Question

lesson 9: the distributive property, part 1
lets use the distributive property to make calculating easier
9.1: number talk: ways to multiply
find each product mentally.
$5 \cdot 102$
$5 \cdot 98$
$5 \cdot 999$

Explanation:

Step1: Rewrite 102 as sum

$5 \cdot 102 = 5 \cdot (100 + 2)$

Step2: Apply distributive property

$5 \cdot 100 + 5 \cdot 2 = 500 + 10$

Step3: Calculate the sum

$500 + 10 = 510$

Step4: Rewrite 98 as difference

$5 \cdot 98 = 5 \cdot (100 - 2)$

Step5: Apply distributive property

$5 \cdot 100 - 5 \cdot 2 = 500 - 10$

Step6: Calculate the difference

$500 - 10 = 490$

Step7: Rewrite 999 as difference

$5 \cdot 999 = 5 \cdot (1000 - 1)$

Step8: Apply distributive property

$5 \cdot 1000 - 5 \cdot 1 = 5000 - 5$

Step9: Calculate the difference

$5000 - 5 = 4995$

Answer:

$5 \cdot 102 = 510$
$5 \cdot 98 = 490$
$5 \cdot 999 = 4995$