Adkins Delgado
07/16/2024 · Primary School
d) \( 3 \cdot \frac{2}{9}+\frac{9}{16}: \frac{3}{8}= \)
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Tutor-Verified Answer
Step-by-step Solution
To solve the expression \( 3 \cdot \frac{2}{9} + \frac{9}{16} : \frac{3}{8} \), we will follow the order of operations (PEMDAS/BODMAS).
1. **Calculate \( 3 \cdot \frac{2}{9} \)**:
\[
3 \cdot \frac{2}{9} = \frac{3 \cdot 2}{9} = \frac{6}{9} = \frac{2}{3}
\]
2. **Calculate \( \frac{9}{16} : \frac{3}{8} \)**:
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{9}{16} : \frac{3}{8} = \frac{9}{16} \cdot \frac{8}{3}
\]
Now, multiply the fractions:
\[
= \frac{9 \cdot 8}{16 \cdot 3} = \frac{72}{48}
\]
Simplifying \( \frac{72}{48} \):
\[
= \frac{72 \div 24}{48 \div 24} = \frac{3}{2}
\]
3. **Now combine the results**:
We have \( \frac{2}{3} + \frac{3}{2} \). To add these fractions, we need a common denominator. The least common multiple of 3 and 2 is 6.
Convert \( \frac{2}{3} \) and \( \frac{3}{2} \) to have a denominator of 6:
\[
\frac{2}{3} = \frac{2 \cdot 2}{3 \cdot 2} = \frac{4}{6}
\]
\[
\frac{3}{2} = \frac{3 \cdot 3}{2 \cdot 3} = \frac{9}{6}
\]
4. **Add the fractions**:
\[
\frac{4}{6} + \frac{9}{6} = \frac{4 + 9}{6} = \frac{13}{6}
\]
Thus, the final result is:
\[
\boxed{\frac{13}{6}}
\]
Quick Answer
The final result is \( \frac{13}{6} \).
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