Grade 5 Maths Resources (Factors and Fractions Printable ... - Free Printable

Problem Overview:

The worksheet involves adding fractions and mixed numbers. The tasks are divided into two sections:

1. Section 1: Add the given fractions directly.
2. Section 2: Add the given fractions by first converting them to equivalent fractions with a common denominator.

We will solve each part step by step.

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Section 1: Add these numbers together

#### a) \( \frac{3}{7} + \frac{4}{7} \)
- Both fractions have the same denominator (7).
- Add the numerators: \( 3 + 4 = 7 \).
- The result is \( \frac{7}{7} \), which simplifies to \( 1 \).

Answer: \( 1 \)

#### b) \( \frac{9}{8} + \frac{11}{8} \)
- Both fractions have the same denominator (8).
- Add the numerators: \( 9 + 11 = 20 \).
- The result is \( \frac{20}{8} \), which simplifies to \( \frac{5}{2} \) (divide numerator and denominator by 4).

Answer: \( \frac{5}{2} \)

#### c) \( \frac{13}{6} + \frac{1}{6} \)
- Both fractions have the same denominator (6).
- Add the numerators: \( 13 + 1 = 14 \).
- The result is \( \frac{14}{6} \), which simplifies to \( \frac{7}{3} \) (divide numerator and denominator by 2).

Answer: \( \frac{7}{3} \)

#### d) \( \frac{16}{3} + \frac{5}{2} \)
- The denominators are different (3 and 2). Find the least common denominator (LCD), which is 6.
- Convert each fraction:
- \( \frac{16}{3} = \frac{16 \times 2}{3 \times 2} = \frac{32}{6} \)
- \( \frac{5}{2} = \frac{5 \times 3}{2 \times 3} = \frac{15}{6} \)
- Add the fractions: \( \frac{32}{6} + \frac{15}{6} = \frac{47}{6} \).

Answer: \( \frac{47}{6} \)

#### e) \( \frac{3}{4} + \frac{7}{8} \)
- The denominators are different (4 and 8). The LCD is 8.
- Convert each fraction:
- \( \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \)
- \( \frac{7}{8} \) remains \( \frac{7}{8} \).
- Add the fractions: \( \frac{6}{8} + \frac{7}{8} = \frac{13}{8} \).

Answer: \( \frac{13}{8} \)

#### f) \( \frac{13}{4} + \frac{5}{4} \)
- Both fractions have the same denominator (4).
- Add the numerators: \( 13 + 5 = 18 \).
- The result is \( \frac{18}{4} \), which simplifies to \( \frac{9}{2} \) (divide numerator and denominator by 2).

Answer: \( \frac{9}{2} \)

#### g) \( \frac{19}{4} + \frac{1}{12} \)
- The denominators are different (4 and 12). The LCD is 12.
- Convert each fraction:
- \( \frac{19}{4} = \frac{19 \times 3}{4 \times 3} = \frac{57}{12} \)
- \( \frac{1}{12} \) remains \( \frac{1}{12} \).
- Add the fractions: \( \frac{57}{12} + \frac{1}{12} = \frac{58}{12} \), which simplifies to \( \frac{29}{6} \) (divide numerator and denominator by 2).

Answer: \( \frac{29}{6} \)

#### h) \( \frac{7}{4} + \frac{9}{5} \)
- The denominators are different (4 and 5). The LCD is 20.
- Convert each fraction:
- \( \frac{7}{4} = \frac{7 \times 5}{4 \times 5} = \frac{35}{20} \)
- \( \frac{9}{5} = \frac{9 \times 4}{5 \times 4} = \frac{36}{20} \)
- Add the fractions: \( \frac{35}{20} + \frac{36}{20} = \frac{71}{20} \).

Answer: \( \frac{71}{20} \)

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Section 2: Add these numbers together. First, convert the fractions to equivalent fractions with the same denominator.

#### a) \( \frac{8}{8} + \frac{17}{8} \)
- Both fractions have the same denominator (8).
- Add the numerators: \( 8 + 17 = 25 \).
- The result is \( \frac{25}{8} \).

Answer: \( \frac{25}{8} \)

#### b) \( \frac{6}{4} + \frac{7}{16} \)
- The denominators are different (4 and 16). The LCD is 16.
- Convert each fraction:
- \( \frac{6}{4} = \frac{6 \times 4}{4 \times 4} = \frac{24}{16} \)
- \( \frac{7}{16} \) remains \( \frac{7}{16} \).
- Add the fractions: \( \frac{24}{16} + \frac{7}{16} = \frac{31}{16} \).

Answer: \( \frac{31}{16} \)

#### c) \( 11 \frac{1}{11} + \frac{5}{11} \)
- Convert the mixed number to an improper fraction:
- \( 11 \frac{1}{11} = \frac{11 \times 11 + 1}{11} = \frac{122}{11} \)
- Add the fractions:
- \( \frac{122}{11} + \frac{5}{11} = \frac{127}{11} \).

