Lesson 1: Estimate and Find Products

Property

To multiply multiples of 10, multiply the non-zero digits and then adjust the place value based on the units being multiplied.

• Tens $\times$ Tens = Hundreds: $(a \times 10) \times (b \times 10) = (a \times b) \times 100$
• Tens $\times$ Ones = Tens: $(a \times 10) \times c = (a \times c) \times 10$

Examples

Property

To estimate the product of two numbers, round one or both factors to a nearby place value (like the nearest ten or hundred) to make the multiplication easier to perform mentally.
The symbol $\approx$ means "approximately equal to".

Examples

• To estimate $48 \times 7$, round $48$ to the nearest ten, which is $50$. Then, calculate $50 \times 7 = 350$. So, $48 \times 7 \approx 350$.

• To estimate $615 \times 4$, round $615$ to the nearest hundred, which is $600$. Then, calculate $600 \times 4 = 2400$. So, $615 \times 4 \approx 2400$.

Property

The distributive property allows us to multiply a sum by multiplying each addend separately and then adding the products.
When we decompose factors by place value, the results of these smaller multiplications are called partial products.

Examples