Question

If -1 2/3 is subtracted from 5 1/2, what will be the result?

equal to 4
greater than 4
positive, but less than 4
negative

Answer 1

To solve the problem, we need to subtract \(-1 \frac{2}{3}\) from \(5 \frac{1}{2}\).

First, convert the mixed numbers to improper fractions:

1. Convert \(5 \frac{1}{2}\):
\[
5 \frac{1}{2} = 5 \times 2 + 1 = 10 + 1 = \frac{11}{2}
\]

2. Convert \(-1 \frac{2}{3}\):
\[
-1 \frac{2}{3} = -\left(1 \times 3 + 2\right) = -\frac{5}{3}
\]

Now we rewrite the subtraction:
\[
5 \frac{1}{2} - \left(-1 \frac{2}{3}\right) = \frac{11}{2} + \frac{5}{3}
\]

Next, we need a common denominator to add these two fractions. The least common multiple of \(2\) and \(3\) is \(6\).

Convert each fraction:
\[
\frac{11}{2} = \frac{11 \times 3}{2 \times 3} = \frac{33}{6}
\]
\[
\frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6}
\]

Now we can add the two fractions:
\[
\frac{33}{6} + \frac{10}{6} = \frac{33 + 10}{6} = \frac{43}{6}
\]

Next, convert \(\frac{43}{6}\) back to a mixed number:
\[
\frac{43}{6} = 7 \frac{1}{6}
\]

Now we analyze our result \(7 \frac{1}{6}\):
- It is greater than 4.

Therefore, the result of subtracting \(-1 \frac{2}{3}\) from \(5 \frac{1}{2}\) is **greater than 4**.