Question

2/5 x 5 5/8 using distributive property

Answer 1

5 5/8 = (5*8)+5)/8 = 45/8

2/5 * 45/8 = (2*45)/(5*8)= 90/40 = 9/4

Explanation:

Answer 2

`\sf (9)/(4) \textsf{ or } 2 (1)/(4)`

Explanation:

The distributive property of multiplication over addition states that for any numbers a, b, and c, the following equation is true:

`\sf a(b + c) = ab + ac`

In other words, when we multiply a number by a sum of two other numbers, we can distribute the multiplication to each of the two numbers and add the products together.

To use the distributive property to simplify the expression
`\sf (2)/(5) * 5 ( 5)/(8)`, we can first rewrite it and distribute and simplify each term and add the two terms:

`\begin{aligned} (2)/(5) * 5 ( 5)/(8) & = (2)/(5) * \left(5 + (5)/(8)\right) \\\\ &= \frac{2}{\cancel{5}} * \cancel{5} + \frac{2}{\cancel{5}} * \frac{\cancel{5}}{8} \\\\ &= 2 + \frac{\cancel{2}}{\cancel{2}\cdot 4 } \\\\ &= 2 + (1)/(4) \\\\ &= (2* 4 + 1)/(4) \\\\ &= (9)/(4) \textsf{ or } 2 (1)/(4) \end{aligned}`

Therefore, the value of the expression using the distributive property is:

`\sf (9)/(4) \textsf{ or } 2 (1)/(4)`