Add or subtract as indicated. Write answers in lowest terms as needed. 4(3/4) - 1(2/5)

Verified step by step guidance

1. First, distribute the numbers outside the parentheses to the fractions inside: $4\times \frac{3}{4}$ and $1\times \frac{2}{5}$.
2. Simplify each expression: $4\times \frac{3}{4}=\frac{12}{4}$ and $1\times \frac{2}{5}=\frac{2}{5}$.
3. Simplify $\frac{12}{4}$ to get $3$.
4. Now, subtract the two results: $3-\frac{2}{5}$.
5. To subtract, convert $3$ to a fraction with a common denominator: $\frac{15}{5}-\frac{2}{5}$.

Key Concepts

Multiplication of Fractions

To multiply a whole number by a fraction, convert the whole number into a fraction by placing it over 1. For example, 4 can be written as 4/1. Then, multiply the numerators together and the denominators together. In this case, 4(3/4) becomes (4/1)(3/4) = 12/4, which simplifies to 3.

Subtraction of Fractions

To subtract fractions, they must have a common denominator. If they do not, find the least common denominator (LCD) and convert each fraction accordingly. For example, to subtract 3 from a fraction with a different denominator, convert both fractions to have the same denominator before performing the subtraction.

Simplifying Fractions

After performing operations on fractions, it is essential to simplify the result to its lowest terms. This involves dividing both the numerator and the denominator by their greatest common divisor (GCD). For instance, if the result is 12/20, both can be divided by 4, simplifying it to 3/5.