How To Add Fractions and Mixed Numbers — Steemit - Free Printable

To solve the problem, we need to analyze each shape in the worksheet and determine the improper fraction and mixed number representation for the colored portions. Let's go through each question step by step.

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1)

- Shapes: 4 circles, with 3 full circles and 1 partial circle (1/3 of a circle).
- Improper Fraction:
- Total parts: \( 3 \times 3 + 1 = 10 \)
- Denominator: 3 (since each circle is divided into 3 parts)
- Improper fraction: \( \frac{10}{3} \)
- Mixed Number:
- Whole number: 3 (from the 3 full circles)
- Fraction: \( \frac{1}{3} \)
- Mixed number: \( 3 \frac{1}{3} \)

Answer:
- Improper Fraction: \( \frac{10}{3} \)
- Mixed Number: \( 3 \frac{1}{3} \)

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2)

- Shapes: 2 squares, both fully shaded.
- Improper Fraction:
- Total parts: \( 2 \times 1 = 2 \)
- Denominator: 1 (since each square is not divided into smaller parts)
- Improper fraction: \( \frac{2}{1} \)
- Mixed Number:
- Whole number: 2
- Fraction: 0
- Mixed number: \( 2 \)

Answer:
- Improper Fraction: \( \frac{2}{1} \)
- Mixed Number: \( 2 \)

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3)

- Shapes: 5 triangles, with 4 full triangles and 1 partial triangle (1/5 of a triangle).
- Improper Fraction:
- Total parts: \( 4 \times 5 + 1 = 21 \)
- Denominator: 5 (since each triangle is divided into 5 parts)
- Improper fraction: \( \frac{21}{5} \)
- Mixed Number:
- Whole number: 4 (from the 4 full triangles)
- Fraction: \( \frac{1}{5} \)
- Mixed number: \( 4 \frac{1}{5} \)

Answer:
- Improper Fraction: \( \frac{21}{5} \)
- Mixed Number: \( 4 \frac{1}{5} \)

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4)

- Shapes: 3 diamonds, all fully shaded.
- Improper Fraction:
- Total parts: \( 3 \times 1 = 3 \)
- Denominator: 1 (since each diamond is not divided into smaller parts)
- Improper fraction: \( \frac{3}{1} \)
- Mixed Number:
- Whole number: 3
- Fraction: 0
- Mixed number: \( 3 \)

Answer:
- Improper Fraction: \( \frac{3}{1} \)
- Mixed Number: \( 3 \)

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5)

- Shapes: 4 pentagons, with 3 full pentagons and 1 partial pentagon (1/4 of a pentagon).
- Improper Fraction:
- Total parts: \( 3 \times 4 + 1 = 13 \)
- Denominator: 4 (since each pentagon is divided into 4 parts)
- Improper fraction: \( \frac{13}{4} \)
- Mixed Number:
- Whole number: 3 (from the 3 full pentagons)
- Fraction: \( \frac{1}{4} \)
- Mixed number: \( 3 \frac{1}{4} \)

Answer:
- Improper Fraction: \( \frac{13}{4} \)
- Mixed Number: \( 3 \frac{1}{4} \)

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6)

- Shapes: 2 rectangles, each divided into 4 parts. The first rectangle is fully shaded, and the second has 3 out of 4 parts shaded.
- Improper Fraction:
- Total parts: \( 4 + 3 = 7 \)
- Denominator: 4 (since each rectangle is divided into 4 parts)
- Improper fraction: \( \frac{7}{4} \)
- Mixed Number:
- Whole number: 1 (from the 1 full rectangle)
- Fraction: \( \frac{3}{4} \)
- Mixed number: \( 1 \frac{3}{4} \)

Answer:
- Improper Fraction: \( \frac{7}{4} \)
- Mixed Number: \( 1 \frac{3}{4} \)

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7)

- Shapes: 3 grids, each divided into 9 parts. The first two grids are fully shaded, and the third has 5 out of 9 parts shaded.
- Improper Fraction:
- Total parts: \( 2 \times 9 + 5 = 23 \)
- Denominator: 9 (since each grid is divided into 9 parts)
- Improper fraction: \( \frac{23}{9} \)
- Mixed Number:
- Whole number: 2 (from the 2 full grids)
- Fraction: \( \frac{5}{9} \)
- Mixed number: \( 2 \frac{5}{9} \)

