Translating Comparison Questions: A ÷ B vs. B ÷ A
Translating Comparison Questions: A ÷ B vs. B ÷ A explains that the order of division in a comparison problem depends on which quantity is described as times as large as the other. Covered in Illustrative Mathematics Grade 6, Unit 4: Dividing Fractions, Grade 6 students learn that A ÷ B answers how many times as large A is than B, while B ÷ A answers how many times as large B is than A — the two quotients are reciprocals of each other. Correctly translating the question into the right expression prevents common order errors.
Key Concepts
The order of division depends on the question being asked. These two questions produce reciprocal answers: "How many times as large is $A$ than $B$?" $\rightarrow$ Divide $A \div B$. "What fraction of $A$ is $B$?" $\rightarrow$ Divide $B \div A$.
Common Questions
How do you translate a comparison question into a division expression?
Ask what is being compared to what. A ÷ B tells you how many times as large A is compared to B. B ÷ A tells you how many times as large B is compared to A.
What is the relationship between A ÷ B and B ÷ A?
They are reciprocals. If A ÷ B = n, then B ÷ A = 1/n. One answer is the flip of the other.
How do you decide whether to write A ÷ B or B ÷ A?
Identify which quantity you are saying is larger. The larger quantity goes first (as the dividend) when asking how many times it exceeds the smaller.
Where is translating comparison questions in Illustrative Mathematics Grade 6?
This topic is in Unit 4: Dividing Fractions of Illustrative Mathematics Grade 6.
Why does order matter in division comparison problems?
Division is not commutative. Dividing in the wrong order gives the reciprocal answer, which answers a completely different question.