Question

How do you simplify `45-13 4/11`?

Answer 1

`\frac(348)(11)`

Explanation:

Conversions:

Convert `45` to eleventh fractional form:
`\color{red}{45=\frac(45\times11)(11)=\frac(495)(11)}`
Convert `13\frac(4)(11)` to improper fraction form:
`\color{blue}{13\frac(4)(11)=\frac((13\times11)+4)(11)=\frac(143+4)(11)=\frac(147)(11)}`

Input in original equation:

`\color{red}{\frac(495)(11)}-\color{blue}{\frac(147)(11)}=\frac{495-147}{11}`
`=\frac(348)(11)`

Answer 2

`31 7/11`

Explanation:

Subtracting a fraction from a whole number is generally quite quick and easy if you remember that a whole number can be written as a fraction with an equal numerator and denominator.

`1 = 8/8 = 15/15 = 23/23 ....`

In `45 -13 4/11" "` subtract the 13 as a whole number first:

`color(red)(45-13) 4/11`

`=color(red)(32) - 4/11`

`= 31+11/11 -4/11`

`=31 7/11`

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Background examples

Consider: `color(blue)(7)-1/2 rarr color(blue)(6+2/2)-1/2 = 6 1/2`

`color(blue)(11) - 3/4 rarr color(blue)(10 +4/4) -3/4 = 10 1/4`

`color(red)(5 - 1) 2/3 = color(red)(4)- 2/3 = 3 2/3`