Questions: 7/10 ÷ 5/8 + 3/4 · 1/3

Solution Steps

To solve the given expression, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). First, we will handle the division of fractions, then the multiplication, and finally the addition.

1. Divide \(\frac{7}{10}\) by \(\frac{5}{8}\).
2. Multiply \(\frac{3}{4}\) by \(\frac{1}{3}\).
3. Add the results from steps 1 and 2.

We start by dividing the fractions: \[ \frac{7}{10} \div \frac{5}{8} = \frac{7}{10} \cdot \frac{8}{5} = \frac{7 \cdot 8}{10 \cdot 5} = \frac{56}{50} = \frac{28}{25} \]

Next, we multiply the fractions: \[ \frac{3}{4} \cdot \frac{1}{3} = \frac{3 \cdot 1}{4 \cdot 3} = \frac{3}{12} = \frac{1}{4} \]

Now, we add the results from the previous steps: \[ \frac{28}{25} + \frac{1}{4} \] To add these fractions, we need a common denominator. The least common multiple of 25 and 4 is 100: \[ \frac{28}{25} = \frac{28 \cdot 4}{25 \cdot 4} = \frac{112}{100} \] \[ \frac{1}{4} = \frac{1 \cdot 25}{4 \cdot 25} = \frac{25}{100} \] Now we can add: \[ \frac{112}{100} + \frac{25}{100} = \frac{112 + 25}{100} = \frac{137}{100} \]

Final Answer