Comparing Scaled Products
Comparing scaled products is a Grade 5 math skill in enVision Mathematics, Chapter 8: Apply Understanding of Multiplication to Multiply Fractions. When two products share a common factor a, you only need to compare the scaling factors b and c to determine which product is larger: if b > c, then a×b > a×c. This property of scaling helps students reason about fraction multiplication without computing exact values.
Key Concepts
To compare two products with a common factor, $a \times b$ and $a \times c$ (where $a 0$), you only need to compare the scaling factors, $b$ and $c$. The relationship between the products will be the same as the relationship between the scaling factors.
If $b c$, then $a \times b a \times c$.
Common Questions
How do you compare two products that share a common factor?
Compare only the other factors (the scaling factors). If a×b and a×c share the factor a, then whichever has the larger scaling factor (b or c) gives the larger product.
Why does multiplying by a fraction less than 1 make a product smaller?
A fraction less than 1 is a scaling factor below 1, so it scales the original number down, producing a smaller product.
Which is greater: 4 × 3/4 or 4 × 5/4?
4 × 5/4 is greater because 5/4 > 3/4. Both share the factor 4, so the larger scaling fraction determines the larger product.
Where is comparing scaled products taught in enVision Grade 5?
Chapter 8: Apply Understanding of Multiplication to Multiply Fractions in enVision Mathematics, Grade 5.
How does scaling help understand fraction multiplication?
Thinking of multiplication as scaling—making something larger or smaller—helps students predict whether a product will be greater or less than the original number without computing exactly.