Answer: \( \frac{127}{11} \)

#### d) \( 6 \frac{1}{6} + 2 \frac{1}{7} \)
- Convert the mixed numbers to improper fractions:
- \( 6 \frac{1}{6} = \frac{6 \times 6 + 1}{6} = \frac{37}{6} \)
- \( 2 \frac{1}{7} = \frac{2 \times 7 + 1}{7} = \frac{15}{7} \)
- The denominators are different (6 and 7). The LCD is 42.
- Convert each fraction:
- \( \frac{37}{6} = \frac{37 \times 7}{6 \times 7} = \frac{259}{42} \)
- \( \frac{15}{7} = \frac{15 \times 6}{7 \times 6} = \frac{90}{42} \)
- Add the fractions: \( \frac{259}{42} + \frac{90}{42} = \frac{349}{42} \).

Answer: \( \frac{349}{42} \)

#### e) \( \frac{5}{9} + \frac{3}{8} \)
- The denominators are different (9 and 8). The LCD is 72.
- Convert each fraction:
- \( \frac{5}{9} = \frac{5 \times 8}{9 \times 8} = \frac{40}{72} \)
- \( \frac{3}{8} = \frac{3 \times 9}{8 \times 9} = \frac{27}{72} \)
- Add the fractions: \( \frac{40}{72} + \frac{27}{72} = \frac{67}{72} \).

Answer: \( \frac{67}{72} \)

#### f) \( 14 \frac{2}{5} + 3 \frac{7}{15} \)
- Convert the mixed numbers to improper fractions:
- \( 14 \frac{2}{5} = \frac{14 \times 5 + 2}{5} = \frac{72}{5} \)
- \( 3 \frac{7}{15} = \frac{3 \times 15 + 7}{15} = \frac{52}{15} \)
- The denominators are different (5 and 15). The LCD is 15.
- Convert each fraction:
- \( \frac{72}{5} = \frac{72 \times 3}{5 \times 3} = \frac{216}{15} \)
- \( \frac{52}{15} \) remains \( \frac{52}{15} \).
- Add the fractions: \( \frac{216}{15} + \frac{52}{15} = \frac{268}{15} \).

Answer: \( \frac{268}{15} \)

#### g) \( 2 \frac{13}{18} + 19 \frac{13}{18} \)
- Convert the mixed numbers to improper fractions:
- \( 2 \frac{13}{18} = \frac{2 \times 18 + 13}{18} = \frac{49}{18} \)
- \( 19 \frac{13}{18} = \frac{19 \times 18 + 13}{18} = \frac{355}{18} \)
- Add the fractions: \( \frac{49}{18} + \frac{355}{18} = \frac{404}{18} \), which simplifies to \( \frac{202}{9} \) (divide numerator and denominator by 2).

Answer: \( \frac{202}{9} \)

#### h) \( 3 \frac{2}{8} + 7 \frac{7}{8} \)
- Simplify the fractions first:
- \( 3 \frac{2}{8} = 3 \frac{1}{4} \) (simplify \( \frac{2}{8} \) to \( \frac{1}{4} \))
- \( 7 \frac{7}{8} \) remains as is.
- Convert the mixed numbers to improper fractions:
- \( 3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{13}{4} \)
- \( 7 \frac{7}{8} = \frac{7 \times 8 + 7}{8} = \frac{63}{8} \)
- The denominators are different (4 and 8). The LCD is 8.
- Convert each fraction:
- \( \frac{13}{4} = \frac{13 \times 2}{4 \times 2} = \frac{26}{8} \)
- \( \frac{63}{8} \) remains \( \frac{63}{8} \).
- Add the fractions: \( \frac{26}{8} + \frac{63}{8} = \frac{89}{8} \).

Answer: \( \frac{89}{8} \)

#### i) \( 2 \frac{3}{4} + 6 \frac{9}{6} \)
- Simplify the fractions first:
- \( 2 \frac{3}{4} \) remains as is.
- \( 6 \frac{9}{6} = 6 \frac{3}{2} = 7 \frac{1}{2} \) (simplify \( \frac{9}{6} \) to \( \frac{3}{2} \), then convert to a mixed number).
- Convert the mixed numbers to improper fractions:
- \( 2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{11}{4} \)
- \( 7 \frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{15}{2} \)
- The denominators are different (4 and 2). The LCD is 4.
- Convert each fraction:
- \( \frac{11}{4} \) remains \( \frac{11}{4} \)
- \( \frac{15}{2} = \frac{15 \times 2}{2 \times 2} = \frac{30}{4} \)
- Add the fractions: \( \frac{11}{4} + \frac{30}{4} = \frac{41}{4} \).

