- Think of the related multiplication fact. - Recall the \(9\)s multiplication facts. - Ask how many groups of \(9\) make each starting number.

1. The first row gives \(27 \div 9 = 3\), \(54 \div 9 = 6\), \(81 \div 9 = 9\), \(18 \div 9 = 2\), and \(45 \div 9 = 5\). 2. The second row gives \(72 \div 9 = 8\), \(63 \div 9 = 7\), \(36 \div 9 = 4\), \(9 \div 9 = 1\), and \(90 \div 9 = 10\).

\(3; 6; 9; 2; 5; 8; 7; 4; 1; 10\)

- Think of the 7s multiplication facts. - What number times \(7\) equals \(42\)?

1. \(7\times6=42\). 2. So \(42\div7=6\).

\(42\div7=6\)

- Think of the multiplication fact related to each division fact. - Ask what number makes the related multiplication fact true. - Check each answer with multiplication.

1. \(24 \div 6 = 4\). 2. \(35 \div 5 = 7\). 3. \(54 \div 9 = 6\). 4. \(72 \div 8 = 9\).

a) \(4\) b) \(7\) c) \(6\) d) \(9\)

- Look for the factor paired with seven. - Division can undo a multiplication fact.

1. The multiplication fact has seven groups of four. 2. Therefore \(28\div7=4\).

\(28\div7=4\).

- What multiplication fact is related to each division equation? - When the first number is missing, multiply the other two numbers. - Check each completed equation with multiplication.

1. Since \(4\times8=32\), \(32\div8=4\). 2. Since \(6\times8=48\), the missing number in \(48\div\square=6\) is \(8\). 3. Since \(3\times8=24\), the missing number in \(\square\div8=3\) is \(24\). 4. Since \(10\times8=80\), the missing number in \(\square\div8=10\) is \(80\).

\(32 \div 8 = 4\) \(48 \div 8 = 6\) \(24 \div 8 = 3\) \(80 \div 8 = 10\)

- Use multiplication to check each division equation. - For each one, ask what number multiplied by the number you divide by makes the starting amount. - Exactly two equations need to be corrected.

1. Part a is correct because \(42 \div 6 = 7\). 2. Part b is incorrect because \(54 \div 9 = 6\). The correction is \(54\,\text{ft} \div 9 = 6\,\text{ft}\). 3. Part c is correct because \(32 \div 4 = 8\). 4. Part d is correct because \(48 \div 8 = 6\). 5. Part e is incorrect because \(63 \div 7 = 9\). The correction is \(\$63 \div 7 = \$9\).

b) \(54\,\text{ft} \div 9 = 6\,\text{ft}\) e) \(\$63 \div 7 = \$9\)

- Find each expression separately. - Write the number answer next to each letter. - Compare the five number answers after you finish.

1. A gives \(56 \div 7 = 8\). 2. B gives \(72 \div 9 = 8\). 3. C gives \(24 \div 3 = 8\). 4. D gives \(45 \div 5 = 9\). 5. E gives \(64 \div 8 = 8\). 6. A, B, C, and E all have the answer \(8\).

A, B, C, and E; each equals \(8\).

- Find the answer to each division fact. - Compare the two answers in each pair. - Use a multiplication fact to check any answer you are unsure about.

1. \(32 \div 4 = 8\) and \(18 \div 2 = 9\), so \(8 < 9\). 2. \(45 \div 5 = 9\) and \(54 \div 6 = 9\), so \(9 = 9\). 3. \(21 \div 3 = 7\) and \(28 \div 7 = 4\), so \(7 > 4\). 4. \(40 \div 8 = 5\) and \(30 \div 5 = 6\), so \(5 < 6\). 5. \(72 \div 9 = 8\) and \(64 \div 8 = 8\), so \(8 = 8\).

a) \(<\) b) \(=\) c) \(>\) d) \(<\) e) \(=\)

- Use multiplication facts to work backward when the missing number comes first. - Check each completed division equation. - The same multiplication and division facts use the same three numbers.

1. \(72\div8=9\). 2. \(32\div4=8\), so the missing number is \(32\). 3. \(45\div5=9\), so the missing number is \(5\).

a) \(9\) b) \(32\) c) \(5\)

- Count the rows and the dots in one row. - Use the whole number of dots as the first number in your division equation. - Multiply the number of rows by the number in each row to check.

1. The array has \(32\) dots arranged in \(8\) rows, with \(4\) dots in each row. 2. The division equation is \(32\div8=4\). 3. The multiplication check is \(8\times4=32\).

