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Pin on Sixth Grade Printables! - Free Printable

Pin on Sixth Grade Printables!

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Problem Analysis


The image contains several sections with mathematical tasks:
1. Find the product: Multiplication problems.
2. Calculate: Arithmetic operations involving fractions and mixed numbers.
3. Round to the underlined digit: Rounding numbers to specific digits.

Below, I will solve each section step by step.

---

Section 1: Find the product



#### Task: Multiply the given numbers.
- Rule: Perform standard multiplication for each pair of numbers.

#### Solutions:
1. 69. \( 1866 \times 11 \)
\[
1866 \times 11 = 1866 \times (10 + 1) = 18660 + 1866 = 20526
\]
Answer: \( 20526 \)

2. 70. \( 486 \times 30 \)
\[
486 \times 30 = 486 \times (3 \times 10) = (486 \times 3) \times 10 = 1458 \times 10 = 14580
\]
Answer: \( 14580 \)

3. 71. \( 1165 \times 5 \)
\[
1165 \times 5 = 5825
\]
Answer: \( 5825 \)

4. 72. \( 1141 \times 9 \)
\[
1141 \times 9 = 1141 \times (10 - 1) = 11410 - 1141 = 10269
\]
Answer: \( 10269 \)

5. 73. \( 1466 \times 50 \)
\[
1466 \times 50 = 1466 \times (5 \times 10) = (1466 \times 5) \times 10 = 7330 \times 10 = 73300
\]
Answer: \( 73300 \)

6. 74. \( 2382 \times 50 \)
\[
2382 \times 50 = 2382 \times (5 \times 10) = (2382 \times 5) \times 10 = 11910 \times 10 = 119100
\]
Answer: \( 119100 \)

7. 75. \( 1600 \times 9 \)
\[
1600 \times 9 = 1600 \times (10 - 1) = 16000 - 1600 = 14400
\]
Answer: \( 14400 \)

8. 76. \( 221 \times 10 \)
\[
221 \times 10 = 2210
\]
Answer: \( 2210 \)

9. 77. \( 3807 \times 4 \)
\[
3807 \times 4 = 15228
\]
Answer: \( 15228 \)

10. 78. \( 818 \times 25 \)
\[
818 \times 25 = 818 \times (20 + 5) = (818 \times 20) + (818 \times 5) = 16360 + 4090 = 20450
\]
Answer: \( 20450 \)

---

Section 2: Calculate



#### Task: Perform arithmetic operations involving fractions and mixed numbers.
- Rule: Convert mixed numbers to improper fractions, perform operations, and simplify if necessary.

#### Solutions:
1. 79. \( 7 \frac{1}{2} - 1 \frac{1}{2} \)
\[
7 \frac{1}{2} = \frac{15}{2}, \quad 1 \frac{1}{2} = \frac{3}{2}
\]
\[
\frac{15}{2} - \frac{3}{2} = \frac{15 - 3}{2} = \frac{12}{2} = 6
\]
Answer: \( 6 \)

2. 80. \( 7 \frac{17}{20} - 5 \frac{18}{20} \)
\[
7 \frac{17}{20} = \frac{157}{20}, \quad 5 \frac{18}{20} = \frac{118}{20}
\]
\[
\frac{157}{20} - \frac{118}{20} = \frac{157 - 118}{20} = \frac{39}{20} = 1 \frac{19}{20}
\]
Answer: \( 1 \frac{19}{20} \)

3. 81. \( 8 \frac{1}{11} - 2 \frac{3}{11} \)
\[
8 \frac{1}{11} = \frac{89}{11}, \quad 2 \frac{3}{11} = \frac{25}{11}
\]
\[
\frac{89}{11} - \frac{25}{11} = \frac{89 - 25}{11} = \frac{64}{11} = 5 \frac{9}{11}
\]
Answer: \( 5 \frac{9}{11} \)

4. 82. \( 4 \frac{7}{9} - 1 \frac{8}{9} \)
\[
4 \frac{7}{9} = \frac{43}{9}, \quad 1 \frac{8}{9} = \frac{17}{9}
\]
\[
\frac{43}{9} - \frac{17}{9} = \frac{43 - 17}{9} = \frac{26}{9} = 2 \frac{8}{9}
\]
Answer: \( 2 \frac{8}{9} \)

5. 83. \( 3 \frac{13}{16} + 2 \frac{9}{16} \)
\[
3 \frac{13}{16} = \frac{55}{16}, \quad 2 \frac{9}{16} = \frac{41}{16}
\]
\[
\frac{55}{16} + \frac{41}{16} = \frac{55 + 41}{16} = \frac{96}{16} = 6
\]
Answer: \( 6 \)

6. 84. \( 8 \frac{2}{17} - 5 \frac{5}{17} \)
\[
8 \frac{2}{17} = \frac{138}{17}, \quad 5 \frac{5}{17} = \frac{90}{17}
\]
\[
\frac{138}{17} - \frac{90}{17} = \frac{138 - 90}{17} = \frac{48}{17} = 2 \frac{14}{17}
\]
Answer: \( 2 \frac{14}{17} \)

7. 85. \( 4 \frac{5}{21} + 8 \frac{12}{21} \)
\[
4 \frac{5}{21} = \frac{89}{21}, \quad 8 \frac{12}{21} = \frac{180}{21}
\]
\[
\frac{89}{21} + \frac{180}{21} = \frac{89 + 180}{21} = \frac{269}{21} = 12 \frac{17}{21}
\]
Answer: \( 12 \frac{17}{21} \)

