Practice Test 7 - 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 science class has 15 grams of clay. They do two experiments: - Experiment X: $15 \times \frac{6}{5}$ grams - Experiment Y: $15 \times \frac{4}{5}$ grams Which statement correctly compares the effects of the two experiments?
2. Look at the pattern of dots arranged in the figure. Ana wants to create a mathematical representation that will help her predict how many dots will be in the 10th figure of this sequence. Which approach would BEST communicate her prediction strategy?
3. Based on the diagram shown, Maria wants to find the area of the shaded triangle by using the parallelogram method. The parallelogram containing the triangle has what area?
4. A garden plot covers $\frac{1}{6}$ of a yard. If 4 different vegetables are planted in equal sections of this plot, what fraction of the entire yard will the tomato section occupy?
5. A teacher has $\tfrac{1}{4}$ of a pan of brownies left. She shares that leftover amount equally among 2 students. Imagine the $\tfrac{1}{4}$ piece is split into 2 equal smaller pieces. What is the result of $\tfrac{1}{4} \div 2$?
6. A coach has $864$ water bottles to pack equally into boxes that each hold $24$ bottles. Which statement gives the correct quotient and shows how multiplication can check the division $864\div 24$?
7. Two solids are built from unit cubes. In both solids, the cubes fill the space completely with no gaps or overlaps. Volume is measured in cubic units. Solid A has 10 unit cubes. Solid B has 12 unit cubes. Which statement about their volumes is correct?
8. Two number patterns are paired and then graphed as ordered pairs $(x, y)$ where $x$ is from Pattern X and $y$ is from Pattern Y. Pattern X rule: start at 1 and add 4. Terms: 1, 5, 9, 13, 17. Pattern Y rule: start at 2 and add 3. Terms: 2, 5, 8, 11, 14. Which ordered pair matches the 4th terms of the two patterns?​
9. A rectangle is $\tfrac{2}{3}$ yard by $\tfrac{3}{4}$ yard. It is partitioned into unit fraction squares that are $\tfrac{1}{3}$ yard by $\tfrac{1}{4}$ yard, making 2 squares by 3 squares. Which statement is the incorrect claim about the area, based on measuring in square units?
10. A recipe uses $0.35$ liters of milk. The cook writes the number sentence $0.35 \times 10^1$ to convert to a different unit. Powers of 10 affect place value positions by shifting digits into new places. Which statement correctly describes the pattern and the result?
11. A baker has 7 identical muffins and packs them equally into 2 boxes. The fraction $\frac{7}{2}$ represents the result of the division $7 \div 2$. The numerator is 7 (muffins) and the denominator is 2 (boxes). Which statement explains what $\frac{7}{2}$ means in this situation, showing equal sharing and that fractions can represent division?
12. Sam is comparing $\frac{9}{10}$ and $\frac{11}{12}$ using the least common multiple method. After converting to the common denominator, which statement about the numerators is correct?
13. A recipe calls for $\frac{5}{6}$ cup of flour and $\frac{7}{8}$ cup of sugar. To compare these amounts, Lisa needs to find a common denominator. What is the smallest common denominator she can use?
14. When 47.8 is multiplied by a power of 10, the result has exactly 2 zeros between the decimal point and the first non-zero digit. Which power of 10 was used?
15. Look at the number line. Point $P$ represents $4.56$ and point $Q$ represents $45.6$. The digit $4$ appears in both numbers. How many times greater is the value of the digit $4$ at point $Q$ compared to the value of the digit $4$ at point $P$?
16. A student correctly found that $\frac{7}{12} = \frac{35}{60}$ and $\frac{3}{4} = \frac{45}{60}$. However, the teacher said there was a more efficient common denominator to use. What should the student have used?
17. Carlos finds three decimal numbers in his math book: $15.847$, $15.851$, and $15.855$. When he rounds each number to the nearest tenth, how many of the rounded results are the same?
18. A student compares the expressions $5 \times \tfrac{4}{5}$ and $5 \times \tfrac{6}{5}$. The factors are 5 and $\tfrac{4}{5}$ (less than 1) in the first expression, and 5 and $\tfrac{6}{5}$ (greater than 1) in the second. Factor size affects product size. Which statement is correct (without calculating the exact products)?
19. A recipe uses 10 cups of flour as the original amount. Two changes are suggested: • Change 1: $10 \times \frac{6}{5}$ • Change 2: $10 \times \frac{2}{5}$ Which explanation correctly matches how each fraction affects the product compared to the original number 10? (Original number: 10; products: $10\times\frac{6}{5}$ and $10\times\frac{2}{5}$.)
20. Sarah's book has 240 pages. She wants to finish reading it in 12 days by reading the same number of pages each day. However, on the first day she only reads 15 pages. How should Sarah adjust her daily reading plan for the remaining 11 days?

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