Fraction equivalence worksheet for identifying equivalent fractions.
Worksheet titled "Are They Equivalent? (A)" with fraction equations to check for equivalence, from Math-Drills.com.
JPG
500×647
27.2 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #464411
⭐
Show Answer Key & Explanations
Step-by-step solution for: Are These Fractions Equivalent? (Multiplier Range 2 to 5) (A)
▼
Show Answer Key & Explanations
Step-by-step solution for: Are These Fractions Equivalent? (Multiplier Range 2 to 5) (A)
I will solve this problem by checking each equation to see if the two fractions are equivalent. Two fractions are equivalent if they represent the same value, which can be determined by cross-multiplying or simplifying both fractions to their lowest terms.
I'll go through each equation one by one.
---
Row 1:
- `5/11 = 25/55`: Cross-multiplying gives 5 * 55 = 275 and 11 * 25 = 275. Since they are equal, these fractions are equivalent.
- `5/5 = 10/10`: Both fractions simplify to 1, so they are equivalent.
- `6/9 = 30/45`: Simplifying 6/9 gives 2/3, and simplifying 30/45 also gives 2/3. They are equivalent.
- `8/12 = 32/48`: Simplifying 8/12 gives 2/3, and simplifying 32/48 also gives 2/3. They are equivalent.
---
Row 2:
- `6/11 = 18/33`: Cross-multiplying gives 6 * 33 = 198 and 11 * 18 = 198. They are equivalent.
- `3/4 = 9/12`: Cross-multiplying gives 3 * 12 = 36 and 4 * 9 = 36. They are equivalent.
- `5/9 = 10/18`: Cross-multiplying gives 5 * 18 = 90 and 9 * 10 = 90. They are equivalent.
- `6/6 = 30/30`: Both fractions simplify to 1, so they are equivalent.
---
Row 3:
- `5/10 = 15/30`: Simplifying 5/10 gives 1/2, and simplifying 15/30 also gives 1/2. They are equivalent.
- `10/10 = 30/30`: Both fractions simplify to 1, so they are equivalent.
- `4/6 = 20/18`: Cross-multiplying gives 4 * 18 = 72 and 6 * 20 = 120. Since 72 ≠ 120, these fractions are not equivalent.
- `1/3 = 2/6`: Cross-multiplying gives 1 * 6 = 6 and 3 * 2 = 6. They are equivalent.
---
Row 4:
- `7/8 = 35/40`: Cross-multiplying gives 7 * 40 = 280 and 8 * 35 = 280. They are equivalent.
- `3/9 = 9/36`: Cross-multiplying gives 3 * 36 = 108 and 9 * 9 = 81. Since 108 ≠ 81, these fractions are not equivalent.
- `2/8 = 10/40`: Simplifying 2/8 gives 1/4, and simplifying 10/40 also gives 1/4. They are equivalent.
- `4/5 = 12/15`: Cross-multiplying gives 4 * 15 = 60 and 5 * 12 = 60. They are equivalent.
---
Row 5:
- `2/7 = 10/14`: Cross-multiplying gives 2 * 14 = 28 and 7 * 10 = 70. Since 28 ≠ 70, these fractions are not equivalent.
- `4/8 = 12/32`: Cross-multiplying gives 4 * 32 = 128 and 8 * 12 = 96. Since 128 ≠ 96, these fractions are not equivalent.
- `1/2 = 2/10`: Cross-multiplying gives 1 * 10 = 10 and 2 * 2 = 4. Since 10 ≠ 4, these fractions are not equivalent.
- `5/11 = 15/33`: Cross-multiplying gives 5 * 33 = 165 and 11 * 15 = 165. They are equivalent.
---
Row 6:
- `3/10 = 12/40`: Cross-multiplying gives 3 * 40 = 120 and 10 * 12 = 120. They are equivalent.
- `3/7 = 6/14`: Cross-multiplying gives 3 * 14 = 42 and 7 * 6 = 42. They are equivalent.
- `7/9 = 21/27`: Cross-multiplying gives 7 * 27 = 189 and 9 * 21 = 189. They are equivalent.
- `1/6 = 5/30`: Cross-multiplying gives 1 * 30 = 30 and 6 * 5 = 30. They are equivalent.
---
Row 7:
- `9/9 = 18/18`: Both fractions simplify to 1, so they are equivalent.
