Rational Numbers and Rates

1. a) The signs are different, so subtract absolute values and keep the sign of the larger absolute value:

$13 - 8 = 5$

So, $-8 + 13 = 5$.

b) Subtracting a positive moves farther below zero:

$-4.5 - 2.75 = -7.25$

c) Use a common denominator of 10:

$3/5 = 6/10$

$6/10 + (-7/10) = -1/10$

The answers are 5, -7.25, and -1/10.

2. Start at sea level:

$0$

Dive 18.5 meters:

$0 - 18.5 = -18.5$

Rise 6.25 meters:

$-18.5 + 6.25 = -12.25$

Dive 4.75 meters:

$-12.25 - 4.75 = -17$

Her final elevation is -17 meters, or 17 meters below sea level.

3. a) Multiply numerators and denominators:

$(-3/4) \times (8/9) = -24/36$

Simplify:

$-24/36 = -2/3$

b) A negative times a negative is positive:

$(-2.6) \times (-5) = 13$

c) Dividing by a fraction means multiplying by its reciprocal:

$(-18) \div (3/5) = (-18) \times (5/3)$

$(-18 \div 3) \times 5 = -6 \times 5 = -30$

The answers are -2/3, 13, and -30.

4. a) Divide pages by minutes:

$96 \div 4 = 24$

The unit rate is 24 pages per minute.

b) Multiply the unit rate by 9 minutes:

$24 \times 9 = 216$

The printer can print 216 pages in 9 minutes.

5. Compare concentrate per cup of water.

Mix A:

$3/12 = 1/4 = 0.25$

Mix B:

$5/18 = 0.277...$

Since $5/18$ is greater than $1/4$, Mix B has the greater concentrate-to-water rate.