To solve these problems, we need to find where each fraction lands on the number line. The trick is to make sure the fraction you are given matches the "steps" (the denominator) shown on the number line.
Here is the step-by-step solution for each problem:
1. Plot $\frac{1}{2}$
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Look at the number line: It is divided into halves ($\frac{0}{2}, \frac{1}{2}, \frac{2}{2}...$).
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Match the fraction: You have $\frac{1}{2}$. The bottom numbers match.
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Plot it: Count 1 step from 0.
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Location: At the mark labeled
$\frac{1}{2}$.
2. Plot $\frac{2}{4}$
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Look at the number line: It is divided into eighths ($\frac{1}{8}, \frac{2}{8}...$).
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Match the fraction: We need to change $\frac{2}{4}$ so the bottom number is 8.
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Calculate: Multiply the top and bottom by 2.
$$2 \times 2 = 4$$
$$4 \times 2 = 8$$
So, $\frac{2}{4}$ is the same as
$\frac{4}{8}$.
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Plot it: Count 4 steps from 0.
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Location: At the mark labeled
$\frac{4}{8}$.
3. Plot $\frac{2}{3}$
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Look at the number line: It is divided into ninths ($\frac{1}{9}, \frac{2}{9}...$).
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Match the fraction: We need to change $\frac{2}{3}$ so the bottom number is 9.
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Calculate: Multiply the top and bottom by 3.
$$2 \times 3 = 6$$
$$3 \times 3 = 9$$
So, $\frac{2}{3}$ is the same as
$\frac{6}{9}$.
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Plot it: Count 6 steps from 0.
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Location: At the mark labeled
$\frac{6}{9}$.
4. Plot $\frac{1}{4}$
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Look at the number line: It is divided into twelfths ($\frac{1}{12}, \frac{2}{12}...$).
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Match the fraction: We need to change $\frac{1}{4}$ so the bottom number is 12.
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Calculate: Multiply the top and bottom by 3.
$$1 \times 3 = 3$$
$$4 \times 3 = 12$$
So, $\frac{1}{4}$ is the same as
$\frac{3}{12}$.
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Plot it: Count 3 steps from 0.
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Location: At the mark labeled
$\frac{3}{12}$.
5. Plot $\frac{1}{3}$
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Look at the number line: It is divided into sixths ($\frac{1}{6}, \frac{2}{6}...$).
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Match the fraction: We need to change $\frac{1}{3}$ so the bottom number is 6.
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Calculate: Multiply the top and bottom by 2.
$$1 \times 2 = 2$$
$$3 \times 2 = 6$$
So, $\frac{1}{3}$ is the same as
$\frac{2}{6}$.
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Plot it: Count 2 steps from 0.
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Location: At the mark labeled
$\frac{2}{6}$.
6. Plot $\frac{9}{15}$
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Look at the number line: It is divided into fifths ($\frac{1}{5}, \frac{2}{5}...$).
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Match the fraction: We need to simplify $\frac{9}{15}$ so the bottom number is 5.
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Calculate: Divide the top and bottom by 3.
$$9 \div 3 = 3$$
$$15 \div 3 = 5$$
So, $\frac{9}{15}$ is the same as
$\frac{3}{5}$.
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Plot it: Count 3 steps from 0.
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Location: At the mark labeled
$\frac{3}{5}$.
Final Answer:
1. Plot at
$\frac{1}{2}$
2. Plot at
$\frac{4}{8}$
3. Plot at
$\frac{6}{9}$
4. Plot at
$\frac{3}{12}$
5. Plot at
$\frac{2}{6}$
6. Plot at
$\frac{3}{5}$
Parent Tip: Review the logic above to help your child master the concept of equivalent fractions on a number line worksheet 3rd grade.
