Answer:
Explanation:
Step 1
Fraction \frac{-2}{3}
3
−2
can be rewritten as -\frac{2}{3}−
3
2
by extracting the negative sign.
-\frac{2}{3}<\frac{-5}{9}\text{ and }\frac{-5}{9}<\frac{3}{7}−
3
2
<
9
−5
and
9
−5
<
7
3
Step 2
Fraction \frac{-5}{9}
9
−5
can be rewritten as -\frac{5}{9}−
9
5
by extracting the negative sign.
-\frac{2}{3}<-\frac{5}{9}\text{ and }\frac{-5}{9}<\frac{3}{7}−
3
2
<−
9
5
and
9
−5
<
7
3
Step 3
Least common multiple of 33 and 99 is 99. Convert -\frac{2}{3}−
3
2
and -\frac{5}{9}−
9
5
to fractions with denominator 99.
-\frac{6}{9}<-\frac{5}{9}\text{ and }\frac{-5}{9}<\frac{3}{7}−
9
6
<−
9
5
and
9
−5
<
7
3
Step 4
Compare -\frac{6}{9}−
9
6
and -\frac{5}{9}−
9
5
.
\text{true}\text{ and }\frac{-5}{9}<\frac{3}{7}true and
9
−5
<
7
3
Step 5
Fraction \frac{-5}{9}
9
−5
can be rewritten as -\frac{5}{9}−
9
5
by extracting the negative sign.
\text{true}\text{ and }-\frac{5}{9}<\frac{3}{7}true and −
9
5
<
7
3
Step 6
Least common multiple of 99 and 77 is 6363. Convert -\frac{5}{9}−
9
5
and \frac{3}{7}
7
3
to fractions with denominator 6363.
\text{true}\text{ and }-\frac{35}{63}<\frac{27}{63}true and −
63
35
<
63
27
Step 7
Compare -\frac{35}{63}−
63
35
and \frac{27}{63}
63
27
.
\text{true}\text{ and }\text{true}true and true
Step 8
The conjunction of \text{true}true and \text{true}true is \text{true}true.
\text{true}true
Hint
Do the arithmetic.
Solution
\text{true}true