Question

6.RP.1 — The ratio of boys to girls on a field trip is 4:5. If there are 20 boys, how many girls are there?

6.RP.2 — A car travels 300 miles on 12 gallons of gas. What is the unit rate in miles per gallon?

6.RP.3 — A recipe calls for 2 cups of sugar for every 5 cups of flour. If you use 20 cups of flour, how much sugar do you need?

6.NS.1 — How many 1/3-cup servings can you get from 2 1/4 cups of yogurt? (Compute (2 1/4) ÷ (1/3).)

6.NS.2 — Divide 6,732 ÷ 18.

6.NS.3 — Compute 4.56 × 0.25.

6.NS.4 — Find the greatest common factor (GCF) and least common multiple (LCM) of 18 and 30.

6.NS.5 — What is |−9|, and which is greater: −4 or −9?

6.NS.6 — Order these numbers from least to greatest: −3/4, 0, 2/5, −1/2.

6.NS.7 — Plot the point (−3, 4) on a coordinate plane. What are the x- and y-coordinates?

6.NS.8 — A submarine is 350 feet below sea level. It rises 140 feet. What is its new depth?

6.EE.1 — Evaluate 2^5 + 3^2.

6.EE.2 — Write an expression for “seven less than three times a number n.”

6.EE.3 — Use the distributive property to rewrite 6(x + 4) as an equivalent expression.

6.EE.4 — Are the expressions 4(2x + 3) and 8x + 12 equivalent? Explain (yes/no).

6.EE.5 — Solve 7x − 9 = 19.

6.EE.6 — The school sells tickets for $a each. Write an expression for the cost of 4 tickets.

6.EE.7 — Solve the equation 3x = 24.

6.EE.8 — Marcus has $50. Each game at an arcade costs $4. Write and solve an inequality to show how many whole games g he can play.

6.EE.9 — A tree’s height h (in feet) is modeled by h = 2t + 5, where t is the tree’s age in years. What is the height when t = 8? What coordinate (t, h) does that make?

6.G.1 — Find the area of a triangle with base 10 cm and height 6 cm.

6.G.2 — Find the volume of a rectangular prism with length 5 cm, width 3 cm, and height 4 cm.

6.G.3 — On a coordinate grid, what is the length of the horizontal segment between (−2, 3) and (4, 3)?

6.G.4 — A cube has edge length 4 cm. What is its total surface area?

6.SP.1 — Explain whether the following is a sample or a population: “Every math test taken by students in Ms. Lee’s homeroom this year.”

6.SP.2 — Find the mean, median, mode, and range of these scores: 6, 9, 7, 9, 10.

6.SP.3 — A dot plot shows the number of books read by students: 0, 1, 1, 2, 3, 3, 3, 4. What value(s) appear most often?

6.SP.4 — Dataset A has mean 12 and range 4. Dataset B has mean 12 and range 10. Which dataset has greater variability? (A or B)

6.SP.5 — A bag contains 4 red, 5 blue, and 1 yellow marble. If a marble is randomly chosen, what is the probability it is blue?


step by step tell me how to solve

Answer 1

Here are step-by-step solutions for each problem.

1) 6.RP.1 — Ratio of boys:girls = 4:5. There are 20 boys. How many girls?
- Step 1: Find scale factor = actual boys / ratio boys = 20 / 4 = 5.
- Step 2: Multiply ratio girls by scale factor = 5 × 5 = 25.
- Answer: 25 girls.

2) 6.RP.2 — A car travels 300 miles on 12 gallons. Unit rate (miles per gallon)?
- Step 1: Divide miles by gallons: 300 ÷ 12 = 25.
- Answer: 25 miles per gallon.

3) 6.RP.3 — Recipe 2 cups sugar : 5 cups flour. If flour = 20 cups, sugar = ?
- Step 1: Scale factor = 20 ÷ 5 = 4.
- Step 2: Sugar = 2 × 4 = 8 cups.
- Answer: 8 cups of sugar.

