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Math worksheet with ten arithmetic problems for practice.

A worksheet with ten math problems involving addition, subtraction, multiplication, division, and parentheses, with a box labeled "Your Marks" at the top.

A worksheet with ten math problems involving addition, subtraction, multiplication, division, and parentheses, with a box labeled "Your Marks" at the top.

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Show Answer Key & Explanations Step-by-step solution for: Hard Math worksheet
To solve the given problems, we will evaluate each expression step by step. Let's go through them one by one:

---

Problem 1: \( 4103 + 1326 \times 4 \)



1. According to the order of operations (PEMDAS/BODMAS), multiplication comes before addition.
2. Calculate \( 1326 \times 4 \):
\[
1326 \times 4 = 5304
\]
3. Add the result to 4103:
\[
4103 + 5304 = 9407
\]

Answer for Problem 1: \( 9407 \)

---

Problem 2: \( 7813 - 819 / 9 \)



1. According to the order of operations, division comes before subtraction.
2. Calculate \( 819 / 9 \):
\[
819 / 9 = 91
\]
3. Subtract the result from 7813:
\[
7813 - 91 = 7722
\]

Answer for Problem 2: \( 7722 \)

---

Problem 3: \( 6814 \times 13 - 4316 \)



1. According to the order of operations, multiplication comes before subtraction.
2. Calculate \( 6814 \times 13 \):
\[
6814 \times 13 = 88582
\]
3. Subtract 4316 from the result:
\[
88582 - 4316 = 84266
\]

Answer for Problem 3: \( 84266 \)

---

Problem 4: \( (7143 - 1748) / 5 \)



1. First, calculate the value inside the parentheses:
\[
7143 - 1748 = 5395
\]
2. Divide the result by 5:
\[
5395 / 5 = 1079
\]

Answer for Problem 4: \( 1079 \)

---

Problem 5: \( 6431 \times (1439 - 194) \)



1. First, calculate the value inside the parentheses:
\[
1439 - 194 = 1245
\]
2. Multiply the result by 6431:
\[
6431 \times 1245 = 8009145
\]

Answer for Problem 5: \( 8009145 \)

---

Problem 6: \( (193 - 17) \times (713 + 91) \)



1. Calculate the value inside the first set of parentheses:
\[
193 - 17 = 176
\]
2. Calculate the value inside the second set of parentheses:
\[
713 + 91 = 804
\]
3. Multiply the two results:
\[
176 \times 804 = 141504
\]

Answer for Problem 6: \( 141504 \)

---

Problem 7: \( (1643 + 781) / (1873 + 461) \)



1. Calculate the value inside the first set of parentheses:
\[
1643 + 781 = 2424
\]
2. Calculate the value inside the second set of parentheses:
\[
1873 + 461 = 2334
\]
3. Divide the first result by the second result:
\[
2424 / 2334 \approx 1.0386
\]

Answer for Problem 7: \( 1.0386 \) (or \( \frac{2424}{2334} \) if exact fraction is required)

---

Problem 8: \( 17844 / 83(7491 - 914) \)



1. First, calculate the value inside the parentheses:
\[
7491 - 914 = 6577
\]
2. The expression becomes:
\[
17844 / (83 \times 6577)
\]
3. Calculate \( 83 \times 6577 \):
\[
83 \times 6577 = 546031
\]
4. Divide 17844 by 546031:
\[
17844 / 546031 \approx 0.0327
\]

Answer for Problem 8: \( 0.0327 \) (or \( \frac{17844}{546031} \) if exact fraction is required)

---

Problem 9: \( 81941 \times 71 / (781 - 134) \)



1. First, calculate the value inside the parentheses:
\[
781 - 134 = 647
\]
2. The expression becomes:
\[
(81941 \times 71) / 647
\]
3. Calculate \( 81941 \times 71 \):
\[
81941 \times 71 = 5817811
\]
4. Divide 5817811 by 647:
\[
5817811 / 647 \approx 9023
\]

Answer for Problem 9: \( 9023 \)

---

Problem 10: \( (1738 - 1619) \times (6713 + 184) \)



1. Calculate the value inside the first set of parentheses:
\[
1738 - 1619 = 119
\]
2. Calculate the value inside the second set of parentheses:
\[
6713 + 184 = 6897
\]
3. Multiply the two results:
\[
119 \times 6897 = 820543
\]

Answer for Problem 10: \( 820543 \)

---

Final Answers:



\[
\boxed{
\begin{aligned}
1. & \ 9407 \\
2. & \ 7722 \\
3. & \ 84266 \\
4. & \ 1079 \\
5. & \ 8009145 \\
6. & \ 141504 \\
7. & \ 1.0386 \\
8. & \ 0.0327 \\
9. & \ 9023 \\
10. & \ 820543
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of hard math worksheet.
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