Question

Hi I’ve been stuck on this question for a while now, I really don’t know what to do because I keep getting 25/12 - 27/12

Answer 1

1 ¹/₃

Explanation:

The given expression consists of mixed numbers and fractions.

First, convert the mixed numbers into improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:



`\begin{aligned}\implies 2 (1)/(12)-1 (1)/(2)+(3)/(4)&=(2 * 12+1)/(12)-(1* 2+1)/(2)+(3)/(4)\\\\&=(24+1)/(12)-(2+1)/(2)+(3)/(4)\\\\&=(25)/(12)-(3)/(2)+(3)/(4)\end{aligned}`

When adding or subtracting fractions, we must ensure that they have the same denominator. To do this, find the least common multiple (LCM) of the three denominators.

As 2 and 4 are factors of 12, then 12 is the LCM.

Convert the fractions into their equivalent fractions (with a denominator of 12) by multiplying the numerator and denominator by the same number.

`\begin{aligned}\implies (25)/(12)-(3)/(2)+(3)/(4)&=(25)/(12)-(3 * 6)/(2 * 6)+(3 * 3)/(4 * 3)\\\\&=(25)/(12)-(18)/(12)+(9)/(12)\end{aligned}`

Now the fractions all have the same denominator, we can carry out the subtraction and addition by simply subtracting and adding the numerators:

`\begin{aligned}\implies (25)/(12)-(18)/(12)+(9)/(12)&=(25-18+9)/(12)\\\\&=(7+9)/(12)\\\\&=(16)/(12)\end{aligned}`

Reduce the improper fraction to its simplest form by dividing the numerator and denominator by the greatest common factor (GCF).

The GCF of 16 and 12 is 4:

`\implies (16)/(12)=(16 / 4)/(12 / 4)=(4)/(3)`

Finally, convert the improper fraction into a mixed number by dividing the numerator by the denominator:

`\implies (4)/(3)=1\; \rm remainder 1`

The mixed number answer is the whole number and the remainder divided by the denominator:

`\implies 1 (1)/(3)`

`\hrulefill`

As one calculation:

`\begin{aligned}\implies 2 (1)/(12)-1 (1)/(2)+(3)/(4)&=(2 * 12+1)/(12)-(1* 2+1)/(2)+(3)/(4)\\\\&=(24+1)/(12)-(2+1)/(2)+(3)/(4)\\\\&=(25)/(12)-(3)/(2)+(3)/(4)\\\\&=(25)/(12)-(3 * 6)/(2 * 6)+(3 * 3)/(4 * 3)\\\\&=(25)/(12)-(18)/(12)+(9)/(12)\\\\&=(25-18+9)/(12)\\\\&=(7+9)/(12)\\\\&=(16)/(12)\\\\&=(16 / 4)/(12 / 4)\\\\&=(4)/(3)\\\\&=1 (1)/(3)\end{aligned}`