Write a Related Multiplication Equation
Writing a related multiplication equation from a division equation is a Grade 5 math skill in enVision Mathematics, Chapter 5: Use Models and Strategies to Divide Whole Numbers. The key property states that if a ÷ b = c, then b × c = a, connecting division to an equivalent multiplication with an unknown factor. This relationship helps students check division answers and solve for missing values.
Key Concepts
Property A division equation can be written as a related multiplication equation with an unknown factor. If $a \div b = c$, then it is also true that $b \times c = a$.
Examples The division problem $360 \div 20 = w$ can be written as the multiplication equation $20 \times w = 360$. The division problem $729 \div 27 = n$ can be written as the multiplication equation $27 \times n = 729$. The division problem $1,250 \div 50 = p$ can be written as the multiplication equation $50 \times p = 1,250$.
Explanation Division and multiplication are inverse operations, meaning they undo each other. You can use this relationship to solve division problems by thinking about them in terms of multiplication. This is helpful when using an area model, where the dividend is the area, the divisor is a known side, and the quotient is the unknown side you need to find.
Common Questions
What is a related multiplication equation for a division problem?
If a ÷ b = c, then b × c = a. For example, 24 ÷ 6 = 4 can be written as the related equation 6 × 4 = 24.
How does writing a related multiplication equation help with division?
It lets you check your answer by multiplying, and helps you find missing numbers by thinking about what factor you need to multiply to get the dividend.
Why are multiplication and division called inverse operations?
They undo each other. Multiplying and then dividing by the same number returns to the original value, making them inverse (opposite) operations.
Where is this skill taught in enVision Grade 5?
Chapter 5: Use Models and Strategies to Divide Whole Numbers in enVision Mathematics, Grade 5.
Can I use a multiplication equation to solve a division problem?
Yes. If you know 7 × ? = 56, you can find ? = 8, which also tells you 56 ÷ 7 = 8.