Math / Numbers & Operations

Question豨 $\frac{1}{4}+\frac{4}{5}-\frac{2}{5} \times \frac{1}{2}$

Studdy Solution

STEP 1

1. The expression to evaluate is $\frac{1}{4} + \frac{4}{5} - \frac{2}{5} \times \frac{1}{2}$ .
2. Follow the order of operations: parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right).

STEP 2

1. Evaluate the multiplication.
2. Perform the addition.
3. Perform the subtraction.

STEP 3

Evaluate the multiplication $\frac{2}{5} \times \frac{1}{2}$ .
$\frac{2}{5} \times \frac{1}{2} = \frac{2 \times 1}{5 \times 2} = \frac{2}{10} = \frac{1}{5}$

STEP 4

Perform the addition $\frac{1}{4} + \frac{4}{5}$ .
To add these fractions, find a common denominator. The least common multiple of $4$ and $5$ is $20$ .
Convert $\frac{1}{4}$ to $\frac{5}{20}$ and $\frac{4}{5}$ to $\frac{16}{20}$ .
$\frac{1}{4} + \frac{4}{5} = \frac{5}{20} + \frac{16}{20} = \frac{21}{20}$

STEP 5

Perform the subtraction $\frac{21}{20} - \frac{1}{5}$ .
Convert $\frac{1}{5}$ to $\frac{4}{20}$ .
$\frac{21}{20} - \frac{1}{5} = \frac{21}{20} - \frac{4}{20} = \frac{17}{20}$
The result of the expression is:
$\boxed{\frac{17}{20}}$

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