8. 86. \( 3 \frac{47}{100} + 3 \frac{4}{100} \)
\[
3 \frac{47}{100} = \frac{347}{100}, \quad 3 \frac{4}{100} = \frac{304}{100}
\]
\[
\frac{347}{100} + \frac{304}{100} = \frac{347 + 304}{100} = \frac{651}{100} = 6 \frac{51}{100}
\]
Answer: \( 6 \frac{51}{100} \)

9. 87. \( 9 \frac{67}{75} - 6 \frac{68}{75} \)
\[
9 \frac{67}{75} = \frac{722}{75}, \quad 6 \frac{68}{75} = \frac{498}{75}
\]
\[
\frac{722}{75} - \frac{498}{75} = \frac{722 - 498}{75} = \frac{224}{75} = 2 \frac{74}{75}
\]
Answer: \( 2 \frac{74}{75} \)

10. 88. \( 2 \frac{49}{50} + 1 \frac{43}{50} \)
\[
2 \frac{49}{50} = \frac{149}{50}, \quad 1 \frac{43}{50} = \frac{93}{50}
\]
\[
\frac{149}{50} + \frac{93}{50} = \frac{149 + 93}{50} = \frac{242}{50} = \frac{121}{25} = 4 \frac{21}{25}
\]
Answer: \( 4 \frac{21}{25} \)

---

Section 3: Round to the underlined digit



#### Task: Round each number to the specified digit.
- Rule: Identify the underlined digit and round based on the next digit to the right.

#### Solutions:
1. 89. \( 3\textbf{8}94 \) (Underlined digit is tens place)
\[
3894 \rightarrow 3900 \quad (\text{Rounded up because } 9 \geq 5)
\]
Answer: \( 3900 \)

2. 90. \( 35\textbf{0}18 \) (Underlined digit is hundreds place)
\[
35018 \rightarrow 35000 \quad (\text{Rounded down because } 1 < 5)
\]
Answer: \( 35000 \)

3. 91. \( 60\textbf{6}1 \) (Underlined digit is hundreds place)
\[
6061 \rightarrow 6100 \quad (\text{Rounded up because } 6 \geq 5)
\]
Answer: \( 6100 \)

4. 92. \( 18\textbf{6}5 \) (Underlined digit is tens place)
\[
1865 \rightarrow 1870 \quad (\text{Rounded up because } 5 \geq 5)
\]
Answer: \( 1870 \)

5. 93. \( 761\textbf{2}8 \) (Underlined digit is tens place)
\[
76128 \rightarrow 76130 \quad (\text{Rounded up because } 8 \geq 5)
\]
Answer: \( 76130 \)

6. 94. \( 99\textbf{6}7 \) (Underlined digit is hundreds place)
\[
9967 \rightarrow 10000 \quad (\text{Rounded up because } 6 \geq 5)
\]
Answer: \( 10000 \)

7. 95. \( 98\textbf{8}1 \) (Underlined digit is hundreds place)
\[
9881 \rightarrow 9900 \quad (\text{Rounded up because } 8 \geq 5)
\]
Answer: \( 9900 \)

8. 96. \( 443\textbf{2}38 \) (Underlined digit is thousands place)
\[
443238 \rightarrow 443000 \quad (\text{Rounded down because } 2 < 5)
\]
Answer: \( 443000 \)

9. 97. \( 95\textbf{2}2 \) (Underlined digit is hundreds place)
\[
9522 \rightarrow 9500 \quad (\text{Rounded down because } 2 < 5)
\]
Answer: \( 9500 \)

10. 98. \( 46\textbf{0}28 \) (Underlined digit is hundreds place)
\[
46028 \rightarrow 46000 \quad (\text{Rounded down because } 0 < 5)
\]
Answer: \( 46000 \)

---

Section 4: Round to the underlined digit



#### Task: Round each number to the specified digit.
- Rule: Identify the underlined digit and round based on the next digit to the right.

#### Solutions:
1. 99. \( 85\textbf{1}897 \) (Underlined digit is thousands place)
\[
851897 \rightarrow 850000 \quad (\text{Rounded down because } 1 < 5)
\]
Answer: \( 850000 \)

2. 100. \( 35\textbf{7}504 \) (Underlined digit is thousands place)
\[
357504 \rightarrow 358000 \quad (\text{Rounded up because } 7 \geq 5)
\]
Answer: \( 358000 \)

3. 101. \( 36\textbf{8}133 \) (Underlined digit is thousands place)
\[
368133 \rightarrow 368000 \quad (\text{Rounded down because } 1 < 5)
\]
Answer: \( 368000 \)

---

Final Answers


\[
\boxed{
\begin{array}{l}
\text{69. } 20526 \\
\text{70. } 14580 \\
\text{71. } 5825 \\
\text{72. } 10269 \\
\text{73. } 73300 \\
\text{74. } 119100 \\
\text{75. } 14400 \\
\text{76. } 2210 \\
\text{77. } 15228 \\
\text{78. } 20450 \\
\text{79. } 6 \\
\text{80. } 1 \frac{19}{20} \\
\text{81. } 5 \frac{9}{11} \\
\text{82. } 2 \frac{8}{9} \\
\text{83. } 6 \\
\text{84. } 2 \frac{14}{17} \\
\text{85. } 12 \frac{17}{21} \\
\text{86. } 6 \frac{51}{100} \\
\text{87. } 2 \frac{74}{75} \\
\text{88. } 4 \frac{21}{25} \\
\text{89. } 3900 \\
\text{90. } 35000 \\
\text{91. } 6100 \\
\text{92. } 1870 \\
\text{93. } 76130 \\
\text{94. } 10000 \\
\text{95. } 9900 \\
\text{96. } 443000 \\
\text{97. } 9500 \\
\text{98. } 46000 \\
\text{99. } 850000 \\
\text{100. } 358000 \\
\text{101. } 368000 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of grade 6 math worksheets.
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