Mental Math 6th Grade - Free Printable
Educational worksheet: Mental Math 6th Grade. Download and print for classroom or home learning activities.
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Step-by-step solution for: Mental Math 6th Grade
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Show Answer Key & Explanations
Step-by-step solution for: Mental Math 6th Grade
Let's solve each problem step by step and provide explanations.
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1) 3 + 4 × 7
- Order of operations (PEMDAS): Multiply before adding.
- 4 × 7 = 28
- 3 + 28 = 31
✔ Answer: 31
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2) 2³ + 3²
- 2³ = 2 × 2 × 2 = 8
- 3² = 3 × 3 = 9
- 8 + 9 = 17
✔ Answer: 17
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3) Tyger travels 135 miles in 3 hours. What is the unit rate? ____ mph
- Unit rate = distance ÷ time
- 135 ÷ 3 = 45 mph
✔ Answer: 45 mph
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4) Which of these numbers are prime numbers?
> 25, 29, 33, 31, 39, 21
- Prime numbers: divisible only by 1 and themselves.
- 25 → 5×5 → not prime
- 29 → no divisors other than 1 and 29 → prime
- 33 → 3×11 → not prime
- 31 → only divisible by 1 and 31 → prime
- 39 → 3×13 → not prime
- 21 → 3×7 → not prime
✔ Answer: 29 and 31
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5) Which two numbers have a sum of 14 and a product of 45?
- Let’s find two numbers that:
- Add to 14
- Multiply to 45
- Try pairs:
- 5 and 9: 5+9=14, 5×9=45 → ✔
✔ Answer: 5 and 9
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6) How many fifths make 3?
- 1 whole = 5 fifths
- So, 3 wholes = 3 × 5 = 15 fifths
✔ Answer: 15
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7) What is the value of x if x + 4 = 25?
- Subtract 4 from both sides:
- x = 25 − 4 = 21
✔ Answer: x = 21
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8) What is the value of this number: LXXIV?
- Roman numerals:
- L = 50
- X = 10
- IV = 4
- LXX = 50 + 10 + 10 = 70
- IV = 4
- So, LXXIV = 70 + 4 = 74
✔ Answer: 74
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9) If a third of a number is 12, what is the number?
- Let the number be x
- (1/3)x = 12
- Multiply both sides by 3:
- x = 12 × 3 = 36
✔ Answer: 36
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10) Which of these numbers is NOT a factor of 36?
> 3, 12, 1, 8, 2, 18, 6
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Check each:
- 3 → yes
- 12 → yes
- 1 → yes
- 8 → ✘ (36 ÷ 8 = 4.5 → not integer)
- 2 → yes
- 18 → yes
- 6 → yes
✔ Answer: 8
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11) How many yards in 81 feet?
- 1 yard = 3 feet
- 81 ÷ 3 = 27 yards
✔ Answer: 27
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12) There is 24 fluid ounces of water in a bottle. I drink ¼ of the water. How many fluid ounces are left?
- ¼ of 24 = 24 ÷ 4 = 6 oz drunk
- Left: 24 − 6 = 18 oz
✔ Answer: 18 fluid ounces
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13) Put these numbers in order, smallest first:
> -3, -8, 0, -2
- Negative numbers: more negative = smaller
- Order: -8 < -3 < -2 < 0
✔ Answer: -8, -3, -2, 0
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14) What is the area of this triangle?
> Base = 8 cm, Height = 3 cm
- Area of triangle = (base × height) ÷ 2
- (8 × 3) ÷ 2 = 24 ÷ 2 = 12 cm²
✔ Answer: 12 cm²
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15) What is 10% of $200?
- 10% = 0.10
- 0.10 × 200 = $20
✔ Answer: $20
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16) The ratio of red balls to blue balls is 1:3. If there are 9 red balls, how many blue balls are there?
- Ratio: 1 red : 3 blue
- So for every 1 red, there are 3 blue
- 9 red → 9 × 3 = 27 blue balls
✔ Answer: 27
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17) 10 × 31.25
- 10 × 31.25 = 312.5
✔ Answer: 312.5
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18) I set off at 07:25. My journey takes me 8 hours and 45 minutes. What time will I arrive? Write in 24-hour clock time.
- Start: 07:25
- Add 8 hours: 07:25 + 8h = 15:25
- Add 45 minutes: 15:25 + 45 min = 16:10
✔ Answer: 16:10
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| Question | Answer |
|--------|--------|
| 1 | 31 |
| 2 | 17 |
| 3 | 45 mph |
| 4 | 29, 31 |
| 5 | 5 and 9 |
| 6 | 15 |
| 7 | 21 |
| 8 | 74 |
| 9 | 36 |
| 10 | 8 |
| 11 | 27 |
| 12 | 18 |
| 13 | -8, -3, -2, 0 |
| 14 | 12 cm² |
| 15 | $20 |
| 16 | 27 |
| 17 | 312.5 |
| 18 | 16:10 |
Let me know if you'd like this formatted as a printable answer sheet!
