Josh and Sam each have a board to cut. The boards are the same size and are in the shape of a rectangle. Josh cuts his board in thirds and uses two-thirds of the board. Sam cuts his board in sixths and uses four-sixths of the board. Do both boys use the same amount of their boards? Show all your mathematical thinking.

They use same amount of their boards.

Step-by-step explanation:

Boards are the same size

2/3 = 4/6 as is;  

3/3 = 1

2/3 = 6.66...rep   to 1

4/6 = 6.66...rep   to 1

They are the same we can now divide

2/3 goes 2.5

4/6 goes 2.5

= the same and equal fractions, Josh board part as a fraction is  just reduced fraction but same scale to 1

15

step-by-step explanation:

we are given the following expression and we are to solve it and find the product:

-13 × (-5)

solving the given expression in the standard order of solving a mathematical expression, beginning with the opening of brackets and then multiplying the terms and changing their signs.

-3 × -5 = 15 (answer is positive because when negative is multiplied with negative, it gives a positive answer)

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: