Question

Andrea used 4 1/3 yards of material to make a dress she has 1 1/4 yards left over how much material did Andrea start with

Answer 1

`1(7)/(12)\quad` yards
`\left(\mathrm{Decimal:\quad }\:1.58333\dots \right)`

Explanation:

To find how much Andrea started with, subtraction is needed. To subtract, we need to set up fractions;

`4(1)/(3)-(11)/(4)`

• Convert the mixed number to an improper fraction:
  `a(b)/(c) = (a \cdot c+b )/(c)`

`4(1)/(3)=(4\cdot 3+1)/(3)`

`=(13)/(3)`

`=(13)/(3)-(11)/(4)`

Least common multiplier: 3,4 = 12

Adjust fractions based on the LCM

`=(52)/(12)-(33)/(12)`

Apply the fraction rule:
`\quad (a)/(c)-(b)/(c)=(a-b)/(c)`

`(52)/(12)-(33)/(12)=(52-33)/(12)`

`=(52-33)/(12)`

Add the numbers:
`52-33=19`

`=(19)/(12)`

• Convert the improper fraction to mixed numbers:
  `Quotient (Remainder)/(Divisor)`

`(19)/(12)=1(7)/(12)`

`=1(7)/(12)`

Therefore, Andrea started with
`1(7)/(12)` yard material.