Finding the Unknown Divisor
Learn to find the unknown divisor by dividing the dividend by the quotient. Solve equations like 180 ÷ m = 9 using the property m = c ÷ a.
Key Concepts
Property In a division problem, an unknown divisor can be found by dividing the dividend by the quotient. If $c \div m = a$, then $m = c \div a$.
Examples To solve for $m$ in $180 \div m = 9$, divide the dividend (180) by the quotient (9). $180 \div 9 = 20$, so $m=20$.
Find the value of $D$ in the problem $D \overline{)169}^{13}$. This is the same as $169 \div D = 13$. So, divide $169 \div 13$ to get $D=13$.
Common Questions
How do you find an unknown divisor in a division problem?
To find an unknown divisor, divide the dividend by the quotient. For example, in 180 ÷ m = 9, you divide 180 ÷ 9 to get m = 20. This works because the divisor and quotient swap roles when the divisor is missing.
What is the property for finding an unknown divisor in Grade 6 math?
The property states that if c ÷ m = a, then m = c ÷ a. This means you divide the dividend by the quotient to find the missing divisor. Saxon Math Course 1 uses this rule in Chapter 1 under Number, Operations, and Algebra.
How do you solve for a missing divisor in a long division problem?
Rewrite the long division as a standard equation first. For example, if D divides 169 with a quotient of 13, rewrite it as 169 ÷ D = 13, then solve D = 169 ÷ 13 = 13. Identifying the dividend and quotient is the key first step.
How can I use division to solve real-world problems with an unknown divisor?
Real-world problems like sharing cookies work the same way. If you have 75 cookies and each person got 3, solve 75 ÷ p = 3 by computing 75 ÷ 3 = 25 people. Dividing the total by the amount each person receives reveals the unknown number of groups.