Mathematics 5 - Free Printable
Educational worksheet: Mathematics 5. Download and print for classroom or home learning activities.
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Step-by-step solution for: Mathematics 5
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Show Answer Key & Explanations
Step-by-step solution for: Mathematics 5
Let's go through each problem in the worksheet and solve them step by step, with explanations.
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1. What kind of angle measures less than 90°? Draw one.
- Answer: An angle that measures less than 90° is called an acute angle.
- Drawing: (You would draw an angle smaller than a right angle, like 45°.)
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2. $ \frac{5}{6} \times \frac{3}{5} = ? $
- Multiply numerators: $ 5 \times 3 = 15 $
- Multiply denominators: $ 6 \times 5 = 30 $
- So, $ \frac{15}{30} = \frac{1}{2} $
✔ Answer: $ \frac{1}{2} $
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3. Estimate the product of 76 and 43.
- Round 76 → 80
- Round 43 → 40
- $ 80 \times 40 = 3,200 $
✔ Answer: Approximately 3,200
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4. How many tons are 16,000 pounds?
- 1 ton = 2,000 pounds
- $ \frac{16,000}{2,000} = 8 $
✔ Answer: 8 tons
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5. Write nine and five thousandths in standard decimal form.
- "Nine" = 9
- "Five thousandths" = $ \frac{5}{1000} = 0.005 $
- So, $ 9 + 0.005 = 9.005 $
✔ Answer: 9.005
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6. Mrs. Smith is taking herself and 12 students to a movie. The cost of each ticket was $6.75. How much did she spend on the tickets?
- Total people = 1 (herself) + 12 = 13
- Cost per ticket = $6.75
- Total cost = $ 13 \times 6.75 $
Break it down:
- $ 10 \times 6.75 = 67.50 $
- $ 3 \times 6.75 = 20.25 $
- Total = $ 67.50 + 20.25 = 87.75 $
✔ Answer: $87.75
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7. $ \frac{5}{9} \bigcirc \frac{7}{10} $ — compare using <, >, or =
- Find common denominator: LCM of 9 and 10 is 90
- $ \frac{5}{9} = \frac{50}{90} $
- $ \frac{7}{10} = \frac{63}{90} $
- Since $ \frac{50}{90} < \frac{63}{90} $, then $ \frac{5}{9} < \frac{7}{10} $
✔ Answer: $ \frac{5}{9} < \frac{7}{10} $
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8. Round 4.583 to the nearest tenth.
- Look at hundredths place: 8 ≥ 5 → round up
- Tenths digit is 5 → becomes 6
- So, 4.583 → 4.6
✔ Answer: 4.6
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9. $ 12\frac{2}{5} + 9\frac{1}{3} = ? $
Convert mixed numbers to improper fractions:
- $ 12\frac{2}{5} = \frac{62}{5} $
- $ 9\frac{1}{3} = \frac{28}{3} $
Find common denominator: LCM of 5 and 3 is 15
- $ \frac{62}{5} = \frac{186}{15} $
- $ \frac{28}{3} = \frac{140}{15} $
- Add: $ \frac{186 + 140}{15} = \frac{326}{15} $
Convert back to mixed number:
- $ 326 ÷ 15 = 21 $ remainder 11 → $ 21\frac{11}{15} $
✔ Answer: $ 21\frac{11}{15} $
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10. Put $ \frac{10}{15} $ in simplest form.
- Divide numerator and denominator by GCF: GCF of 10 and 15 is 5
- $ \frac{10 ÷ 5}{15 ÷ 5} = \frac{2}{3} $
✔ Answer: $ \frac{2}{3} $
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11. $ 75 + 83 + 91 = ? $
- $ 75 + 83 = 158 $
- $ 158 + 91 = 249 $
✔ Answer: 249
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12. How many quarts are in 5 gallons?
- 1 gallon = 4 quarts
- $ 5 \times 4 = 20 $
✔ Answer: 20 quarts
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13. Find the area of Maria’s bedroom if it is 13 ft long and 14 ft wide.
