2: \( 16\times2 = 32 \)

Let's solve the twentieth problem \( 8\div(4^{2}-8) \)

Step1: Calculate the exponent

First, calculate the exponent: \( 4^{2} = 16 \)

Step2: Solve the parentheses

Now, calculate the expression inside the parentheses: \( 16 - 8 = 8 \)

Step3: Perform division

Finally, divide 8 by the result from Step 2: \( 8\div8 = 1 \)

Answers:

1. \( 3\times(10\times2)\div5 = 12 \)
2. \( 8 + 3 + 3\times6 = 29 \)
3. \( 5\times10-(6 - 3) = 47 \)
4. \( 12\div(6 + 4 - 8) = 6 \)
5. \( 4+(3 - 3)^{3} = 4 \)
6. \( (15 - 9)\div(9 - 3) = 1 \)
7. \( (4^{2}-2)\times7 = 98 \)
8. \( 8\times14\div(6 - 4) = 56 \)
9. \( 8(5\times3 - 9) = 48 \)
10. \( 30\div(8-(7 - 4)) = 6 \)
11. \( 10\div((8 - 7)\times2) = 5 \)
12. \( (16\times2)\div(9 - 5) = 8 \)
13. \( 10 - 12\div4 - 4 = 3 \)
14. \( 3 + 30\div10\times2 = 9 \)
15. \( 2(5\times8 - 2) = 76 \)
16. \( 30\div(3 + 2)\times8 = 48 \)
17. \( (1 + 5)(8 - 7) = 6 \)
18. \( (20 - 10)\div(1 + 4) = 2 \)
19. \( (3 + 4 + 9)\times2 = 32 \)
20. \( 8\div(4^{2}-8) = 1 \)

Answer:

s:

1. \( 3\times(10\times2)\div5 = 12 \)
2. \( 8 + 3 + 3\times6 = 29 \)
3. \( 5\times10-(6 - 3) = 47 \)
4. \( 12\div(6 + 4 - 8) = 6 \)
5. \( 4+(3 - 3)^{3} = 4 \)
6. \( (15 - 9)\div(9 - 3) = 1 \)
7. \( (4^{2}-2)\times7 = 98 \)
8. \( 8\times14\div(6 - 4) = 56 \)
9. \( 8(5\times3 - 9) = 48 \)
10. \( 30\div(8-(7 - 4)) = 6 \)
11. \( 10\div((8 - 7)\times2) = 5 \)
12. \( (16\times2)\div(9 - 5) = 8 \)
13. \( 10 - 12\div4 - 4 = 3 \)
14. \( 3 + 30\div10\times2 = 9 \)
15. \( 2(5\times8 - 2) = 76 \)
16. \( 30\div(3 + 2)\times8 = 48 \)
17. \( (1 + 5)(8 - 7) = 6 \)
18. \( (20 - 10)\div(1 + 4) = 2 \)
19. \( (3 + 4 + 9)\times2 = 32 \)
20. \( 8\div(4^{2}-8) = 1 \)