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Division fact families

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5158083
Use each set of three numbers to write a fact family with two multiplication equations and two division equations. a) \(7, 9, 63\) b) \(4, 8, 32\)

Hints

- A fact family uses the same three numbers in every equation. - The greatest number is the product in the multiplication equations. - The greatest number is the dividend in the division equations. - Switch the factors to write the second multiplication equation.

Solution

1. For \(7, 9, 63\), the equations are \(7 \times 9 = 63\), \(9 \times 7 = 63\), \(63 \div 9 = 7\), and \(63 \div 7 = 9\). 2. For \(4, 8, 32\), the equations are \(4 \times 8 = 32\), \(8 \times 4 = 32\), \(32 \div 8 = 4\), and \(32 \div 4 = 8\).

Answer

a) \(7 \times 9 = 63\), \(9 \times 7 = 63\), \(63 \div 9 = 7\), \(63 \div 7 = 9\) b) \(4 \times 8 = 32\), \(8 \times 4 = 32\), \(32 \div 8 = 4\), \(32 \div 4 = 8\)
5211153
In a division equation, the numbers are called the dividend, divisor, and quotient. Find the requested number. a) The dividend is \(72\), and the divisor is \(8\). What is the quotient? b) The divisor is \(4\), and the quotient is \(8\). What is the dividend? c) The dividend is \(45\), and the quotient is \(9\). What is the divisor?

Hints

- Use the structure dividend divided by divisor equals quotient. - When the dividend is missing, multiply the divisor and quotient. - When the divisor is missing, use the related multiplication fact.

Solution

1. Part a: \(72 \div 8 = 9\), so the quotient is \(9\). 2. Part b: Use multiplication: \(8 \times 4 = 32\), so the dividend is \(32\). 3. Part c: Since \(45 \div 5 = 9\), the divisor is \(5\).

Answer

a) The quotient is \(9\). b) The dividend is \(32\). c) The divisor is \(5\).
5158013
Each number triple is missing one number. Fill in the number so that the three numbers make a related multiplication and division fact family. a) \((6, 8, \square)\) b) \((\square, 7, 63)\) c) \((36, \square, 4)\) d) \((4, \square, 32)\)

Hints

- Decide whether the missing number is a factor or a product. - Use known multiplication facts. - Can a related division equation help you find the missing value?

Solution

1. For part a, \(6 \times 8 = 48\), so the missing number is \(48\). 2. For part b, \(63 \div 7 = 9\), so the missing number is \(9\). 3. For part c, \(36 \div 4 = 9\), so the missing number is \(9\). 4. For part d, \(32 \div 4 = 8\), so the missing number is \(8\).

Answer

a) \(48\) b) \(9\) c) \(9\) d) \(8\)
5158863
Complete each number triple so it forms a multiplication and division fact family. Then write the four related equations. a) \(5, 45, \square\) b) \(\square, 4, 28\)

Hints

- The greatest number in each triple is the product. - Which number multiplied by \(5\) gives \(45\)? - Which number multiplied by \(4\) gives \(28\)? - Use commutative multiplication and related division facts.

Solution

1. For part a, \(45 \div 5 = 9\), so the missing number is \(9\). The fact family is \(5 \times 9 = 45\), \(9 \times 5 = 45\), \(45 \div 9 = 5\), and \(45 \div 5 = 9\). 2. For part b, \(28 \div 4 = 7\), so the missing number is \(7\). The fact family is \(7 \times 4 = 28\), \(4 \times 7 = 28\), \(28 \div 4 = 7\), and \(28 \div 7 = 4\).

Answer

a) Missing number: \(9\) \(5 \times 9 = 45\), \(9 \times 5 = 45\), \(45 \div 9 = 5\), \(45 \div 5 = 9\) b) Missing number: \(7\) \(7 \times 4 = 28\), \(4 \times 7 = 28\), \(28 \div 4 = 7\), \(28 \div 7 = 4\)
5201053
In a division equation, the dividend is \(48\) and the quotient is \(6\). What is the divisor? Write the complete equation.

Hints

- Identify where the dividend, divisor, and quotient appear in a division equation. - Use the related multiplication fact. - Check the complete equation.

Solution

1. Use the structure \(\text{dividend} \div \text{divisor} = \text{quotient}\). 2. Substitute the known values: \(48 \div \text{divisor} = 6\). 3. Since \(6 \times 8 = 48\), the divisor is \(8\). 4. The complete equation is \(48 \div 8 = 6\).

Answer

The divisor is \(8\). The equation is \(48 \div 8 = 6\).
5158023
Two given numbers can sometimes belong to two different multiplication and division fact families. Example with \(10\) and \(5\): If \(10\) and \(5\) are factors, the third number is \(50\): \(10 \times 5 = 50\) and \(50 \div 5 = 10\). If \(10\) is the product and \(5\) is a factor, the third number is \(2\): \(2 \times 5 = 10\) and \(10 \div 5 = 2\). For each pair, find two possible third numbers. For each third number, write one multiplication equation and one related division equation. a) \(8\) and \(4\) b) \(9\) and \(3\) c) \(10\) and \(2\)

Hints

- First use the two given numbers as factors. What product completes that fact family? - Then treat the larger given number as the product. What missing factor completes that fact family? - Check each third number with one multiplication equation and one related division equation.

Solution

1. For \(8\) and \(4\), one third number is \(32\): \(8 \times 4 = 32\) and \(32 \div 4 = 8\). Another third number is \(2\): \(2 \times 4 = 8\) and \(8 \div 4 = 2\). 2. For \(9\) and \(3\), one third number is \(27\): \(9 \times 3 = 27\) and \(27 \div 3 = 9\). Another third number is \(3\): \(3 \times 3 = 9\) and \(9 \div 3 = 3\). 3. For \(10\) and \(2\), one third number is \(20\): \(10 \times 2 = 20\) and \(20 \div 2 = 10\). Another third number is \(5\): \(5 \times 2 = 10\) and \(10 \div 2 = 5\).

Answer

a) \(32\): \(8 \times 4 = 32\), \(32 \div 4 = 8\); \(2\): \(2 \times 4 = 8\), \(8 \div 4 = 2\) b) \(27\): \(9 \times 3 = 27\), \(27 \div 3 = 9\); \(3\): \(3 \times 3 = 9\), \(9 \div 3 = 3\) c) \(20\): \(10 \times 2 = 20\), \(20 \div 2 = 10\); \(5\): \(5 \times 2 = 10\), \(10 \div 2 = 5\)

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