Number Teaching Resources - Free Printable

Let's solve each problem step-by-step and simplify the answers as required.

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Section A: Add or Subtract. Simplify Answers

1) $\frac{1}{7} + \frac{3}{7} = \frac{4}{7}$
→ Same denominator, add numerators: $1 + 3 = 4$

2) $\frac{2}{5} + \frac{8}{15}$
→ Find common denominator: LCM of 5 and 15 is 15
$\frac{2}{5} = \frac{6}{15}$, so $\frac{6}{15} + \frac{8}{15} = \frac{14}{15}$

3) $\frac{2}{3} + \frac{1}{4}$
→ LCM of 3 and 4 is 12
$\frac{2}{3} = \frac{8}{12}, \frac{1}{4} = \frac{3}{12}$ → $\frac{8+3}{12} = \frac{11}{12}$

4) $\frac{3}{10} - \frac{1}{10} = \frac{2}{10} = \frac{1}{5}$
→ Same denominator, subtract numerators, then simplify

5) $\frac{11}{24} - \frac{3}{8}$
→ Convert $\frac{3}{8} = \frac{9}{24}$
$\frac{11}{24} - \frac{9}{24} = \frac{2}{24} = \frac{1}{12}$

6) $\frac{5}{6} - \frac{1}{16}$
→ LCM of 6 and 16 is 48
$\frac{5}{6} = \frac{40}{48}, \frac{1}{16} = \frac{3}{48}$
$\frac{40 - 3}{48} = \frac{37}{48}$

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Section B: Multiply or Divide. Simplify Answers

1) $\frac{2}{7} \times \frac{3}{5} = \frac{6}{35}$
→ Multiply numerators and denominators: $2×3=6$, $7×5=35$ → already simplified

2) $\frac{5}{8} \times \frac{2}{3} = \frac{10}{24} = \frac{5}{12}$
→ $5×2=10$, $8×3=24$, simplify by dividing numerator and denominator by 2

3) $\frac{8}{9} \times \frac{3}{10} = \frac{24}{90} = \frac{4}{15}$
→ $8×3=24$, $9×10=90$, divide numerator and denominator by 6

4) $\frac{9}{11} \div \frac{5}{6} = \frac{9}{11} \times \frac{6}{5} = \frac{54}{55}$
→ Change division to multiplication by reciprocal: $\frac{9×6}{11×5} = \frac{54}{55}$ → already simplified

5) $\frac{3}{8} \div \frac{5}{12} = \frac{3}{8} \times \frac{12}{5} = \frac{36}{40} = \frac{9}{10}$
→ $3×12=36$, $8×5=40$, simplify by dividing by 4

6) $\frac{8}{12} \div 4 = \frac{8}{12} \times \frac{1}{4} = \frac{8}{48} = \frac{1}{6}$
→ First simplify $\frac{8}{12} = \frac{2}{3}$, but we can do directly: $\frac{8}{12} × \frac{1}{4} = \frac{8}{48} = \frac{1}{6}$

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Section C: Simplify and Leave as Mixed Numbers

1) $12 + \frac{8}{11} = 12\frac{8}{11}$
→ Already a mixed number

2) $\frac{7}{15} \times 9 = \frac{63}{15} = \frac{21}{5} = 4\frac{1}{5}$
→ $7×9=63$, $63 ÷ 15 = 4.2$, or $\frac{63}{15} = \frac{21}{5} = 4\frac{1}{5}$

3) $12 - \frac{8}{3}$
→ Convert 12 to thirds: $12 = \frac{36}{3}$, so $\frac{36}{3} - \frac{8}{3} = \frac{28}{3} = 9\frac{1}{3}$

4) $1\frac{2}{3} - \frac{2}{9}$
→ Convert $1\frac{2}{3} = \frac{5}{3} = \frac{15}{9}$
$\frac{15}{9} - \frac{2}{9} = \frac{13}{9} = 1\frac{4}{9}$

5) $\frac{12}{5} + \frac{4}{6}$
→ Simplify $\frac{4}{6} = \frac{2}{3}$
Now find LCM of 5 and 3 = 15
$\frac{12}{5} = \frac{36}{15}, \frac{2}{3} = \frac{10}{15}$ → $\frac{46}{15} = 3\frac{1}{15}$

6) $10 \div \frac{4}{7} = 10 \times \frac{7}{4} = \frac{70}{4} = \frac{35}{2} = 17\frac{1}{2}$

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Extension Problem

$$
\frac{2}{10}\left(\left(\frac{1}{12} + \frac{3}{4}\right) \div \frac{4}{7}\right)
$$

Step 1: Simplify inside parentheses:
$\frac{1}{12} + \frac{3}{4}$
LCM of 12 and 4 is 12
$\frac{1}{12} + \frac{9}{12} = \frac{10}{12} = \frac{5}{6}$

Step 2: Divide by $\frac{4}{7}$:
$\frac{5}{6} \div \frac{4}{7} = \frac{5}{6} \times \frac{7}{4} = \frac{35}{24}$

Step 3: Multiply by $\frac{2}{10} = \frac{1}{5}$:
$\frac{1}{5} \times \frac{35}{24} = \frac{35}{120} = \frac{7}{24}$

→ Final answer: $\boxed{\frac{7}{24}}$

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✔ Final Answers:

#### Section A
1) $\frac{4}{7}$
2) $\frac{14}{15}$
3) $\frac{11}{12}$
4) $\frac{1}{5}$
5) $\frac{1}{12}$
6) $\frac{37}{48}$

#### Section B
1) $\frac{6}{35}$
2) $\frac{5}{12}$
3) $\frac{4}{15}$
4) $\frac{54}{55}$
5) $\frac{9}{10}$
6) $\frac{1}{6}$

#### Section C
1) $12\frac{8}{11}$
2) $4\frac{1}{5}$
3) $9\frac{1}{3}$
4) $1\frac{4}{9}$
5) $3\frac{1}{15}$
6) $17\frac{1}{2}$

#### Extension
$\boxed{\frac{7}{24}}$

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