Math / Numbers & Operations

Question $\frac{9}{10}+\frac{30}{100}$

Studdy Solution

STEP 1

1. We are adding two fractions: $\frac{9}{10}$ and $\frac{30}{100}$ .
2. The goal is to find the sum of these two fractions.

STEP 2

1. Find a common denominator.
2. Convert each fraction to have the common denominator.
3. Add the fractions.
4. Simplify the result, if necessary.

STEP 3

Identify the denominators of the fractions: $10$ and $100$ . The least common denominator (LCD) is $100$ .

STEP 4

Convert $\frac{9}{10}$ to a fraction with a denominator of $100$ .
Multiply the numerator and the denominator of $\frac{9}{10}$ by $10$ :
$\frac{9}{10} = \frac{9 \times 10}{10 \times 10} = \frac{90}{100}$

STEP 5

Add the fractions $\frac{90}{100}$ and $\frac{30}{100}$ :
$\frac{90}{100} + \frac{30}{100} = \frac{90 + 30}{100} = \frac{120}{100}$

STEP 6

Simplify $\frac{120}{100}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $20$ :
$\frac{120}{100} = \frac{120 \div 20}{100 \div 20} = \frac{6}{5}$
The sum of $\frac{9}{10} + \frac{30}{100}$ is:
$\boxed{\frac{6}{5}}$

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