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Mathematics

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Here are the solutions for the number line problems shown in the image:

Adding fractions using number lines

  • a) The number line is divided into 4 equal parts.
  1. The first jump covers 2 parts, representing 24\frac{2}{4}.

    The second jump covers 1 part, representing 14\frac{1}{4}.

  2. Add the fractions.

    $$
    \frac{2}{4} + \frac{1}{4} = \frac{2+1}{4} = \boxed{\frac{3}{4}}
    $$
    
    • b) The number line is divided into 3 equal parts.
  3. The first jump covers 1 part, representing 13\frac{1}{3}.

    The second jump covers 1 part, representing 13\frac{1}{3}.

  4. Add the fractions.

    $$
    \frac{1}{3} + \frac{1}{3} = \frac{1+1}{3} = \boxed{\frac{2}{3}}
    $$
    
    • c) The number line is divided into 5 equal parts.
  5. The first jump covers 2 parts, representing 25\frac{2}{5}.

    The second jump covers 2 parts, representing 25\frac{2}{5}.

  6. Add the fractions.

    $$
    \frac{2}{5} + \frac{2}{5} = \frac{2+2}{5} = \boxed{\frac{4}{5}}
    $$
    
    • d) The number line is divided into 6 equal parts.
  7. The first jump covers 2 parts, representing 26\frac{2}{6}.

    The second jump covers 3 parts, representing 36\frac{3}{6}.

  8. Add the fractions.

    $$
    \frac{2}{6} + \frac{3}{6} = \frac{2+3}{6} = \boxed{\frac{5}{6}}
    $$
    
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