Question

how do I subtract mixed numbers im confused and I have to do a test on it for tomorrow morning and I need to get my grades u

Answer 1

Subtracting mixed numbers.

Let's explain the process to subtract mixed numbers using the following example:

`5(1)/(2)-2(3)/(7)`

Step 1. Convert each mixed number to a fraction by using the following rule:

`A(b)/(c)=((A* c)+b)/(c)`

Converting 5 1/2 to a fraction:

`5(1)/(2)=((5*2)+1)/(2)`

Solving the operations:

`\begin{gathered} 5(1)/(2)=(10+1)/(2) \\ 5(1)/(2)=(11)/(2) \end{gathered}`

And then we convert the second mixed number 2 3/7 following the same rule:

`2(3)/(7)=((2*7)+3)/(7)`

Solving the operations:

`\begin{gathered} 2(3)/(7)=(14+3)/(7) \\ \\ 2(3)/(7)=(17)/(7) \end{gathered}`

Step 2. Now that we have converted the two mixed number to fractions, the original subtraction, which was:

`5(1)/(2)-2(3)/(7)`

Becomes the following expression by substituting the fractions:

`(11)/(2)-(17)/(7)`

Step 3. Use the formula for subtracting fractions.

The formula for subtracting fraction is:

`(a)/(b)-(c)/(d)=((a* d)-(b* c))/(b* d)`

We apply it to our subtraction, in our case a=11, b=2, c=17, and d=7:

`(11)/(2)-(17)/(7)=((11*7)-(2*17))/(2*7)`

Step 4. Solve the operations to find the result:

`(11)/(2)-(17)/(7)=(77-34)/(14)`
`=(43)/(14)`

Step 5. The result of the subtraction in fraction form is:

43/14

But if we need to present it in mixed form, we just find how many times does 14 fits into 43, in this case, 3 times because 14x3=42, so the result in mixed form is 3 as the integer, ans 1/14 as the fraction:

`(43)/(14)=3(1)/(14)`