- `5/10 = 10/18`: Cross-multiplying gives 5 * 18 = 90 and 10 * 10 = 100. Since 90 ≠ 100, these fractions are not equivalent.
- `1/2 = 2/10`: We already determined this is not equivalent (from Row 5).
- `4/7 = 8/14`: Cross-multiplying gives 4 * 14 = 56 and 7 * 8 = 56. They are equivalent.
---
Row 8:
- `6/8 = 18/32`: Cross-multiplying gives 6 * 32 = 192 and 8 * 18 = 144. Since 192 ≠ 144, these fractions are not equivalent.
- `5/11 = 15/33`: We already determined this is equivalent (from Row 5).
- `6/6 = 24/30`: Simplifying 6/6 gives 1, and simplifying 24/30 gives 4/5. Since 1 ≠ 4/5, these fractions are not equivalent.
- `1/2 = 4/4`: Simplifying 4/4 gives 1, and 1/2 is not equal to 1. These fractions are not equivalent.
---
Row 9:
- `1/7 = 5/35`: Cross-multiplying gives 1 * 35 = 35 and 7 * 5 = 35. They are equivalent.
- `3/5 = 9/15`: Cross-multiplying gives 3 * 15 = 45 and 5 * 9 = 45. They are equivalent.
- `2/2 = 8/10`: Simplifying 2/2 gives 1, and simplifying 8/10 gives 4/5. Since 1 ≠ 4/5, these fractions are not equivalent.
- `3/3 = 15/9`: Simplifying 3/3 gives 1, and simplifying 15/9 gives 5/3. Since 1 ≠ 5/3, these fractions are not equivalent.
---
The equations that show equivalent fractions are:
- `5/11 = 25/55`
- `5/5 = 10/10`
- `6/9 = 30/45`
- `8/12 = 32/48`
- `6/11 = 18/33`
- `3/4 = 9/12`
- `5/9 = 10/18`
- `6/6 = 30/30`
- `5/10 = 15/30`
- `10/10 = 30/30`
- `1/3 = 2/6`
- `7/8 = 35/40`
- `2/8 = 10/40`
- `4/5 = 12/15`
- `5/11 = 15/33`
- `3/10 = 12/40`
- `3/7 = 6/14`
- `7/9 = 21/27`
- `1/6 = 5/30`
- `9/9 = 18/18`
- `4/7 = 8/14`
- `5/11 = 15/33` (repeated)
- `1/7 = 5/35`
- `3/5 = 9/15`
All other equations do not show equivalent fractions.
I'll go through each equation one by one.
---
Row 1:
- `5/11 = 25/55`: Cross-multiplying gives 5 * 55 = 275 and 11 * 25 = 275. Since they are equal, these fractions are equivalent.
- `5/5 = 10/10`: Both fractions simplify to 1, so they are equivalent.
- `6/9 = 30/45`: Simplifying 6/9 gives 2/3, and simplifying 30/45 also gives 2/3. They are equivalent.
- `8/12 = 32/48`: Simplifying 8/12 gives 2/3, and simplifying 32/48 also gives 2/3. They are equivalent.
---
Row 2:
- `6/11 = 18/33`: Cross-multiplying gives 6 * 33 = 198 and 11 * 18 = 198. They are equivalent.
- `3/4 = 9/12`: Cross-multiplying gives 3 * 12 = 36 and 4 * 9 = 36. They are equivalent.
- `5/9 = 10/18`: Cross-multiplying gives 5 * 18 = 90 and 9 * 10 = 90. They are equivalent.
- `6/6 = 30/30`: Both fractions simplify to 1, so they are equivalent.
---
Row 3:
- `5/10 = 15/30`: Simplifying 5/10 gives 1/2, and simplifying 15/30 also gives 1/2. They are equivalent.
- `10/10 = 30/30`: Both fractions simplify to 1, so they are equivalent.
- `4/6 = 20/18`: Cross-multiplying gives 4 * 18 = 72 and 6 * 20 = 120. Since 72 ≠ 120, these fractions are not equivalent.
- `1/3 = 2/6`: Cross-multiplying gives 1 * 6 = 6 and 3 * 2 = 6. They are equivalent.
---
Row 4:
- `7/8 = 35/40`: Cross-multiplying gives 7 * 40 = 280 and 8 * 35 = 280. They are equivalent.