---
1) 3 + 4 × 7
- Order of operations (PEMDAS): Multiply before adding.
- 4 × 7 = 28
- 3 + 28 = 31
✔ Answer: 31
---
2) 2³ + 3²
- 2³ = 2 × 2 × 2 = 8
- 3² = 3 × 3 = 9
- 8 + 9 = 17
✔ Answer: 17
---
3) Tyger travels 135 miles in 3 hours. What is the unit rate? ____ mph
- Unit rate = distance ÷ time
- 135 ÷ 3 = 45 mph
✔ Answer: 45 mph
---
4) Which of these numbers are prime numbers?
> 25, 29, 33, 31, 39, 21
- Prime numbers: divisible only by 1 and themselves.
- 25 → 5×5 → not prime
- 29 → no divisors other than 1 and 29 → prime
- 33 → 3×11 → not prime
- 31 → only divisible by 1 and 31 → prime
- 39 → 3×13 → not prime
- 21 → 3×7 → not prime
✔ Answer: 29 and 31
---
5) Which two numbers have a sum of 14 and a product of 45?
- Let’s find two numbers that:
- Add to 14
- Multiply to 45
- Try pairs:
- 5 and 9: 5+9=14, 5×9=45 → ✔
✔ Answer: 5 and 9
---
6) How many fifths make 3?
- 1 whole = 5 fifths
- So, 3 wholes = 3 × 5 = 15 fifths
✔ Answer: 15
---
7) What is the value of x if x + 4 = 25?
- Subtract 4 from both sides:
- x = 25 − 4 = 21
✔ Answer: x = 21
---
8) What is the value of this number: LXXIV?
- Roman numerals:
- L = 50
- X = 10
- IV = 4
- LXX = 50 + 10 + 10 = 70
- IV = 4
- So, LXXIV = 70 + 4 = 74
✔ Answer: 74
---
9) If a third of a number is 12, what is the number?
- Let the number be x
- (1/3)x = 12
- Multiply both sides by 3:
- x = 12 × 3 = 36
✔ Answer: 36
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10) Which of these numbers is NOT a factor of 36?
> 3, 12, 1, 8, 2, 18, 6
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Check each:
- 3 → yes
- 12 → yes
- 1 → yes
- 8 → ✘ (36 ÷ 8 = 4.5 → not integer)
- 2 → yes
- 18 → yes
- 6 → yes
✔ Answer: 8
---
11) How many yards in 81 feet?
- 1 yard = 3 feet
- 81 ÷ 3 = 27 yards
✔ Answer: 27
---
12) There is 24 fluid ounces of water in a bottle. I drink ¼ of the water. How many fluid ounces are left?
- ¼ of 24 = 24 ÷ 4 = 6 oz drunk
- Left: 24 − 6 = 18 oz
✔ Answer: 18 fluid ounces
---
13) Put these numbers in order, smallest first:
> -3, -8, 0, -2
- Negative numbers: more negative = smaller
- Order: -8 < -3 < -2 < 0
✔ Answer: -8, -3, -2, 0
---
14) What is the area of this triangle?
> Base = 8 cm, Height = 3 cm
- Area of triangle = (base × height) ÷ 2
- (8 × 3) ÷ 2 = 24 ÷ 2 = 12 cm²
✔ Answer: 12 cm²
---
15) What is 10% of $200?
- 10% = 0.10
- 0.10 × 200 = $20
✔ Answer: $20
---
16) The ratio of red balls to blue balls is 1:3. If there are 9 red balls, how many blue balls are there?
- Ratio: 1 red : 3 blue
- So for every 1 red, there are 3 blue
- 9 red → 9 × 3 = 27 blue balls
✔ Answer: 27
---
17) 10 × 31.25
- 10 × 31.25 = 312.5
✔ Answer: 312.5
---
18) I set off at 07:25. My journey takes me 8 hours and 45 minutes. What time will I arrive? Write in 24-hour clock time.
- Start: 07:25
- Add 8 hours: 07:25 + 8h = 15:25
- Add 45 minutes: 15:25 + 45 min = 16:10
✔ Answer: 16:10
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✔ Final Answers:
| Question | Answer |
|--------|--------|
| 1 | 31 |
| 2 | 17 |
| 3 | 45 mph |
| 4 | 29, 31 |
| 5 | 5 and 9 |
| 6 | 15 |
| 7 | 21 |
| 8 | 74 |
| 9 | 36 |
| 10 | 8 |
| 11 | 27 |
| 12 | 18 |
| 13 | -8, -3, -2, 0 |
| 14 | 12 cm² |
| 15 | $20 |
| 16 | 27 |
| 17 | 312.5 |
| 18 | 16:10 |
Let me know if you'd like this formatted as a printable answer sheet!
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