- Area = length × width = $ 13 \times 14 $
- $ 13 \times 14 = 182 $
✔ Answer: 182 square feet
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14. $ 316 - 177 = ? $
- $ 316 - 177 = 139 $
✔ Answer: 139
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15. List the factors of 24.
- Factors are numbers that divide 24 evenly:
- $ 1, 2, 3, 4, 6, 8, 12, 24 $
✔ Answer: 1, 2, 3, 4, 6, 8, 12, 24
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16. Draw intersecting lines.
- (You would draw two lines that cross each other at a point.)
- They don't need to be perpendicular; just cross.
✔ Answer: (Draw two lines crossing)
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17. Find the circumference of this circle. (Diameter = 6 mm)
- Formula: $ C = \pi \times d $
- $ C = \pi \times 6 \approx 3.14 \times 6 = 18.84 $ mm
✔ Answer: 18.84 mm (or $ 6\pi $ mm)
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18. Is the number 29 prime or composite?
- A prime number has only two factors: 1 and itself.
- 29 is only divisible by 1 and 29 → Prime
✔ Answer: Prime
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19. Order these decimals from least to greatest: 6.41, 6.4, 6.04, 6.341
- Align decimals:
- 6.04
- 6.341
- 6.4
- 6.41
Compare:
- 6.04 < 6.341 < 6.4 < 6.41
✔ Answer: 6.04, 6.341, 6.4, 6.41
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20. What is the top number in a fraction called?
- The top number is the numerator
✔ Answer: Numerator
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1. Acute angle
2. $ \frac{1}{2} $
3. ~3,200
4. 8 tons
5. 9.005
6. $87.75
7. $ \frac{5}{9} < \frac{7}{10} $
8. 4.6
9. $ 21\frac{11}{15} $
10. $ \frac{2}{3} $
11. 249
12. 20 quarts
13. 182 sq ft
14. 139
15. 1, 2, 3, 4, 6, 8, 12, 24
16. Draw two lines crossing
17. 18.84 mm
18. Prime
19. 6.04, 6.341, 6.4, 6.41
20. Numerator
Let me know if you'd like a printable version or visual diagrams for any of the problems!
---
1. What kind of angle measures less than 90°? Draw one.
- Answer: An angle that measures less than 90° is called an acute angle.
- Drawing: (You would draw an angle smaller than a right angle, like 45°.)
---
2. $ \frac{5}{6} \times \frac{3}{5} = ? $
- Multiply numerators: $ 5 \times 3 = 15 $
- Multiply denominators: $ 6 \times 5 = 30 $
- So, $ \frac{15}{30} = \frac{1}{2} $
✔ Answer: $ \frac{1}{2} $
---
3. Estimate the product of 76 and 43.
- Round 76 → 80
- Round 43 → 40
- $ 80 \times 40 = 3,200 $
✔ Answer: Approximately 3,200
---
4. How many tons are 16,000 pounds?
- 1 ton = 2,000 pounds
- $ \frac{16,000}{2,000} = 8 $
✔ Answer: 8 tons
---
5. Write nine and five thousandths in standard decimal form.
- "Nine" = 9
- "Five thousandths" = $ \frac{5}{1000} = 0.005 $
- So, $ 9 + 0.005 = 9.005 $
✔ Answer: 9.005
---
6. Mrs. Smith is taking herself and 12 students to a movie. The cost of each ticket was $6.75. How much did she spend on the tickets?
- Total people = 1 (herself) + 12 = 13
- Cost per ticket = $6.75
- Total cost = $ 13 \times 6.75 $
Break it down:
