Question

1. consider $-1 < -\frac{1}{2}$. jada says this inequality means

egative one is less than negative one - half.\ scott says it means
egative one - half is greater than negative one.\ who is correct? explain.
for problems 2 - 5, write the number that is less than the other number. use the number line if needed.

1. 4, -2
2. 0, -7
3. -3.46, -3.64
4. $-\frac{99}{100}, -\frac{201}{100}$

for problems 6 - 9, indicate whether each inequality is true or false.

1. $-2 < -3.5$
2. $-1\frac{1}{3} > 0.5$
3. $2.25 > -2\frac{1}{4}$
4. $-1.75 < -1\frac{1}{2}$

Explanation:

Step1: Analyze inequality meaning

The inequality $-1 < -\frac{1}{2}$ reads directly as "negative one is less than negative one-half." Scott's statement ("negative one-half is greater than negative one") is also equivalent because if $a < b$, then $b > a$. Both are correct.

Step2: Compare 4 and -2

On the number line, -2 is left of 4, so -2 < 4.

Step3: Compare 0 and -7

On the number line, -7 is left of 0, so -7 < 0.

Step4: Compare -3.46 and -3.64

For negatives, larger absolute value means smaller number: $|-3.64| > |-3.46|$, so -3.64 < -3.46.

Step5: Compare $-\frac{99}{100}$ and $-\frac{201}{100}$

$-\frac{99}{100} = -0.99$, $-\frac{201}{100} = -2.01$. -2.01 is left of -0.99, so $-\frac{201}{100} < -\frac{99}{100}$.

Step6: Check $-2 < -3.5$

$|-3.5| > |-2|$, so -3.5 < -2. The inequality is false.

Step7: Check $-1\frac{1}{3} > 0.5$

Negative numbers are less than positive numbers. The inequality is false.

Step8: Check $2.25 > -2\frac{1}{4}$

Positive numbers are greater than negative numbers. The inequality is true.

Step9: Check $-1.75 < -1\frac{1}{2}$

$-1\frac{1}{2} = -1.5$. $|-1.75| > |-1.5|$, so -1.75 < -1.5. The inequality is true.

Answer:

1. Both Jada and Scott are correct (since $-1 < -\frac{1}{2}$ is equivalent to $-\frac{1}{2} > -1$)
2. -2
3. -7
4. -3.64
5. $-\frac{201}{100}$
6. False
7. False
8. True
9. True

Inequality	True	False
$-1\frac{1}{3} > 0.5$		X
$2.25 > -2\frac{1}{4}$	X
$-1.75 < -1\frac{1}{2}$	X