Question

Reina and Sam are multiplying (84)5 (73)9. Reina's Work Sam's Work (84)5 (73)9 = 84 + 573 + 9 = 89712 (84)5 (73)9 = 84⋅573⋅9 = 820727 Is either of them correct? Explain your reasoning. (5 points)

Answer 1

Concept

When we multiply a value by the sum of two or more integers, we exploit the distributive property of multiplication over addition. For example, consider the expression: $5(5 + 9)$. You may solve this formula by multiplying 5 by both addends. As a result, $5(5) + 5(9) = 25 + 45 = 70.$

The distributive property of multiplication over addition is applied when you multiply a value by a sum.

Given

to multiply - $(84)5$ × $(73)9.$

Find

$(84)5$ × $(73)9.$, who has done this multiplication correctly.

Solution

Reena's work =$(84)5$ × $(73)9 = 84 + 573 + 9 = 89712$

which is wrong, due to incorrect use of the distributive property.

Sam's Work $= (84)5$ ×  $(73)9$ $= 84$ × $573$ × $9 = 820727$

which is correct

Actually,  they are doing or multiplying using exponents.

#SPJ3

Answer 2

Answer:

They are multiplying using exponents.

Step-by-step explanation:

Given:

Reina and Sam are multiplying $(84)5 (73)9.$

Reina's Work Sam's Work

$(84)5 (73)9 = 84 + 573 + 9 = 89712 (84)5 (73)9 = 84*573*9 = 820727$

When we multiply a value by the sum of two or more integers, we use the distributive property of multiplication over addition.

Step 1

For illustration, evaluate the phrase:

$5(5+9)$.

You may solve this formula by multiplying 5 addends. As a result,

$5(5)+5(9)$

$=25+45$

$=70 .$

The distributive property of multiplication over addition exists used when you multiply a value by a sum.

Step 2

To multiply $- (84)5 \times(73) 9 .$

Find $(84) 5 \times(73) 9$, who has done this multiplication correctly.

Reena's work $=(84) 5 \times(73) 9$

$=84+573+9$

$=89712$

which is wrong, due to incorrect use of the distributive property.

Step 3

Sam's Work $=(84) 5 \times(73) 9$

$=84 \times 573 \times 9$

$=820727$

which is correct

Actually,  they are multiplying using exponents.

#SPJ3