4) 6.NS.1 — How many 1/3-cup servings from 2 1/4 cups? Compute (2 1/4) ÷ (1/3).
- Step 1: Convert to improper fraction: 2 1/4 = 9/4.
- Step 2: Divide: (9/4) ÷ (1/3) = (9/4) × (3/1) = 27/4.
- Step 3: Convert to mixed number: 27/4 = 6 3/4 = 6.75.
- Answer: 6 3/4 servings (or 6 full servings and a 3/4 serving).

5) 6.NS.2 — Divide 6,732 ÷ 18.
- Step 1: Long division: 18 into 67 goes 3 (3×18=54), remainder 13.
- Step 2: Bring down 3 → 133. 18 into 133 goes 7 (7×18=126), remainder 7.
- Step 3: Bring down 2 → 72. 18 into 72 goes 4 (4×18=72), remainder 0.
- Answer: 374.

6) 6.NS.3 — Compute 4.56 × 0.25.
- Step 1: Note 0.25 = 1/4, so 4.56 × 0.25 = 4.56 ÷ 4.
- Step 2: 4.56 ÷ 4 = 1.14.
- Answer: 1.14.

7) 6.NS.4 — GCF and LCM of 18 and 30.
- Step 1: Prime factors: 18 = 2 × 3^2; 30 = 2 × 3 × 5.
- Step 2: GCF = product of common primes to lowest powers = 2 × 3 = 6.
- Step 3: LCM = product of all primes to highest powers = 2 × 3^2 × 5 = 90.
- Answer: GCF = 6, LCM = 90.

8) 6.NS.5 — What is |−9|, and which is greater: −4 or −9?
- Step 1: |−9| = 9 (absolute value is distance from 0).
- Step 2: Compare −4 and −9: −4 is closer to 0, so −4 > −9.
- Answer: |−9| = 9; −4 is greater than −9.

9) 6.NS.6 — Order from least to greatest: −3/4, 0, 2/5, −1/2.
- Step 1: Convert to decimals (or compare fractions): −3/4 = −0.75; −1/2 = −0.5; 0 = 0; 2/5 = 0.4.
- Step 2: Order: −0.75, −0.5, 0, 0.4.
- Answer: −3/4, −1/2, 0, 2/5.

10) 6.NS.7 — Plot point (−3, 4). What are x- and y-coordinates?
- Step 1: The ordered pair (−3, 4) means x = −3, y = 4.
- Answer: x-coordinate = −3; y-coordinate = 4.

11) 6.NS.8 — Submarine is 350 ft below sea level (−350). It rises 140 ft. New depth?
- Step 1: −350 + 140 = −210.
- Step 2: That means 210 ft below sea level.
- Answer: 210 feet below sea level (or −210).

12) 6.EE.1 — Evaluate 2^5 + 3^2.
- Step 1: 2^5 = 32; 3^2 = 9.
- Step 2: 32 + 9 = 41.
- Answer: 41.

13) 6.EE.2 — Write expression for “seven less than three times a number n.”
- Step 1: Three times n = 3n.
- Step 2: Seven less than that = 3n − 7.
- Answer: 3n − 7.

14) 6.EE.3 — Use distributive property to rewrite 6(x + 4).
- Step 1: Multiply 6 by each term: 6×x + 6×4 = 6x + 24.
- Answer: 6x + 24.

15) 6.EE.4 — Are 4(2x + 3) and 8x + 12 equivalent? Explain.
- Step 1: Distribute: 4(2x + 3) = 8x + 12.
- Step 2: They are identical, so yes, they are equivalent.
- Answer: Yes — because distributing gives 8x + 12.

16) 6.EE.5 — Solve 7x − 9 = 19.
- Step 1: Add 9 to both sides: 7x = 28.
- Step 2: Divide by 7: x = 4.
- Answer: x = 4.

