Arithmetic Readiness and Repair: cumulative review

A teacher has $24$ red and $36$ blue markers. Find the greatest number of identical packs with no markers left.

Write a complete attempt before opening the response guide.

Buses arrive every $20$ and $30$ minutes. If they arrive together now, when is the next shared arrival?

Write a complete attempt before opening the response guide.

Is $1$ prime? Explain.

Write a complete attempt before opening the response guide.

A student says $GCF(18,24) = 72$ because $72$ is a common multiple. Repair the answer.

Write a complete attempt before opening the response guide.

Find the missing exponent$$540 = 2^{2}\cdot 3^{3}\cdot 5^k$$

Write a complete attempt before opening the response guide.

Find the smallest number divisible by $6, 8,$ and $15$.

Write a complete attempt before opening the response guide.

Tiles measuring $18$ cm by $24$ cm are cut into the largest possible equal square tiles. Find the side length.

Write a complete attempt before opening the response guide.

Explain why $GCF(a,b)\cdot LCM(a,b) = a\cdot b$ for $a = 12$ and $b = 18$.

Write a complete attempt before opening the response guide.

Use prime exponents to find $GCF(180, 252)$ and $LCM(180, 252)$.

Write a complete attempt before opening the response guide.

A rectangular floor is $168$ cm by $216$ cm. Find the largest square tile side that fits exactly.

Write a complete attempt before opening the response guide.

Three alarms repeat every $8, 12,$ and $30$ minutes. If they sound together now, when do they next align?

Write a complete attempt before opening the response guide.

A student finds $LCM(12,18) = 6$ by keeping only shared prime factors. Diagnose the choice, not just the arithmetic.

Write a complete attempt before opening the response guide.

Locate $\frac{3}{5}$ between $0$ and $1$ and write its decimal value.

Write a complete attempt before opening the response guide.

Rewrite $\frac{11}{4}$ as a mixed number.

Write a complete attempt before opening the response guide.

Rewrite $3\frac{2}{5}$ as an improper fraction.

Write a complete attempt before opening the response guide.

Generate a fraction equivalent to $\frac{7}{12}$ with denominator $60$.

Write a complete attempt before opening the response guide.

Simplify$$\frac{42}{56}$$

Write a complete attempt before opening the response guide.

Compare$$\frac{4}{7} \qquad \frac{5}{9}$$

Write a complete attempt before opening the response guide.

Order $\frac{\frac{2}{3,} 3}{4,}$ and $\frac{5}{8}$ from least to greatest.

Write a complete attempt before opening the response guide.

Which benchmark is closer to $\frac{9}{10}$: $0, \frac{1}{2,}$ or $1$?

Write a complete attempt before opening the response guide.

Interpret $\frac{8}{3}$ as division.

Write a complete attempt before opening the response guide.

A class has $12$ musicians and $18$ non-musicians. Write the ratio musicians to all students as a simplified fraction.

Write a complete attempt before opening the response guide.

Find $\frac{7}{8}$ of $32$.

Write a complete attempt before opening the response guide.

Explain why $\frac{2}{3} = \frac{8}{12}$.

Write a complete attempt before opening the response guide.

A student says $\frac{3}{8} > \frac{3}{5}$ because $8 > 5$. Repair the comparison.

Write a complete attempt before opening the response guide.

Find a fraction strictly between$$\frac{1}{3} \qquad \frac{1}{2}$$

Write a complete attempt before opening the response guide.

State the restriction on $\frac{a}{b}$ and explain it.

Write a complete attempt before opening the response guide.

Use number, quotient, ratio, and operator meanings to describe $\frac{3}{4}$.

Write a complete attempt before opening the response guide.

Place $-\frac{7}{4,} -\frac{1}{2,}$ and $\frac{5}{4}$ in increasing order and justify the order with locations.

Write a complete attempt before opening the response guide.

Explain why multiplying $\frac{5}{12}$ by $\frac{3}{3}$ changes its name but not its value.

Write a complete attempt before opening the response guide.

Compare $\frac{17}{24}$ and $\frac{5}{7}$ without using a calculator.

Write a complete attempt before opening the response guide.

A recipe uses $\frac{3}{4}$ cup per batch. Interpret $\frac{3}{4}$ as $a$ number, quotient, ratio, and operator in this context.

Write a complete attempt before opening the response guide.

Compute$$\frac{\frac{2}{3} \cdot 5}{7}$$

Write a complete attempt before opening the response guide.

Compute $\frac{\frac{4}{9} \cdot 3}{8}$ using cancellation.

Write a complete attempt before opening the response guide.

Find $\frac{5}{12}$ of $36$.

Write a complete attempt before opening the response guide.