Lesson 1: Mental Math and Estimation Strategies

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

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 you to multiply a number by a sum or difference by multiplying each part of the sum or difference separately and then adding or subtracting the products.

Examples

Property

To multiply mentally, you can break a factor into its own factors and then use the Commutative and Associative Properties to rearrange the multiplication into an easier problem.
$a \times (b \times c) = (a \times b) \times c$

Examples

• To solve $25 \times 8$, break apart $8$ into $4 \times 2$. The problem becomes $25 \times 4 \times 2$. Rearrange to get $(25 \times 4) \times 2$, which simplifies to $100 \times 2 = 200$.
• To solve $5 \times 28$, break apart $28$ into $2 \times 14$. The problem becomes $5 \times 2 \times 14$. Rearrange to get $(5 \times 2) \times 14$, which simplifies to $10 \times 14 = 140$.
• To solve $5 \times 48$, break apart $48$ into $4 \times 12$. The problem becomes $5 \times 4 \times 12$. Rearrange to get $(5 \times 4) \times 12$, which simplifies to $20 \times 12 = 240$.

Explanation

This mental math strategy involves breaking one of the numbers in a multiplication problem into its factors. Then, you can rearrange the factors to create an easier multiplication, often by making a multiple of 10 or 100. This uses the Associative Property of Multiplication, which allows you to group and multiply factors in any order. The goal is to transform a difficult problem into a series of simpler calculations.