\(32\div8=4\); check: \(8\times4=32\)

- For each division fact, think of a related multiplication fact with one missing number. - Keep the starting total as the product in your multiplication check. - Check one answer by multiplying the two smaller numbers.

1. \(56 \div 7 = 8\). 2. \(72 \div 9 = 8\). 3. \(45 \div 5 = 9\). 4. One possible check is \(7 \times 8 = 56\), which verifies part a).

a) \(8\) b) \(8\) c) \(9\) One possible check: \(7 \times 8 = 56\).

- Work backward with multiplication. - Multiply the number after \(\div\) by the answer. - Check the completed division fact.

1. \(6 \times 7 = 42\), so \(42 \div 6 = 7\). 2. \(8 \times 5 = 40\), so \(40 \div 8 = 5\). 3. \(9 \times 4 = 36\), so \(36 \div 9 = 4\). 4. \(3 \times 8 = 24\), so \(24 \div 3 = 8\).

a) \(42\) b) \(40\) c) \(36\) d) \(24\)

- Use related multiplication facts instead of guessing. - Look for facts that make \(6\) or \(8\) as the division answer. - Check every division fact before placing it in a group.

1. \(42 \div 7 = 6\) and \(54 \div 9 = 6\). 2. \(48 \div 6 = 8\) and \(64 \div 8 = 8\).

Answer \(6\): \(42\div7\), \(54\div9\) Answer \(8\): \(48\div6\), \(64\div8\)

- Turn each answer into a multiplication question. - Which multiplication facts make \(63\) and \(64\)? - Compare the two whole-number answers after finding them.

1. Since \(7 \times 9 = 63\), \(63 \div 7 = 9\). 2. Since \(8 \times 8 = 64\), \(64 \div 8 = 8\). 3. Therefore, \(63 \div 7\) is greater by \(1\).

\(63 \div 7\) is greater. The answers are \(9\) and \(8\).

- Keep the quotient fixed while changing the divisor. - Find the dividend from the related multiplication fact. - Write a separate multiplication check for each division fact.

1. The first fact is \(20\div4=5\), checked by \(4\times5=20\). 2. The second fact is \(35\div7=5\), checked by \(7\times5=35\). 3. The third fact is \(45\div9=5\), checked by \(9\times5=45\).

\(20\div4=5\); check: \(4\times5=20\). \(35\div7=5\); check: \(7\times5=35\). \(45\div9=5\); check: \(9\times5=45\).

- Use known multiplication facts to find each quotient. - For each check, multiply the divisor by your answer.

1. \(32\div4=8\), \(40\div5=8\), and \(48\div6=8\). 2. The common answer is \(8\). 3. For instance, \(4\times8=32\) and \(6\times8=48\) check two of the divisions.

All three quotients are \(8\). Checks include \(4\times8=32\) and \(6\times8=48\).

- What number makes \(18\div\square=2\) true? - Use that same number in every row. - For a row with a missing starting number, use multiplication to work backward.

1. Since \(18 \div 9 = 2\), the number you divide by is \(9\). 2. Complete the second row: \(54 \div 9 = 6\). 3. Work backward in the third row: \(9 \times 9 = 81\), so \(81 \div 9 = 9\). 4. Any correct division fact with number you divide by \(9\) works in the last row, such as \(90 \div 9 = 10\).

The rule is divide by \(9\). The missing entries are \(6\) and \(81\). One possible final row is \(90\) and \(10\), because \(90 \div 9 = 10\).

- Repeated subtraction to \(0\) can be represented by equal groups. - In each part, the number of subtractions is one factor and \(n\) is the other factor. - Use division to find the missing number from the starting total.

1. In part a, the repeated amount is the missing number in \(4 \times n=36\). Since \(36 \div 4=9\), \(n=9\). 2. In part b, the repeated amount is the missing number in \(7 \times n=63\). Since \(63 \div 7=9\), \(n=9\).

a) \(n=9\) b) \(n=9\)

- Check each division answer with multiplication. - Work through all four facts one at a time. - Exactly one equation needs to change.

1. The incorrect equation is \(49 \div 7 = 6\). 2. Since \(7 \times 7 = 49\), the correct equation is \(49 \div 7 = 7\). 3. The other three equations are correct.

The wrong fact is \(49 \div 7 = 6\). It should be \(49 \div 7 = 7\), because \(7 \times 7 = 49\).