- $ 10 \times 6.75 = 67.50 $
- $ 3 \times 6.75 = 20.25 $
- Total = $ 67.50 + 20.25 = 87.75 $
✔ Answer: $87.75
---
7. $ \frac{5}{9} \bigcirc \frac{7}{10} $ — compare using <, >, or =
- Find common denominator: LCM of 9 and 10 is 90
- $ \frac{5}{9} = \frac{50}{90} $
- $ \frac{7}{10} = \frac{63}{90} $
- Since $ \frac{50}{90} < \frac{63}{90} $, then $ \frac{5}{9} < \frac{7}{10} $
✔ Answer: $ \frac{5}{9} < \frac{7}{10} $
---
8. Round 4.583 to the nearest tenth.
- Look at hundredths place: 8 ≥ 5 → round up
- Tenths digit is 5 → becomes 6
- So, 4.583 → 4.6
✔ Answer: 4.6
---
9. $ 12\frac{2}{5} + 9\frac{1}{3} = ? $
Convert mixed numbers to improper fractions:
- $ 12\frac{2}{5} = \frac{62}{5} $
- $ 9\frac{1}{3} = \frac{28}{3} $
Find common denominator: LCM of 5 and 3 is 15
- $ \frac{62}{5} = \frac{186}{15} $
- $ \frac{28}{3} = \frac{140}{15} $
- Add: $ \frac{186 + 140}{15} = \frac{326}{15} $
Convert back to mixed number:
- $ 326 ÷ 15 = 21 $ remainder 11 → $ 21\frac{11}{15} $
✔ Answer: $ 21\frac{11}{15} $
---
10. Put $ \frac{10}{15} $ in simplest form.
- Divide numerator and denominator by GCF: GCF of 10 and 15 is 5
- $ \frac{10 ÷ 5}{15 ÷ 5} = \frac{2}{3} $
✔ Answer: $ \frac{2}{3} $
---
11. $ 75 + 83 + 91 = ? $
- $ 75 + 83 = 158 $
- $ 158 + 91 = 249 $
✔ Answer: 249
---
12. How many quarts are in 5 gallons?
- 1 gallon = 4 quarts
- $ 5 \times 4 = 20 $
✔ Answer: 20 quarts
---
13. Find the area of Maria’s bedroom if it is 13 ft long and 14 ft wide.
- Area = length × width = $ 13 \times 14 $
- $ 13 \times 14 = 182 $
✔ Answer: 182 square feet
---
14. $ 316 - 177 = ? $
- $ 316 - 177 = 139 $
✔ Answer: 139
---
15. List the factors of 24.
- Factors are numbers that divide 24 evenly:
- $ 1, 2, 3, 4, 6, 8, 12, 24 $
✔ Answer: 1, 2, 3, 4, 6, 8, 12, 24
---
16. Draw intersecting lines.
- (You would draw two lines that cross each other at a point.)
- They don't need to be perpendicular; just cross.
✔ Answer: (Draw two lines crossing)
---
17. Find the circumference of this circle. (Diameter = 6 mm)
- Formula: $ C = \pi \times d $
- $ C = \pi \times 6 \approx 3.14 \times 6 = 18.84 $ mm
✔ Answer: 18.84 mm (or $ 6\pi $ mm)
---
18. Is the number 29 prime or composite?
- A prime number has only two factors: 1 and itself.
- 29 is only divisible by 1 and 29 → Prime
✔ Answer: Prime
---
19. Order these decimals from least to greatest: 6.41, 6.4, 6.04, 6.341
- Align decimals:
- 6.04
- 6.341
- 6.4
- 6.41
Compare:
- 6.04 < 6.341 < 6.4 < 6.41
✔ Answer: 6.04, 6.341, 6.4, 6.41
---
20. What is the top number in a fraction called?
- The top number is the numerator
✔ Answer: Numerator
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✔ Final Answers Summary:
1. Acute angle
2. $ \frac{1}{2} $
3. ~3,200
4. 8 tons
5. 9.005
6. $87.75
7. $ \frac{5}{9} < \frac{7}{10} $
8. 4.6
9. $ 21\frac{11}{15} $
10. $ \frac{2}{3} $
11. 249
12. 20 quarts
13. 182 sq ft
14. 139
15. 1, 2, 3, 4, 6, 8, 12, 24
16. Draw two lines crossing
17. 18.84 mm
18. Prime
19. 6.04, 6.341, 6.4, 6.41
20. Numerator
Let me know if you'd like a printable version or visual diagrams for any of the problems!
Parent Tip: Review the logic above to help your child master the concept of math grade 5.
