Skill: Solve missing-factor problems

Explanation and Free Practice Resources

Understands that an unknown factor in a multiplication relationship can be found by using the inverse division relationship: in $a \times ? = b$ , the missing factor is $b \div a$ , and in $? \times a = b$ , it is likewise the number of equal groups or the size of each group needed to make $b$ . Arrays, equal-group diagrams, and equations connect these interpretations, using whole-number quantities and excluding fractions, decimals, and more advanced algebraic generalizations.

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Detailed Explanation: Solve missing-factor problems

When one factor is missing in a multiplication equation, use division to find it. Multiplication and division are inverse operations.

For example:

6 \times ? = 42

Step 1: Identify the known factor and the product.

Known factor: $6$
Product: $42$

Step 2: Divide the product by the known factor.

42 \div 6 = 7

So, the missing factor is $7$ .

Step 3: Check your answer with multiplication.

6 \times 7 = 42

Therefore,

6 \times \boxed{7} = 42

The answer is $7$ because $42$ can be divided into $6$ equal groups of $7$ .

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