Review worksheet 1: natural numbers and fractions

• For multiple-choice items, circle the letter of the only correct answer.
• For items with parts a) and b), write complete solutions in your notebook.

A. Natural numbers. Powers. Divisibility

1. The result of $56:7 + 3 \cdot (12 - 5)$ is equal to:

   • a) $29$
   • b) $77$
   • c) $35$
   • d) $23$

2. The result of $2^{5} \cdot 2^{3}:2^{6}$ is equal to:

   • a) $2^{2}$
   • b) $2^{14}$
   • c) $2^{9}$
   • d) $2^{8}$

3. The result of $37 \cdot 25 + 37 \cdot 75$ is equal to:

   • a) $3700$
   • b) $2775$
   • c) $4625$
   • d) $1000$

4. Among the numbers $245$, $312$, $540$ and $723$, the number divisible by $2$, by $3$ and by $5$ is:

   • a) $245$
   • b) $312$
   • c) $540$
   • d) $723$

5. The remainder of dividing $2026$ by $9$ is:

   • a) $1$
   • b) $2$
   • c) $4$
   • d) $7$

6. Among the numbers $2^{8}$, $3^{5}$, $5^{7}$ and $7^{3}$, the square of a natural number is:

   • a) $2^{8}$
   • b) $3^{5}$
   • c) $5^{7}$
   • d) $7^{3}$

B. Common and decimal fractions. Organizing data

7. Among the fractions $\frac{7}{9}$, $\frac{9}{9}$, $\frac{11}{8}$ and $\frac{3}{10}$, the improper fraction is:

   • a) $\frac{7}{9}$
   • b) $\frac{9}{9}$
   • c) $\frac{11}{8}$
   • d) $\frac{3}{10}$

8. The result of $\frac{5}{6} - \frac{1}{4}$ is:

   • a) $\frac{7}{12}$
   • b) $\frac{4}{2}$
   • c) $\frac{1}{3}$
   • d) $\frac{4}{10}$

9. A book costs $150$ lei. $20\%$ of the price of the book is:

   • a) $30$ lei
   • b) $75$ lei
   • c) $130$ lei
   • d) $3$ lei

10. The result of $3,75 \cdot 100$ is:

    • a) $375$
    • b) $0,0375$
    • c) $37,5$
    • d) $3750$

11. The fraction $\frac{7}{20}$, written as a decimal, is:

    • a) $0,35$
    • b) $0,72$
    • c) $3,5$
    • d) $0,035$

12. The table below shows how many books the pupils of a class read during the holidays. The number of pupils who read at least $3$ books is:

    Number of books	$0$	$1$	$2$	$3$	$4$
    Number of pupils	$2$	$5$	$9$	$8$	$4$

    • a) $12$
    • b) $8$
    • c) $21$
    • d) $4$

C. Problems

13. Consider the natural numbers of the form $\overline{2a4b}$.

    a) Write the largest number of this form that is divisible by $5$.

    b) Find all numbers of this form that are divisible by both $5$ and $9$.

14. I am thinking of a number. I multiply it by $3$, I add $12$ to the result, I divide the sum by $5$ and I get $9$.

    a) Check whether the number I thought of can be $10$.

    b) Find the number I thought of.

15. A cyclist rides a route in three days. On the first day they ride $\frac{2}{5}$ of the route, on the second day $\frac{1}{3}$ of the route, and on the third day they ride the remaining $24\text{ km}$.

    a) What fraction of the route did the cyclist ride in the first two days?

    b) Find the length of the route.

16. In a yard there are hens and rabbits. Together they have $20$ heads and $56$ legs.

    a) Show that there cannot be $10$ hens and $10$ rabbits in the yard.

    b) Find how many rabbits are in the yard.