Question

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. $\frac{1}{12} \times \frac{1}{3}$

1. 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:

Problem 11: $\boldsymbol{\frac{1}{5} \times \frac{1}{8}}$

Step 1: Multiply numerators

Multiply the numerators \(1\) and \(1\): \(1 \times 1 = 1\)

Step 2: Multiply denominators

Multiply the denominators \(5\) and \(8\): \(5 \times 8 = 40\)

Step 3: Form the product

The product of the fractions is \(\frac{\text{product of numerators}}{\text{product of denominators}}=\frac{1}{40}\)

Step 1: Multiply numerators

Multiply the numerators \(1\) and \(1\): \(1 \times 1 = 1\)

Step 2: Multiply denominators

Multiply the denominators \(5\) and \(10\): \(5 \times 10 = 50\)

Step 3: Form the product

The product of the fractions is \(\frac{\text{product of numerators}}{\text{product of denominators}}=\frac{1}{50}\)

Step 1: Multiply numerators

Multiply the numerators \(1\) and \(1\): \(1 \times 1 = 1\)

Step 2: Multiply denominators

Multiply the denominators \(8\) and \(7\): \(8 \times 7 = 56\)

Step 3: Form the product

The product of the fractions is \(\frac{\text{product of numerators}}{\text{product of denominators}}=\frac{1}{56}\)

Answer:

\(\frac{1}{40}\)

Problem 12: $\boldsymbol{\frac{1}{5} \times \frac{1}{10}}$