Question

solve.
$-5\frac{3}{4} - 3\frac{1}{2} = \square$
$-2\frac{1}{4}$ $-8\frac{2}{3}$ $-9\frac{1}{4}$ $2\frac{1}{4}$

Explanation:

To solve \(-5\frac{3}{4}-3\frac{1}{2}\), we first convert the mixed numbers to improper fractions.

Step 1: Convert mixed numbers to improper fractions

• For \(-5\frac{3}{4}\):
• The formula to convert a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\).
• Here, \(a = 5\), \(b = 3\), and \(c = 4\). So, \(-5\frac{3}{4}=-\frac{5\times4 + 3}{4}=-\frac{20 + 3}{4}=-\frac{23}{4}\)
• For \(3\frac{1}{2}\):
• Using the same formula, with \(a = 3\), \(b = 1\), and \(c = 2\). So, \(3\frac{1}{2}=\frac{3\times2+1}{2}=\frac{6 + 1}{2}=\frac{7}{2}\)
• But since we have a subtraction, it becomes \(-\frac{7}{2}\)

Step 2: Find a common denominator

The denominators are \(4\) and \(2\). The least common denominator of \(4\) and \(2\) is \(4\).
We rewrite \(-\frac{7}{2}\) with a denominator of \(4\):
\(-\frac{7}{2}=-\frac{7\times2}{2\times2}=-\frac{14}{4}\)

Step 3: Subtract the fractions

Now we have \(-\frac{23}{4}-\frac{14}{4}\). When subtracting fractions with the same denominator, we subtract the numerators and keep the denominator the same:
\(-\frac{23}{4}-\frac{14}{4}=-\frac{23 + 14}{4}=-\frac{37}{4}\)

Step 4: Convert back to a mixed number (optional, but often preferred)

To convert \(-\frac{37}{4}\) to a mixed number, we divide \(37\) by \(4\):
\(37\div4 = 9\) with a remainder of \(1\) (since \(4\times9=36\) and \(37-36 = 1\))
So, \(-\frac{37}{4}=-9\frac{1}{4}\)

So, \(-5\frac{3}{4}-3\frac{1}{2}=-9\frac{1}{4}\)

Answer:

To solve \(-5\frac{3}{4}-3\frac{1}{2}\), we first convert the mixed numbers to improper fractions.

Step 1: Convert mixed numbers to improper fractions

• For \(-5\frac{3}{4}\):
• The formula to convert a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\).
• Here, \(a = 5\), \(b = 3\), and \(c = 4\). So, \(-5\frac{3}{4}=-\frac{5\times4 + 3}{4}=-\frac{20 + 3}{4}=-\frac{23}{4}\)
• For \(3\frac{1}{2}\):
• Using the same formula, with \(a = 3\), \(b = 1\), and \(c = 2\). So, \(3\frac{1}{2}=\frac{3\times2+1}{2}=\frac{6 + 1}{2}=\frac{7}{2}\)
• But since we have a subtraction, it becomes \(-\frac{7}{2}\)

Step 2: Find a common denominator

The denominators are \(4\) and \(2\). The least common denominator of \(4\) and \(2\) is \(4\).
We rewrite \(-\frac{7}{2}\) with a denominator of \(4\):
\(-\frac{7}{2}=-\frac{7\times2}{2\times2}=-\frac{14}{4}\)

Step 3: Subtract the fractions

Now we have \(-\frac{23}{4}-\frac{14}{4}\). When subtracting fractions with the same denominator, we subtract the numerators and keep the denominator the same:
\(-\frac{23}{4}-\frac{14}{4}=-\frac{23 + 14}{4}=-\frac{37}{4}\)

Step 4: Convert back to a mixed number (optional, but often preferred)

To convert \(-\frac{37}{4}\) to a mixed number, we divide \(37\) by \(4\):
\(37\div4 = 9\) with a remainder of \(1\) (since \(4\times9=36\) and \(37-36 = 1\))
So, \(-\frac{37}{4}=-9\frac{1}{4}\)

So, \(-5\frac{3}{4}-3\frac{1}{2}=-9\frac{1}{4}\)