To find the number by which [tex]\(-4 \frac{3}{8}\)[/tex] should be divided to obtain [tex]\(-3 \frac{1}{2}\)[/tex], follow these steps:
1. Convert the mixed numbers into improper fractions:
- For [tex]\(-4 \frac{3}{8}\)[/tex]:
[tex]\[
-4 \frac{3}{8} = -\left(4 + \frac{3}{8}\right) = -\frac{32}{8} - \frac{3}{8} = -\frac{32 + 3}{8} = -\frac{35}{8}
\][/tex]
- For [tex]\(-3 \frac{1}{2}\)[/tex]:
[tex]\[
-3 \frac{1}{2} = -\left(3 + \frac{1}{2}\right) = -\frac{6}{2} - \frac{1}{2} = -\frac{6 + 1}{2} = -\frac{7}{2}
\][/tex]
2. Set up the division problem:
We need to find the number [tex]\(x\)[/tex] such that:
[tex]\[
-4 \frac{3}{8} \div x = -3 \frac{1}{2}
\][/tex]
Substituting the improper fractions:
[tex]\[
-\frac{35}{8} \div x = -\frac{7}{2}
\][/tex]
3. Isolate [tex]\(x\)[/tex] by cross-multiplying:
Rearrange the equation to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-\frac{35}{8}}{-\frac{7}{2}}
\][/tex]
4. Simplify the division of fractions:
Dividing by a fraction is the same as multiplying by its reciprocal:
[tex]\[
x = -\frac{35}{8} \times -\frac{2}{7}
\][/tex]
5. Multiply the fractions:
[tex]\[
x = \left(-\frac{35}{8}\right) \times \left(-\frac{2}{7}\right) = \frac{(35 \times 2)}{(8 \times 7)} = \frac{70}{56}
\][/tex]
6. Simplify the resulting fraction:
Simplify [tex]\(\frac{70}{56}\)[/tex]:
[tex]\[
\frac{70}{56} = \frac{70 \div 14}{56 \div 14} = \frac{5}{4}
\][/tex]
7. Convert to a decimal:
Finally, convert [tex]\(\frac{5}{4}\)[/tex] to a decimal:
[tex]\[
\frac{5}{4} = 1.25
\][/tex]
Therefore, [tex]\(-4 \frac{3}{8}\)[/tex] should be divided by [tex]\(1.25\)[/tex] to obtain [tex]\(-3 \frac{1}{2}\)[/tex].