Answer:
- Improper Fraction: \( \frac{23}{9} \)
- Mixed Number: \( 2 \frac{5}{9} \)

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8)

- Shapes: 3 parallelograms, with 2 full parallelograms and 1 partial parallelogram (1/2 of a parallelogram).
- Improper Fraction:
- Total parts: \( 2 \times 2 + 1 = 5 \)
- Denominator: 2 (since each parallelogram is divided into 2 parts)
- Improper fraction: \( \frac{5}{2} \)
- Mixed Number:
- Whole number: 2 (from the 2 full parallelograms)
- Fraction: \( \frac{1}{2} \)
- Mixed number: \( 2 \frac{1}{2} \)

Answer:
- Improper Fraction: \( \frac{5}{2} \)
- Mixed Number: \( 2 \frac{1}{2} \)

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9)

- Shapes: 6 rectangles, all fully shaded.
- Improper Fraction:
- Total parts: \( 6 \times 1 = 6 \)
- Denominator: 1 (since each rectangle is not divided into smaller parts)
- Improper fraction: \( \frac{6}{1} \)
- Mixed Number:
- Whole number: 6
- Fraction: 0
- Mixed number: \( 6 \)

Answer:
- Improper Fraction: \( \frac{6}{1} \)
- Mixed Number: \( 6 \)

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10)

- Shapes: 2 grids, each divided into 6 parts. The first grid is fully shaded, and the second has 4 out of 6 parts shaded.
- Improper Fraction:
- Total parts: \( 6 + 4 = 10 \)
- Denominator: 6 (since each grid is divided into 6 parts)
- Improper fraction: \( \frac{10}{6} \)
- Simplify: \( \frac{10}{6} = \frac{5}{3} \)
- Mixed Number:
- Whole number: 1 (from the 1 full grid)
- Fraction: \( \frac{2}{3} \)
- Mixed number: \( 1 \frac{2}{3} \)

Answer:
- Improper Fraction: \( \frac{5}{3} \)
- Mixed Number: \( 1 \frac{2}{3} \)

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Final Answers:

1. Improper Fraction: \( \frac{10}{3} \), Mixed Number: \( 3 \frac{1}{3} \)
2. Improper Fraction: \( \frac{2}{1} \), Mixed Number: \( 2 \)
3. Improper Fraction: \( \frac{21}{5} \), Mixed Number: \( 4 \frac{1}{5} \)
4. Improper Fraction: \( \frac{3}{1} \), Mixed Number: \( 3 \)
5. Improper Fraction: \( \frac{13}{4} \), Mixed Number: \( 3 \frac{1}{4} \)
6. Improper Fraction: \( \frac{7}{4} \), Mixed Number: \( 1 \frac{3}{4} \)
7. Improper Fraction: \( \frac{23}{9} \), Mixed Number: \( 2 \frac{5}{9} \)
8. Improper Fraction: \( \frac{5}{2} \), Mixed Number: \( 2 \frac{1}{2} \)
9. Improper Fraction: \( \frac{6}{1} \), Mixed Number: \( 6 \)
10. Improper Fraction: \( \frac{5}{3} \), Mixed Number: \( 1 \frac{2}{3} \)

\boxed{
\begin{array}{ccc}
1) & \frac{10}{3} & 3 \frac{1}{3} \\
2) & \frac{2}{1} & 2 \\
3) & \frac{21}{5} & 4 \frac{1}{5} \\
4) & \frac{3}{1} & 3 \\
5) & \frac{13}{4} & 3 \frac{1}{4} \\
6) & \frac{7}{4} & 1 \frac{3}{4} \\
7) & \frac{23}{9} & 2 \frac{5}{9} \\
8) & \frac{5}{2} & 2 \frac{1}{2} \\
9) & \frac{6}{1} & 6 \\
10) & \frac{5}{3} & 1 \frac{2}{3} \\
\end{array}
}