Let's solve each of the rational numbers and write them in
standard form.
🔷 What is the Standard Form of a Rational Number?
A rational number is in
standard form if:
- The denominator is
positive.
- The numerator and denominator have
no common factors other than 1 (i.e., the fraction is simplified).
- If the numerator is negative, the denominator should be positive.
So, we simplify each fraction and ensure the denominator is positive.
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Now, let's go through each one:
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1. (2/10)
Simplify:
GCD of 2 and 10 is 2.
→ (2 ÷ 2)/(10 ÷ 2) =
(1/5)
✔ Answer:
(1/5)
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2. (-8/36)
Simplify:
GCD of 8 and 36 is 4.
→ (-8 ÷ 4)/(36 ÷ 4) = (-2/9)
Denominator is positive → already in standard form.
✔ Answer:
(-2/9)
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3. (4/-16)
Negative denominator → convert to positive denominator by moving the negative sign to numerator:
= (-4/16)
Now simplify: GCD of 4 and 16 is 4
→ (-4 ÷ 4)/(16 ÷ 4) =
(-1/4)
✔ Answer:
(-1/4)
---
4. (-15/-35)
Both numerator and denominator are negative → becomes positive:
= (15/35)
Simplify: GCD of 15 and 35 is 5
→ (15 ÷ 5)/(35 ÷ 5) =
(3/7)
✔ Answer:
(3/7)
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5. (299/-161)
Negative denominator → move negative to numerator:
= (-299/161)
Now simplify:
Check GCD of 299 and 161.
Let’s find GCD:
- 299 ÷ 161 = 1 remainder 138
- 161 ÷ 138 = 1 remainder 23
- 138 ÷ 23 = 6 remainder 0 → GCD = 23
So divide both by 23:
- 299 ÷ 23 = 13
- 161 ÷ 23 = 7
→ (-13/7)
✔ Answer:
(-13/7)
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6. (-63/-210)
Both negative → becomes positive:
= (63/210)
Simplify: GCD of 63 and 210.
- 63 = 7×9 = 7×3²
- 210 = 2×3×5×7 → GCD = 21
Divide:
- 63 ÷ 21 = 3
- 210 ÷ 21 = 10
→ (3/10)
✔ Answer:
(3/10)
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7. (68/-119)
Negative denominator → move negative to numerator:
= (-68/119)
Simplify: GCD of 68 and 119.
- 68 = 2×2×17
- 119 = 7×17 → GCD = 17
Divide:
- 68 ÷ 17 = 4
- 119 ÷ 17 = 7
→ (-4/7)
✔ Answer:
(-4/7)
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8. (-195/275)
Denominator is positive, numerator negative → keep as is.
Simplify: GCD of 195 and 275.
- 195 = 5×39 = 5×3×13
- 275 = 5×55 = 5×5×11 → GCD = 5
Divide:
- 195 ÷ 5 = 39
- 275 ÷ 5 = 55
→ (-39/55)
Can this be simplified further?
GCD of 39 and 55:
- 39 = 3×13
- 55 = 5×11 → no common factors
So, final answer:
(-39/55)
✔ Answer:
(-39/55)
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9. (-2/-10)
Both negative → becomes positive:
= (2/10)
Simplify: GCD of 2 and 10 is 2
→ (1/5)
✔ Answer:
(1/5)
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10. (-7/14)
Simplify: GCD of 7 and 14 is 7
→ (-7 ÷ 7)/(14 ÷ 7) = (-1/2)
✔ Answer:
(-1/2)
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✔ Final Answers:
1. (2/10) =
(1/5)
2. (-8/36) =
(-2/9)
3. (4/-16) =
(-1/4)
4. (-15/-35) =
(3/7)
5. (299/-161) =
(-13/7)
6. (-63/-210) =
(3/10)
7. (68/-119) =
(-4/7)
8. (-195/275) =
(-39/55)
9. (-2/-10) =
(1/5)
10. (-7/14) =
(-1/2)
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Let me know if you'd like these explained step-by-step with diagrams or extra practice! 😊
Parent Tip: Review the logic above to help your child master the concept of numbers in standard form worksheet.
