Lesson 2: Estimate Products

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 $32 \times 88$, round $32$ down to $30$ and round $88$ up to $90$. Then, calculate $30 \times 90 = 2700$. So, $32 \times 88 \approx 2700$.
• To estimate $615 \times 4$, round $615$ to the nearest hundred, which is $600$. Then, calculate $600 \times 4 = 2400$. So, $615 \times 4 \approx 2400$.

Explanation

Rounding is a strategy used to find an answer that is close to the exact answer. To estimate a product, first round the factors to numbers that are easier to work with, typically by rounding to the greatest place value. After rounding, multiply the new numbers to get your estimate. This technique is useful for checking the reasonableness of an exact answer or for quickly finding an approximate value.

Property

To estimate a product $a \times b$, replace the factors with nearby compatible numbers, $c$ and $d$, such that $c \approx a$ and $d \approx b$. The estimate is the product $c \times d$.

Examples

Property

An overestimate is an estimated product that is greater than the actual product. An underestimate is an estimated product that is less than the actual product. The direction you round or adjust the factors helps determine if the estimate is an over- or underestimate.

Examples