Question

Karen wanted to cut three lengths of wood from a 10 foot long board. The length of three pieces she wanted to were 1 2/3 feet 2 3/4 feet and 3 5/6 feet

Answer 1

1¾ ft ≈ 1,75 ft

Explanation:

`\sf 1(2)/(3) + 2 (3)/(4) + 3(5)/(6)`

`\sf = (3 + 2)/(3) + (4 * 2 + 3)/(4) + (6 * 3 + 5)/(6)`

`= \sf (5)/(3) + (11)/(4) + (23)/(6)`

`\sf = (5 * 4 + 11 * 3)/(3 * 4) + (23)/(6)`

`= \sf (20 +33 )/(12) + (23)/(6)`

`\sf = (53)/(12) + (23)/(6)`

`= \sf (53)/(12) + (23 * 2)/(6 * 2)`

`\sf = (53)/(12) + (46)/(12)`

`\sf = (99)/(12)`

`\sf = (10)/(1) - (99)/(12)`

`\sf = (10 * 12 - 99)/(12)`

`= \sf (120 - 99)/(12)`

`\sf = (21)/(12)`

= 1¾ ft ≈ 1,75 ft

Answer 2

`\\ \sf\longmapsto 1(2)/(3)+2(3)/(4)+3(5)/(6)`

`\\ \sf\longmapsto (5)/(3)+(11)/(4)+(23)/(6)`

`\\ \sf\longmapsto (20+33+46)/(12)`

`\\ \sf\longmapsto (99)/(12)`

`\\ \sf\longmapsto 8.2ft`

Rope left

`\\ \sf\longmapsto 10-8.2=1.8ft`