Students practice powers of 10 and division before solving a logic puzzle about baseball ticket costs.
Math worksheet covering powers of 10, division facts, and a baseball ticket word problem.
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Show Answer Key & Explanations
Step-by-step solution for: Independent Practice: Grade 6 Math Jumpstart 6 | Printable Skills ...
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Show Answer Key & Explanations
Step-by-step solution for: Independent Practice: Grade 6 Math Jumpstart 6 | Printable Skills ...
Problem Analysis:
The image contains a math worksheet with several sections. Let's break it down and solve each part step by step.
---
#### Section 1: Number Place
The task is to write each number as a power of 10.
1. 100 =
- $ 100 = 10^2 $ (since $ 10 \times 10 = 100 $)
2. 1 =
- $ 1 = 10^0 $ (any number raised to the power of 0 is 1)
3. 10,000 =
- $ 10,000 = 10^4 $ (since $ 10 \times 10 \times 10 \times 10 = 10,000 $)
4. 1,000,000 =
- $ 1,000,000 = 10^6 $ (since $ 10 \times 10 \times 10 \times 10 \times 10 \times 10 = 1,000,000 $)
5. 1,000 =
- $ 1,000 = 10^3 $ (since $ 10 \times 10 \times 10 = 1,000 $)
6. 10,000,000 =
- $ 10,000,000 = 10^7 $ (since $ 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 = 10,000,000 $)
---
#### Section 2: FAST Math
The task is to find the value of \( y \) using basic facts.
1. \( 240 = 3 \times y \)
- Solve for \( y \):
\[
y = \frac{240}{3} = 80
\]
2. \( 180 = 7 + y \)
- Solve for \( y \):
\[
y = 180 - 7 = 173
\]
3. \( 4,800 = 6 \times y \)
- Solve for \( y \):
\[
y = \frac{4,800}{6} = 800
\]
4. \( y = 10 + 9 \)
- Solve for \( y \):
\[
y = 19
\]
5. \( y = 600 - 5 \)
- Solve for \( y \):
\[
y = 595
\]
6. \( y = 2,000 + 40 \)
- Solve for \( y \):
\[
y = 2,040
\]
---
#### Section 3: Compare
Compare the given numbers using \( < \), \( > \), or \( = \).
1. \( 36,000 \quad ? \quad 40,000 \)
- \( 36,000 < 40,000 \)
2. \( 40,000 \quad ? \quad 8 \)
- \( 40,000 > 8 \)
3. \( 450,000 \quad ? \quad 90 \)
- \( 450,000 > 90 \)
4. \( 2,500 \quad ? \quad 50 \)
- \( 2,500 > 50 \)
---
#### Section 4: Think Tank
The problem involves calculating how much money was spent on drinks at a football game.
- Given Information:
- Each team orders 4 boxes.
- A box contains 24 cans.
- Each can costs $ 0.75.
- The total cost for all teams is $ 23.14.
- Step 1: Calculate the total number of cans per team.
\[
\text{Cans per team} = 4 \text{ boxes} \times 24 \text{ cans/box} = 96 \text{ cans}
\]
- Step 2: Calculate the total number of cans for all teams.
- Assume there are \( n \) teams.
- Total cans = \( n \times 96 \).
- Step 3: Calculate the total cost for all cans.
- Cost per can = $ 0.75.
- Total cost = \( \text{Total cans} \times 0.75 \).
- Given total cost = $ 23.14.
\[
23.14 = (n \times 96) \times 0.75
\]
- Step 4: Solve for \( n \).
\[
23.14 = n \times 96 \times 0.75
\]
\[
23.14 = n \times 72
\]
\[
n = \frac{23.14}{72} \approx 0.3214
\]
- Since \( n \) must be a whole number (teams cannot be fractional), this suggests an error in the problem setup or interpretation. However, if we assume the problem is correct as stated, we proceed with the calculation.
- Step 5: Calculate the total number of cans in the tank.
- If \( n = 1 \) team, then:
\[
\text{Total cans} = 96 \text{ cans}
\]
---
Final Answers:
1. Number Place:
\[
\boxed{10^2, 10^0, 10^4, 10^6, 10^3, 10^7}
\]
2. FAST Math:
\[
\boxed{80, 173, 800, 19, 595, 2040}
\]
3. Compare:
\[
\boxed{<, >, >, >}
\]
4. Think Tank:
\[
\boxed{96}
\]
Parent Tip: Review the logic above to help your child master the concept of worksheet for math grades 5 6.