Answer: \( \frac{41}{4} \)

#### j) \( 5 \frac{5}{36} + 3 \frac{8}{36} \)
- Add the whole numbers and the fractions separately:
- Whole numbers: \( 5 + 3 = 8 \)
- Fractions: \( \frac{5}{36} + \frac{8}{36} = \frac{13}{36} \)
- Combine: \( 8 \frac{13}{36} \).

Answer: \( 8 \frac{13}{36} \)

#### k) \( 4 \frac{1}{9} + 4 \frac{1}{12} \)
- Convert the mixed numbers to improper fractions:
- \( 4 \frac{1}{9} = \frac{4 \times 9 + 1}{9} = \frac{37}{9} \)
- \( 4 \frac{1}{12} = \frac{4 \times 12 + 1}{12} = \frac{49}{12} \)
- The denominators are different (9 and 12). The LCD is 36.
- Convert each fraction:
- \( \frac{37}{9} = \frac{37 \times 4}{9 \times 4} = \frac{148}{36} \)
- \( \frac{49}{12} = \frac{49 \times 3}{12 \times 3} = \frac{147}{36} \)
- Add the fractions: \( \frac{148}{36} + \frac{147}{36} = \frac{295}{36} \).

Answer: \( \frac{295}{36} \)

#### l) \( 1 \frac{1}{3} + 5 \frac{2}{7} \)
- Convert the mixed numbers to improper fractions:
- \( 1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{4}{3} \)
- \( 5 \frac{2}{7} = \frac{5 \times 7 + 2}{7} = \frac{37}{7} \)
- The denominators are different (3 and 7). The LCD is 21.
- Convert each fraction:
- \( \frac{4}{3} = \frac{4 \times 7}{3 \times 7} = \frac{28}{21} \)
- \( \frac{37}{7} = \frac{37 \times 3}{7 \times 3} = \frac{111}{21} \)
- Add the fractions: \( \frac{28}{21} + \frac{111}{21} = \frac{139}{21} \).

Answer: \( \frac{139}{21} \)

#### m) \( 14 \frac{2}{5} + 11 \frac{7}{15} \)
- Convert the mixed numbers to improper fractions:
- \( 14 \frac{2}{5} = \frac{14 \times 5 + 2}{5} = \frac{72}{5} \)
- \( 11 \frac{7}{15} = \frac{11 \times 15 + 7}{15} = \frac{172}{15} \)
- The denominators are different (5 and 15). The LCD is 15.
- Convert each fraction:
- \( \frac{72}{5} = \frac{72 \times 3}{5 \times 3} = \frac{216}{15} \)
- \( \frac{172}{15} \) remains \( \frac{172}{15} \).
- Add the fractions: \( \frac{216}{15} + \frac{172}{15} = \frac{388}{15} \).

Answer: \( \frac{388}{15} \)

#### n) \( 2 \frac{2}{4} + 10 \frac{7}{7} \)
- Simplify the fractions first:
- \( 2 \frac{2}{4} = 2 \frac{1}{2} \) (simplify \( \frac{2}{4} \) to \( \frac{1}{2} \))
- \( 10 \frac{7}{7} = 11 \) (simplify \( \frac{7}{7} \) to 1, then add to the whole number).
- Convert the mixed numbers to improper fractions:
- \( 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2} \)
- \( 11 = \frac{11}{1} \)
- The denominators are different (2 and 1). The LCD is 2.
- Convert each fraction:
- \( \frac{5}{2} \) remains \( \frac{5}{2} \)
- \( \frac{11}{1} = \frac{11 \times 2}{1 \times 2} = \frac{22}{2} \)
- Add the fractions: \( \frac{5}{2} + \frac{22}{2} = \frac{27}{2} \).

Answer: \( \frac{27}{2} \)

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Final Answers:

1. Section 1:
- a) \( \boxed{1} \)
- b) \( \boxed{\frac{5}{2}} \)
- c) \( \boxed{\frac{7}{3}} \)
- d) \( \boxed{\frac{47}{6}} \)
- e) \( \boxed{\frac{13}{8}} \)
- f) \( \boxed{\frac{9}{2}} \)
- g) \( \boxed{\frac{29}{6}} \)
- h) \( \boxed{\frac{71}{20}} \)

2. Section 2:
- a) \( \boxed{\frac{25}{8}} \)
- b) \( \boxed{\frac{31}{16}} \)
- c) \( \boxed{\frac{127}{11}} \)
- d) \( \boxed{\frac{349}{42}} \)
- e) \( \boxed{\frac{67}{72}} \)
- f) \( \boxed{\frac{268}{15}} \)
- g) \( \boxed{\frac{202}{9}} \)
- h) \( \boxed{\frac{89}{8}} \)
- i) \( \boxed{\frac{41}{4}} \)
- j) \( \boxed{8 \frac{13}{36}} \)
- k) \( \boxed{\frac{295}{36}} \)
- l) \( \boxed{\frac{139}{21}} \)
- m) \( \boxed{\frac{388}{15}} \)
- n) \( \boxed{\frac{27}{2}} \)