Of course! Let's solve each problem step by step by finding the equivalent fractions shown on the number lines.
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Problem ①
Top number line: Marked in fifths: `0, 1/5, 2/5, 3/5, 4/5, 1`
The orange dot is at
3/5.
Bottom number line: Marked in tenths: `0, 1/10, 2/10, ..., 9/10, 1`
We need to find which tenth aligns with 3/5.
Since 5 × 2 = 10, we multiply numerator and denominator of 3/5 by 2:
>
3/5 = (3×2)/(5×2) = 6/10
✔ The dot on the bottom line is at
6/10, which matches.
Answer: 3/5 = 6/10
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Problem ②
Top number line: Marked in tenths: `0, 4/10, 6/10, 8/10, 1`
The orange dot is at
8/10.
Bottom number line: Marked in twentieths: `0, 8/20, 10/20, ..., 18/20, 1`
We need to find which twentieth aligns with 8/10.
Since 10 × 2 = 20, multiply numerator and denominator of 8/10 by 2:
>
8/10 = (8×2)/(10×2) = 16/20
✔ The dot on the bottom line is at
16/20, which matches.
Answer: 8/10 = 16/20
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Problem ③
Top number line: Marked in sevenths: `0, 3/7, 4/7, 5/7, 6/7, 1`
The orange dot is at
5/7.
Bottom number line: Marked in twenty-eighths: `0, 12/28, 14/28, ..., 26/28, 1`
We need to find which twenty-eighth aligns with 5/7.
Since 7 × 4 = 28, multiply numerator and denominator of 5/7 by 4:
>
5/7 = (5×4)/(7×4) = 20/28
✔ The dot on the bottom line is at
20/28, which matches.
Answer: 5/7 = 20/28
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Problem ④
Top number line: Marked in fourteenths: `0, 2/14, 4/14, 6/14, 8/14, 10/14, 12/14, 1`
The orange dot is at
10/14.
Bottom number line: Marked in sevenths: `0, 1/7, 3/7, 5/7, 1`
We need to find which seventh aligns with 10/14.
Since 14 ÷ 2 = 7, divide numerator and denominator of 10/14 by 2:
>
10/14 = (10÷2)/(14÷2) = 5/7
✔ The dot on the bottom line is at
5/7, which matches.
Answer: 10/14 = 5/7
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✔ Final Answers:
1.
3/5 = 6/10
2.
8/10 = 16/20
3.
5/7 = 20/28
4.
10/14 = 5/7
These are all examples of
equivalent fractions — different fractions that represent the same point on a number line, or the same value. We found them by multiplying or dividing both numerator and denominator by the same number (finding a common denominator or simplifying).
Parent Tip: Review the logic above to help your child master the concept of plot fractions on a number line worksheet.
