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:

$5\frac{1}{2}-2\frac{3}{7}$

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

$A\frac{b}{c}=\frac{(A\times c)+b}{c}$

Converting 5 1/2 to a fraction:

$5\frac{1}{2}=\frac{(5\times2)+1}{2}$

Solving the operations:

$\begin{gathered} 5\frac{1}{2}=\frac{10+1}{2} \\ 5\frac{1}{2}=\frac{11}{2} \end{gathered}$

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

$2\frac{3}{7}=\frac{(2\times7)+3}{7}$

Solving the operations:

$\begin{gathered} 2\frac{3}{7}=\frac{14+3}{7} \\ \\ 2\frac{3}{7}=\frac{17}{7} \end{gathered}$

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

$5\frac{1}{2}-2\frac{3}{7}$

Becomes the following expression by substituting the fractions:

$\frac{11}{2}-\frac{17}{7}$

Step 3. Use the formula for subtracting fractions.

The formula for subtracting fraction is:

$\frac{a}{b}-\frac{c}{d}=\frac{(a\times d)-(b\times c)}{b\times d}$

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

$\frac{11}{2}-\frac{17}{7}=\frac{(11\times7)-(2\times17)}{2\times7}$

Step 4. Solve the operations to find the result:

$\frac{11}{2}-\frac{17}{7}=\frac{77-34}{14}$$=\frac{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:

$\frac{43}{14}=3\frac{1}{14}$