College

Add the following numbers and provide the answer as a mixed number in lowest terms.

[tex] 2 \frac{15}{25} + 1 \frac{12}{25} [/tex]

Answer :

We start by writing each number as a mixed number. The first number is given as a decimal, which we interpret as a mixed number:

[tex]$$
2.15 = 2 + \frac{15}{100}.
$$[/tex]

Notice that the fraction can be simplified by dividing the numerator and denominator by 5:

[tex]$$
\frac{15}{100} = \frac{15\div5}{100\div5} = \frac{3}{20}.
$$[/tex]

Thus, the first number becomes

[tex]$$
2\frac{3}{20}.
$$[/tex]

The second number is already given as a mixed number:

[tex]$$
1\frac{12}{25}.
$$[/tex]

Next, we add the fractional parts. To do this, we need a common denominator for [tex]$\frac{3}{20}$[/tex] and [tex]$\frac{12}{25}$[/tex]. The least common denominator of 20 and 25 is 100.

Convert each fraction to an equivalent fraction with a denominator of 100:

For the first fraction:

[tex]$$
\frac{3}{20} = \frac{3 \times 5}{20 \times 5} = \frac{15}{100},
$$[/tex]

and for the second fraction:

[tex]$$
\frac{12}{25} = \frac{12 \times 4}{25 \times 4} = \frac{48}{100}.
$$[/tex]

Now, add these fractions:

[tex]$$
\frac{15}{100}+\frac{48}{100} = \frac{15+48}{100} = \frac{63}{100}.
$$[/tex]

Then, add the whole numbers:

[tex]$$
2 + 1 = 3.
$$[/tex]

Thus, the complete sum expressed as a mixed number is:

[tex]$$
3\frac{63}{100}.
$$[/tex]

The fraction [tex]$\frac{63}{100}$[/tex] is already in lowest terms because the greatest common divisor of 63 and 100 is 1.