Equivalent Fraction Patterns Worksheet Download - Free Printable
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Step-by-step solution for: Equivalent Fraction Patterns Worksheet Download
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Show Answer Key & Explanations
Step-by-step solution for: Equivalent Fraction Patterns Worksheet Download
To find the missing equivalent fractions, we need to look at the pattern in each row. Equivalent fractions are created by multiplying both the top number (numerator) and the bottom number (denominator) by the same number.
Here is the step-by-step solution for each problem:
1) The pattern starts with $\frac{8}{9}$. To get to the denominator 45, we multiply 9 by 5 ($9 \times 5 = 45$). So, we must multiply the numerator 8 by 5 as well.
$8 \times 5 = 40$.
The missing fraction is $\frac{40}{45}$.
2) The pattern ends with $\frac{6}{36}$. To get from the starting numerator 1 to 6, we multiply by 6. Let's check the denominator: $6 \times 6 = 36$. This matches.
The missing fraction is $\frac{6}{36}$.
3) The pattern ends with $\frac{12}{54}$. To get from the starting denominator 9 to 54, we multiply by 6 ($9 \times 6 = 54$). So, we multiply the starting numerator 2 by 6.
$2 \times 6 = 12$.
The missing fraction is $\frac{12}{54}$.
4) The pattern ends with $\frac{24}{36}$. To get from the starting denominator 6 to 36, we multiply by 6 ($6 \times 6 = 36$). So, we multiply the starting numerator 4 by 6.
$4 \times 6 = 24$.
The missing fraction is $\frac{24}{36}$.
5) The pattern ends with $\frac{6}{12}$. To get from the starting denominator 2 to 12, we multiply by 6 ($2 \times 6 = 12$). So, we multiply the starting numerator 1 by 6.
$1 \times 6 = 6$.
The missing fraction is $\frac{6}{12}$.
6) The pattern ends with $\frac{18}{36}$. To get from the starting denominator 6 to 36, we multiply by 6 ($6 \times 6 = 36$). So, we multiply the starting numerator 3 by 6.
$3 \times 6 = 18$.
The missing fraction is $\frac{18}{36}$.
7) The pattern ends with $\frac{30}{42}$. To get from the starting denominator 7 to 42, we multiply by 6 ($7 \times 6 = 42$). So, we multiply the starting numerator 5 by 6.
$5 \times 6 = 30$.
The missing fraction is $\frac{30}{42}$.
8) The pattern ends with $\frac{18}{24}$. To get from the starting denominator 4 to 24, we multiply by 6 ($4 \times 6 = 24$). So, we multiply the starting numerator 3 by 6.
$3 \times 6 = 18$.
The missing fraction is $\frac{18}{24}$.
9) The pattern ends with $\frac{24}{30}$. To get from the starting denominator 5 to 30, we multiply by 6 ($5 \times 6 = 30$). So, we multiply the starting numerator 4 by 6.
$4 \times 6 = 24$.
The missing fraction is $\frac{24}{30}$.
10) The pattern ends with $\frac{12}{18}$. To get from the starting denominator 3 to 18, we multiply by 6 ($3 \times 6 = 18$). So, we multiply the starting numerator 2 by 6.
$2 \times 6 = 12$.
The missing fraction is $\frac{12}{18}$.
11) The pattern ends with $\frac{30}{36}$. To get from the starting denominator 6 to 36, we multiply by 6 ($6 \times 6 = 36$). So, we multiply the starting numerator 5 by 6.
$5 \times 6 = 30$.
The missing fraction is $\frac{30}{36}$.
12) The pattern ends with $\frac{48}{60}$. To get from the starting denominator 10 to 60, we multiply by 6 ($10 \times 6 = 60$). So, we multiply the starting numerator 8 by 6.
$8 \times 6 = 48$.
The missing fraction is $\frac{48}{60}$.
13) The pattern ends with $\frac{15}{40}$. To get from the starting denominator 8 to 40, we multiply by 5 ($8 \times 5 = 40$). So, we multiply the starting numerator 3 by 5.
$3 \times 5 = 15$.
The missing fraction is $\frac{15}{40}$.
