Question

rodrigo practiced playing guitar 15 1/3 hours over the past 3 weeks he practiced for 6 1/4 hours during the first week and 4 2/3 hours during the second week how much time did rodrigo spend practicing during the third week

Answer 1

We want to know how much time was spent practicing the guitar in week #3. We know the time in week #1 and week #2 and the total time. So, the amount of time in week #1 and week # 2 and week #3 will equal the total time. In a math sentence with all the practice times,

week 1 + week 2 + week 3 = total

`6(1)/(4) + 4(2)/(3) + ? = 15(1)/(3)`

? here represents what you don't know - and you could (if this were an algebra class) make that x. Our goal is to get the ? thing alone on one side and all the stuff on the other side.

`6(1)/(4) + 4(2)/(3) + ? = 15(1)/(3)`

`6(3)/(12) + 4(8)/(12) + ? = 15(4)/(12)` by getting common demonimators. The lowest common denominator, or LCD, is 12.

`10(11)/(12) + ? = 15(4)/(12)` by combining fraction parts with fraction parts and whole numbers with whole numbers

`? = 15(4)/(12) - 10(11)/(12)` by subtracting
`10(11)/(12) [\tex] from both sides</p><p>[tex] ? = 14(16)/(12) - 10(11)/(12)` by rewriting and borrowing from the whole number column and one being twelve over twelve.

`? = 4(5)/(12)` by subtracting whole numbers from whole numbers and fractions from fractions

Therefore, he spent
`4(5)/(12)` hours practicing.