Lesson 3: Estimation and Reasonableness in Operations

Property

To estimate a sum or difference, first round each number to a specified place value, then perform the addition or subtraction on the rounded numbers. The result is an approximation, denoted by the $\approx$ symbol. For numbers $A$ and $B$, an estimated sum is $\text{round}(A) + \text{round}(B)$ and an estimated difference is $\text{round}(A) - \text{round}(B)$.

Examples

Property

To estimate a product or quotient, round each number to its greatest place value or to compatible numbers that make the calculation easier.
For a product: $a \times b \approx \text{rounded}(a) \times \text{rounded}(b)$
For a quotient: $a \div b \approx \text{rounded}(a) \div \text{rounded}(b)$

Examples

• To estimate $48 \times 7$, round 48 to 50. The estimated product is $50 \times 7 = 350$.

• To estimate $18 \div 2$, round 18 to 20. The estimated quotient is $20 \div 2 = 10$.

Property

To check if an answer is reasonable, compare the exact answer to an estimated answer found by using rounded numbers. The exact answer should be close to the estimate.