17) 6.EE.6 — School sells tickets for $a each. Expression for cost of 4 tickets?
- Step 1: Cost = price per ticket × number of tickets = a × 4 = 4a.
- Answer: 4a.

18) 6.EE.7 — Solve 3x = 24.
- Step 1: Divide both sides by 3: x = 24 ÷ 3 = 8.
- Answer: x = 8.

19) 6.EE.8 — Marcus has $50. Each game costs $4. Write and solve inequality for whole games g he can play.
- Step 1: Cost for g games = 4g. He can spend at most $50: 4g ≤ 50.
- Step 2: Solve: g ≤ 50 ÷ 4 = 12.5.
- Step 3: g must be a whole number (cannot play half a game), so g ≤ 12.
- Answer: Inequality 4g ≤ 50; maximum whole games = 12.

20) 6.EE.9 — Tree height h = 2t + 5. Find height when t = 8 and the coordinate (t,h).
- Step 1: Plug in t = 8: h = 2(8) + 5 = 16 + 5 = 21.
- Step 2: Coordinate is (t, h) = (8, 21).
- Answer: Height = 21 ft; coordinate (8, 21).

21) 6.G.1 — Area of triangle with base = 10 cm, height = 6 cm.
- Step 1: Area = 1/2 × base × height = 1/2 × 10 × 6.
- Step 2: Compute: 0.5 × 10 × 6 = 30.
- Answer: 30 cm².

22) 6.G.2 — Volume of rectangular prism length 5 cm, width 3 cm, height 4 cm.
- Step 1: Volume = length × width × height = 5 × 3 × 4.
- Step 2: 5×3=15; 15×4=60.
- Answer: 60 cm³.

23) 6.G.3 — Length of horizontal segment between (−2, 3) and (4, 3).
- Step 1: For horizontal segment, y’s are same; length = difference of x-values: 4 − (−2) = 6.
- Answer: 6 units.

24) 6.G.4 — Cube edge length 4 cm. Total surface area?
- Step 1: Surface area of cube = 6 × side^2 = 6 × 4^2 = 6 × 16.
- Step 2: 6 × 16 = 96.
- Answer: 96 cm².

25) 6.SP.1 — Explain sample or population: “Every math test taken by students in Ms. Lee’s homeroom this year.”
- Step 1: This phrase includes every test in that specific group (Ms. Lee’s homeroom this year).
- Answer: It is a population (because it includes every member of the group of interest).

26) 6.SP.2 — Mean, median, mode, range of scores: 6, 9, 7, 9, 10.
- Step 1: Mean = (6 + 9 + 7 + 9 + 10) ÷ 5 = 41 ÷ 5 = 8.2.
- Step 2: Order data: 6, 7, 9, 9, 10. Median = middle value = 9.
- Step 3: Mode = most frequent value = 9.
- Step 4: Range = max − min = 10 − 6 = 4.
- Answer: Mean 8.2, Median 9, Mode 9, Range 4.

27) 6.SP.3 — Dot plot values: 0, 1, 1, 2, 3, 3, 3, 4. Which value(s) appear most often?
- Step 1: Count frequencies: 0 (1), 1 (2), 2 (1), 3 (3), 4 (1).
- Answer: 3 appears most often (mode = 3).

28) 6.SP.4 — Dataset A mean 12 range 4; Dataset B mean 12 range 10. Which has greater variability?
- Step 1: Range measures spread; larger range = more variability.
- Answer: Dataset B (range 10) has greater variability.

29) 6.SP.5 — Bag: 4 red, 5 blue, 1 yellow marble. Probability of choosing a blue marble?
- Step 1: Total marbles = 4 + 5 + 1 = 10.
- Step 2: Number of blue = 5.
- Step 3: Probability = 5/10 = 1/2 = 0.5.
- Answer: 1/2 (50%).

If you want, I can show any of these with more detailed arithmetic (long division, fraction work, or visual diagrams).