Practice Test 12 - 5th Grade Math

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. A full bottle holds 1 whole gallon (the same-sized whole). A gardener mixes $\tfrac{2}{3}$ gallon of water with fertilizer. The fertilizer amount is $\tfrac{3}{10}$ of the water amount. Since fraction multiplication represents taking part of a quantity, what is the correct answer to the problem: How many gallons of fertilizer does the gardener use?
2. Tom has $\frac{1}{5}$ meter of rope. He cuts it into 3 equal pieces, then realizes he needs pieces that are twice as long. How many of the new longer pieces can Tom make from his original rope?
3. Which comparison is true?
4. A teacher posts this shape hierarchy based on properties: - Quadrilateral: 4 sides - Parallelogram: 2 pairs of parallel sides - Rectangle: 4 right angles - Rhombus: 4 equal sides - Square: 4 equal sides and 4 right angles Shape A has 4 sides, 2 pairs of parallel sides, 4 right angles, and all 4 sides are equal. Which categories does Shape A belong to?
5. A class is comparing products. Look at $\frac{2}{5} \times 20$. The factors are $\frac{2}{5}$ and $20$. Which claim about the product is incorrect (do not calculate the exact product)?
6. A student writes $[50 - (12 + 8)] \div 5$. What is the value of the expression $[50 - (12 + 8)] \div 5$?
7. A right rectangular prism is packed with unit cubes. The base has 3 rows of cubes with 8 cubes in each row, and there are 2 layers stacked straight up. Because the cubes fill the prism completely (no gaps or overlaps), the number of cubes equals the volume and also matches multiplying the three dimensions. What is the volume of the prism?
8. A classroom has the multiplication expression $1\tfrac{1}{2} \times 12$ for the total length of ribbon used. The factors are $1\tfrac{1}{2}$ and $12$. Since $1\tfrac{1}{2}$ is greater than 1, it affects the product size. Which statement correctly describes the size of the product compared to 12, without calculating the exact product?
9. Emma measures her desk in millimeters and gets $1250$ mm for the length and $800$ mm for the width. Her friend Alex measures the same desk in centimeters and gets $125$ cm for the length. What measurement should Alex get for the width in centimeters?
10. Refer to the diagram. If the height of the rectangular prism is tripled, what will be the ratio of the new volume to the original volume?
11. Sofia is planning her weekly spending. She receives $15.00 allowance and earns $22.50 from pet-sitting. Her expenses are: lunch money $8.75, movie ticket $7.25, gift for friend $12.50, and she wants to save $6.00. After one week, what will be true about Sofia's budget?
12. Use the coordinate plane shown to answer this question. A pizza delivery driver starts at the restaurant located at point R and needs to deliver to houses at points A, B, and C, then return to the restaurant. Each grid unit equals 4 city blocks. What is the total distance if the driver visits the houses in alphabetical order?
13. Marcus is solving $84 \div 7$ and notices he can express the answer as $12$, $12.0$, $12\frac{0}{7}$, or $12$ remainder $0$. His friend says these are all different answers. What should Marcus explain about these expressions?
14. Study the partially built structure shown in the diagram. This structure will be completed by filling in all the empty spaces to form a complete $3 \times 4 \times 2$ rectangular prism. What is the volume of the unit cubes that are already in place?
15. A coach has 2 gallons of sports drink. Each player gets $\tfrac{1}{4}$ gallon. This is $2 \div \tfrac{1}{4}$, which answers "how many $\tfrac{1}{4}$-gallon servings are in 2 gallons." How many players can get a full serving? Model: Think of 2 whole gallons. Each gallon can be split into 4 fourths; count the total fourths.
16. A recipe uses $0.25$ cup of sugar per batch. You make $4$ batches. Using place value (hundredths) and the idea that decimal operations rely on place value understanding, what is $0.25 \times 4$?
17. Look at the cube shown in the figure with edge length 4 centimeters. Jake says the volume is 16 cubic centimeters because "4 times 4 equals 16." What is wrong with Jake's reasoning, and what is the correct volume?
18. A science class uses the same 1-meter strip as the whole length. One group measures $\tfrac{5}{8}$ meter. Another group measures $\tfrac{1}{4}$ meter. They add the lengths and use equivalent fractions: $\tfrac{1}{4}=\tfrac{2}{8}$. Which statement about the size of the result is correct?
19. A student writes the number $58.309$. The digit 3 is in the tenths place and the digit 3 is also used in the hundredths place in the number $58.039$. Which statement correctly compares the value of the digit 3 in these two numbers?
20. During a read-a-thon, Liam reads for 90 minutes each day for 3 days. What is his total reading time in hours?

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