Let's solve each problem step by step, following the format provided in the worksheet. We'll perform operations with rational numbers (fractions) and simplify answers.
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1) $\frac{2}{3} + \frac{7}{2}$
To add fractions, find a common denominator. The least common denominator (LCD) of 3 and 2 is
6.
$$
\frac{2}{3} + \frac{7}{2} = \frac{2(2) + 7(3)}{(3)(2)} = \frac{4 + 21}{6} = \frac{25}{6}
$$
✔ Final answer: $\boxed{\frac{25}{6}}$
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2) $-\frac{4}{5} + \frac{7}{10}$
LCD of 5 and 10 is
10.
$$
-\frac{4}{5} + \frac{7}{10} = \frac{-4(2) + 7(1)}{(5)(2)} = \frac{-8 + 7}{10} = \frac{-1}{10}
$$
✔ Final answer: $\boxed{-\frac{1}{10}}$
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3) $\frac{6}{5} - 5$
Write 5 as $\frac{5}{1}$, then subtract.
$$
\frac{6}{5} - 5 = \frac{6(1) - 5(5)}{(5)(1)} = \frac{6 - 25}{5} = \frac{-19}{5}
$$
✔ Final answer: $\boxed{-\frac{19}{5}}$
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4) $-\frac{7}{4} - \frac{3}{2}$
LCD of 4 and 2 is
4.
$$
-\frac{7}{4} - \frac{3}{2} = \frac{-7(1) - 3(2)}{(4)(1)} = \frac{-7 - 6}{4} = \frac{-13}{4}
$$
✔ Final answer: $\boxed{-\frac{13}{4}}$
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5) $\frac{2}{3} \cdot \left(-\frac{7}{4}\right)$
Multiply numerators and denominators:
$$
\frac{2}{3} \cdot \left(-\frac{7}{4}\right) = \frac{2 \cdot (-7)}{3 \cdot 4} = \frac{-14}{12}
$$
Simplify: divide numerator and denominator by 2 → $\frac{-7}{6}$
✔ Final answer: $\boxed{-\frac{7}{6}}$
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6) $-4 \cdot \left(-\frac{3}{2}\right)$
Convert $-4$ to fraction: $\frac{-4}{1}$
$$
-4 \cdot \left(-\frac{3}{2}\right) = \frac{-4 \cdot (-3)}{1 \cdot 2} = \frac{12}{2} = 6
$$
✔ Final answer: $\boxed{6}$
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7) $-\frac{3}{4} \div \frac{2}{5}$
Dividing fractions: multiply by reciprocal.
$$
-\frac{3}{4} \div \frac{2}{5} = -\frac{3}{4} \cdot \frac{5}{2} = \frac{-3 \cdot 5}{4 \cdot 2} = \frac{-15}{8}
$$
✔ Final answer: $\boxed{-\frac{15}{8}}$
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✔ Final Answers Summary:
1) $\frac{25}{6}$
2) $-\frac{1}{10}$
3) $-\frac{19}{5}$
4) $-\frac{13}{4}$
5) $-\frac{7}{6}$
6) $6$
7) $-\frac{15}{8}$
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Let me know if you'd like this filled into the worksheet format!
Parent Tip: Review the logic above to help your child master the concept of rational number worksheet.
