Question

remember
for problems 11–14, multiply.

1. $\frac{1}{5} \times \frac{1}{8}$
2. $\frac{1}{5} \times \frac{1}{10}$
3. $\frac{1}{8} \times \frac{1}{7}$
4. $\frac{1}{12} \times \frac{1}{3}$
5. distribute and combine like terms to write an equivalent expression.

a. $4(3a + 2) - 5$
b. $10w + \frac{1}{2}(12w - 40)$

1. choose the correct statement.

a. all rectangles are squares because rectangles have four equal sides.
b. all parallelograms are quadrilaterals because all parallelograms have four sides.
c. all trapezoids are parallelograms because all trapezoids have two pairs of parallel sides.
d. all rhombuses are squares because all rhombuses have four right angles.

Explanation:

Step1: Multiply numerators and denominators

$\frac{1}{5} \times \frac{1}{8} = \frac{1 \times 1}{5 \times 8} = \frac{1}{40}$

Step2: Multiply numerators and denominators

$\frac{1}{5} \times \frac{1}{10} = \frac{1 \times 1}{5 \times 10} = \frac{1}{50}$

Step3: Multiply numerators and denominators

$\frac{1}{8} \times \frac{1}{7} = \frac{1 \times 1}{8 \times 7} = \frac{1}{56}$

Step4: Multiply numerators and denominators

$\frac{1}{12} \times \frac{1}{3} = \frac{1 \times 1}{12 \times 3} = \frac{1}{36}$

Step5: Distribute the 4

$4(3a + 2) - 5 = 12a + 8 - 5$

Step6: Combine constant terms

$12a + 8 - 5 = 12a + 3$

Step7: Distribute the $\frac{1}{2}$

$10w + \frac{1}{2}(12w - 40) = 10w + 6w - 20$

Step8: Combine like terms

$10w + 6w - 20 = 16w - 20$

Step9: Analyze quadrilateral definitions

• A: Rectangles have 2 pairs of equal sides, not 4 equal sides, so false.
• B: Quadrilaterals have 4 sides; parallelograms have 4 sides, so true.
• C: Trapezoids have only 1 pair of parallel sides, so false.
• D: Rhombuses do not have right angles unless they are squares, so false.

Answer:

1. $\frac{1}{40}$
2. $\frac{1}{50}$
3. $\frac{1}{56}$
4. $\frac{1}{36}$

15a. $12a + 3$
15b. $16w - 20$

1. B. All parallelograms are quadrilaterals because all parallelograms have four sides.