14) The pattern ends with $\frac{18}{30}$. To get from the starting denominator 5 to 30, we multiply by 6 ($5 \times 6 = 30$). So, we multiply the starting numerator 3 by 6.
$3 \times 6 = 18$.
The missing fraction is $\frac{18}{30}$.
15) The pattern ends with $\frac{54}{60}$. To get from the starting denominator 10 to 60, we multiply by 6 ($10 \times 6 = 60$). So, we multiply the starting numerator 9 by 6.
$9 \times 6 = 54$.
The missing fraction is $\frac{54}{60}$.
16) The pattern ends with $\frac{12}{42}$. To get from the starting denominator 7 to 42, we multiply by 6 ($7 \times 6 = 42$). So, we multiply the starting numerator 2 by 6.
$2 \times 6 = 12$.
The missing fraction is $\frac{12}{42}$.
17) The pattern ends with $\frac{30}{48}$. To get from the starting denominator 8 to 48, we multiply by 6 ($8 \times 6 = 48$). So, we multiply the starting numerator 5 by 6.
$5 \times 6 = 30$.
The missing fraction is $\frac{30}{48}$.
18) The pattern ends with $\frac{36}{60}$. To get from the starting denominator 10 to 60, we multiply by 6 ($10 \times 6 = 60$). So, we multiply the starting numerator 6 by 6.
$6 \times 6 = 36$.
The missing fraction is $\frac{36}{60}$.
19) The pattern ends with $\frac{10}{20}$. To get from the starting denominator 4 to 20, we multiply by 5 ($4 \times 5 = 20$). So, we multiply the starting numerator 2 by 5.
$2 \times 5 = 10$.
The missing fraction is $\frac{10}{20}$.
20) The pattern ends with $\frac{12}{60}$. To get from the starting denominator 10 to 60, we multiply by 6 ($10 \times 6 = 60$). So, we multiply the starting numerator 2 by 6.
$2 \times 6 = 12$.
The missing fraction is $\frac{12}{60}$.
Final Answer:
1. 40/45
2. 6/36
3. 12/54
4. 24/36
5. 6/12
6. 18/36
7. 30/42
8. 18/24
9. 24/30
10. 12/18
11. 30/36
12. 48/60
13. 15/40
14. 18/30
15. 54/60
16. 12/42
17. 30/48
18. 36/60
19. 10/20
20. 12/60
Here is the step-by-step solution for each problem:
1) The pattern starts with $\frac{8}{9}$. To get to the denominator 45, we multiply 9 by 5 ($9 \times 5 = 45$). So, we must multiply the numerator 8 by 5 as well.
$8 \times 5 = 40$.
The missing fraction is $\frac{40}{45}$.
2) The pattern ends with $\frac{6}{36}$. To get from the starting numerator 1 to 6, we multiply by 6. Let's check the denominator: $6 \times 6 = 36$. This matches.
The missing fraction is $\frac{6}{36}$.
3) The pattern ends with $\frac{12}{54}$. To get from the starting denominator 9 to 54, we multiply by 6 ($9 \times 6 = 54$). So, we multiply the starting numerator 2 by 6.
$2 \times 6 = 12$.
The missing fraction is $\frac{12}{54}$.
4) The pattern ends with $\frac{24}{36}$. To get from the starting denominator 6 to 36, we multiply by 6 ($6 \times 6 = 36$). So, we multiply the starting numerator 4 by 6.
$4 \times 6 = 24$.
The missing fraction is $\frac{24}{36}$.
5) The pattern ends with $\frac{6}{12}$. To get from the starting denominator 2 to 12, we multiply by 6 ($2 \times 6 = 12$). So, we multiply the starting numerator 1 by 6.
$1 \times 6 = 6$.
The missing fraction is $\frac{6}{12}$.
6) The pattern ends with $\frac{18}{36}$. To get from the starting denominator 6 to 36, we multiply by 6 ($6 \times 6 = 36$). So, we multiply the starting numerator 3 by 6.
$3 \times 6 = 18$.
The missing fraction is $\frac{18}{36}$.
7) The pattern ends with $\frac{30}{42}$. To get from the starting denominator 7 to 42, we multiply by 6 ($7 \times 6 = 42$). So, we multiply the starting numerator 5 by 6.
$5 \times 6 = 30$.
