Question

assessment practice
choose all that are true.
$\frac{1}{4} \times 1\frac{7}{8} = \frac{15}{32}$
$2\frac{1}{2} \times 2\frac{1}{2} = 5\frac{1}{2}$
$3\frac{1}{5} \times 2\frac{1}{4} = 6\frac{2}{5}$
$4\frac{1}{2} \times 1\frac{1}{3} = 6$
$5\frac{1}{4} \times \frac{1}{2} = 2\frac{5}{8}$

Explanation:

Step1: Convert mixed numbers to fractions

For $\frac{1}{4} \times 1\frac{7}{8}$:
$1\frac{7}{8} = \frac{1\times8 + 7}{8} = \frac{15}{8}$
Expression: $\frac{1}{4} \times \frac{15}{8}$

Step2: Calculate the product

Multiply numerators and denominators:
$\frac{1\times15}{4\times8} = \frac{15}{32}$
This equation is true.

---

Step1: Convert mixed numbers to fractions

For $2\frac{1}{2} \times 2\frac{1}{2}$:
$2\frac{1}{2} = \frac{2\times2 + 1}{2} = \frac{5}{2}$
Expression: $\frac{5}{2} \times \frac{5}{2}$

Step2: Calculate the product

$\frac{5\times5}{2\times2} = \frac{25}{4} = 6\frac{1}{4}$
$6\frac{1}{4}
eq 5\frac{1}{2}$, so this equation is false.

---

Step1: Convert mixed numbers to fractions

For $3\frac{1}{5} \times 2\frac{1}{4}$:
$3\frac{1}{5} = \frac{3\times5 + 1}{5} = \frac{16}{5}$, $2\frac{1}{4} = \frac{2\times4 + 1}{4} = \frac{9}{4}$
Expression: $\frac{16}{5} \times \frac{9}{4}$

Step2: Simplify and calculate

$\frac{16\times9}{5\times4} = \frac{4\times9}{5} = \frac{36}{5} = 7\frac{1}{5}$
$7\frac{1}{5}
eq 6\frac{2}{5}$, so this equation is false.

---

Step1: Convert mixed numbers to fractions

For $4\frac{1}{2} \times 1\frac{1}{3}$:
$4\frac{1}{2} = \frac{4\times2 + 1}{2} = \frac{9}{2}$, $1\frac{1}{3} = \frac{1\times3 + 1}{3} = \frac{4}{3}$
Expression: $\frac{9}{2} \times \frac{4}{3}$

Step2: Simplify and calculate

$\frac{9\times4}{2\times3} = \frac{3\times2}{1} = 6$
This equation is true.

---

Step1: Convert mixed numbers to fractions

For $5\frac{1}{4} \times \frac{1}{2}$:
$5\frac{1}{4} = \frac{5\times4 + 1}{4} = \frac{21}{4}$
Expression: $\frac{21}{4} \times \frac{1}{2}$

Step2: Calculate the product

$\frac{21\times1}{4\times2} = \frac{21}{8} = 2\frac{5}{8}$
This equation is true.

Answer:

$\frac{1}{4} \times 1\frac{7}{8} = \frac{15}{32}$
$4\frac{1}{2} \times 1\frac{1}{3} = 6$
$5\frac{1}{4} \times \frac{1}{2} = 2\frac{5}{8}$