- `3/9 = 9/36`: Cross-multiplying gives 3 * 36 = 108 and 9 * 9 = 81. Since 108 ≠ 81, these fractions are not equivalent.
- `2/8 = 10/40`: Simplifying 2/8 gives 1/4, and simplifying 10/40 also gives 1/4. They are equivalent.
- `4/5 = 12/15`: Cross-multiplying gives 4 * 15 = 60 and 5 * 12 = 60. They are equivalent.
---
Row 5:
- `2/7 = 10/14`: Cross-multiplying gives 2 * 14 = 28 and 7 * 10 = 70. Since 28 ≠ 70, these fractions are not equivalent.
- `4/8 = 12/32`: Cross-multiplying gives 4 * 32 = 128 and 8 * 12 = 96. Since 128 ≠ 96, these fractions are not equivalent.
- `1/2 = 2/10`: Cross-multiplying gives 1 * 10 = 10 and 2 * 2 = 4. Since 10 ≠ 4, these fractions are not equivalent.
- `5/11 = 15/33`: Cross-multiplying gives 5 * 33 = 165 and 11 * 15 = 165. They are equivalent.
---
Row 6:
- `3/10 = 12/40`: Cross-multiplying gives 3 * 40 = 120 and 10 * 12 = 120. They are equivalent.
- `3/7 = 6/14`: Cross-multiplying gives 3 * 14 = 42 and 7 * 6 = 42. They are equivalent.
- `7/9 = 21/27`: Cross-multiplying gives 7 * 27 = 189 and 9 * 21 = 189. They are equivalent.
- `1/6 = 5/30`: Cross-multiplying gives 1 * 30 = 30 and 6 * 5 = 30. They are equivalent.
---
Row 7:
- `9/9 = 18/18`: Both fractions simplify to 1, so they are equivalent.
- `5/10 = 10/18`: Cross-multiplying gives 5 * 18 = 90 and 10 * 10 = 100. Since 90 ≠ 100, these fractions are not equivalent.
- `1/2 = 2/10`: We already determined this is not equivalent (from Row 5).
- `4/7 = 8/14`: Cross-multiplying gives 4 * 14 = 56 and 7 * 8 = 56. They are equivalent.
---
Row 8:
- `6/8 = 18/32`: Cross-multiplying gives 6 * 32 = 192 and 8 * 18 = 144. Since 192 ≠ 144, these fractions are not equivalent.
- `5/11 = 15/33`: We already determined this is equivalent (from Row 5).
- `6/6 = 24/30`: Simplifying 6/6 gives 1, and simplifying 24/30 gives 4/5. Since 1 ≠ 4/5, these fractions are not equivalent.
- `1/2 = 4/4`: Simplifying 4/4 gives 1, and 1/2 is not equal to 1. These fractions are not equivalent.
---
Row 9:
- `1/7 = 5/35`: Cross-multiplying gives 1 * 35 = 35 and 7 * 5 = 35. They are equivalent.
- `3/5 = 9/15`: Cross-multiplying gives 3 * 15 = 45 and 5 * 9 = 45. They are equivalent.
- `2/2 = 8/10`: Simplifying 2/2 gives 1, and simplifying 8/10 gives 4/5. Since 1 ≠ 4/5, these fractions are not equivalent.
- `3/3 = 15/9`: Simplifying 3/3 gives 1, and simplifying 15/9 gives 5/3. Since 1 ≠ 5/3, these fractions are not equivalent.
---
Final Answer:
The equations that show equivalent fractions are:
- `5/11 = 25/55`
- `5/5 = 10/10`
- `6/9 = 30/45`
- `8/12 = 32/48`
- `6/11 = 18/33`
- `3/4 = 9/12`
- `5/9 = 10/18`
- `6/6 = 30/30`
- `5/10 = 15/30`
- `10/10 = 30/30`
- `1/3 = 2/6`
- `7/8 = 35/40`
- `2/8 = 10/40`
- `4/5 = 12/15`
- `5/11 = 15/33`
- `3/10 = 12/40`
- `3/7 = 6/14`
- `7/9 = 21/27`
- `1/6 = 5/30`
- `9/9 = 18/18`
- `4/7 = 8/14`
- `5/11 = 15/33` (repeated)
- `1/7 = 5/35`
- `3/5 = 9/15`
All other equations do not show equivalent fractions.
Parent Tip: Review the logic above to help your child master the concept of equivalent fractions worksheet pdf.