The missing fraction is $\frac{30}{42}$.
8) The pattern ends with $\frac{18}{24}$. To get from the starting denominator 4 to 24, we multiply by 6 ($4 \times 6 = 24$). So, we multiply the starting numerator 3 by 6.
$3 \times 6 = 18$.
The missing fraction is $\frac{18}{24}$.
9) The pattern ends with $\frac{24}{30}$. To get from the starting denominator 5 to 30, we multiply by 6 ($5 \times 6 = 30$). So, we multiply the starting numerator 4 by 6.
$4 \times 6 = 24$.
The missing fraction is $\frac{24}{30}$.
10) The pattern ends with $\frac{12}{18}$. To get from the starting denominator 3 to 18, we multiply by 6 ($3 \times 6 = 18$). So, we multiply the starting numerator 2 by 6.
$2 \times 6 = 12$.
The missing fraction is $\frac{12}{18}$.
11) The pattern ends with $\frac{30}{36}$. To get from the starting denominator 6 to 36, we multiply by 6 ($6 \times 6 = 36$). So, we multiply the starting numerator 5 by 6.
$5 \times 6 = 30$.
The missing fraction is $\frac{30}{36}$.
12) The pattern ends with $\frac{48}{60}$. To get from the starting denominator 10 to 60, we multiply by 6 ($10 \times 6 = 60$). So, we multiply the starting numerator 8 by 6.
$8 \times 6 = 48$.
The missing fraction is $\frac{48}{60}$.
13) The pattern ends with $\frac{15}{40}$. To get from the starting denominator 8 to 40, we multiply by 5 ($8 \times 5 = 40$). So, we multiply the starting numerator 3 by 5.
$3 \times 5 = 15$.
The missing fraction is $\frac{15}{40}$.
14) The pattern ends with $\frac{18}{30}$. To get from the starting denominator 5 to 30, we multiply by 6 ($5 \times 6 = 30$). So, we multiply the starting numerator 3 by 6.
$3 \times 6 = 18$.
The missing fraction is $\frac{18}{30}$.
15) The pattern ends with $\frac{54}{60}$. To get from the starting denominator 10 to 60, we multiply by 6 ($10 \times 6 = 60$). So, we multiply the starting numerator 9 by 6.
$9 \times 6 = 54$.
The missing fraction is $\frac{54}{60}$.
16) The pattern ends with $\frac{12}{42}$. To get from the starting denominator 7 to 42, we multiply by 6 ($7 \times 6 = 42$). So, we multiply the starting numerator 2 by 6.
$2 \times 6 = 12$.
The missing fraction is $\frac{12}{42}$.
17) The pattern ends with $\frac{30}{48}$. To get from the starting denominator 8 to 48, we multiply by 6 ($8 \times 6 = 48$). So, we multiply the starting numerator 5 by 6.
$5 \times 6 = 30$.
The missing fraction is $\frac{30}{48}$.
18) The pattern ends with $\frac{36}{60}$. To get from the starting denominator 10 to 60, we multiply by 6 ($10 \times 6 = 60$). So, we multiply the starting numerator 6 by 6.
$6 \times 6 = 36$.
The missing fraction is $\frac{36}{60}$.
19) The pattern ends with $\frac{10}{20}$. To get from the starting denominator 4 to 20, we multiply by 5 ($4 \times 5 = 20$). So, we multiply the starting numerator 2 by 5.
$2 \times 5 = 10$.
The missing fraction is $\frac{10}{20}$.
20) The pattern ends with $\frac{12}{60}$. To get from the starting denominator 10 to 60, we multiply by 6 ($10 \times 6 = 60$). So, we multiply the starting numerator 2 by 6.
$2 \times 6 = 12$.
The missing fraction is $\frac{12}{60}$.
Final Answer:
1. 40/45
2. 6/36
3. 12/54
4. 24/36
5. 6/12
6. 18/36
7. 30/42
8. 18/24
9. 24/30
10. 12/18
11. 30/36
12. 48/60
13. 15/40
14. 18/30
15. 54/60
16. 12/42
17. 30/48
18. 36/60
19. 10/20
20. 12/60
Parent Tip: Review the logic above to help your child master the concept of patterns with fractions worksheet.
