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

9 sandwiches per hour

step-by-step explanation:

when we have a rate, we want a 1 in the denominator

27/3 = 9

27 sandwiches/ 3 hours = 9 sandwiches/hour