Question

there is a grid paper with some hand - written numbers and symbols, including 4, 3/5, 9/10 and a + sign, and there is also a coordinate - like structure with an x - axis (the horizontal arrow) and a y - axis (the vertical line with a dot at the top).

Explanation:

Answer:

To solve the addition of the mixed number \( 4\frac{3}{5} \) and the fraction \( \frac{9}{10} \), we follow these steps:

Step 1: Convert the mixed number to an improper fraction

A mixed number \( a\frac{b}{c} \) can be converted to an improper fraction using the formula \( \frac{a \times c + b}{c} \). For \( 4\frac{3}{5} \):

$$ 4\frac{3}{5} = \frac{4 \times 5 + 3}{5} = \frac{20 + 3}{5} = \frac{23}{5} $$

Step 2: Find a common denominator

The denominators of the two fractions are 5 and 10. The least common denominator (LCD) of 5 and 10 is 10. We convert \( \frac{23}{5} \) to a fraction with denominator 10:

$$ \frac{23}{5} = \frac{23 \times 2}{5 \times 2} = \frac{46}{10} $$

Step 3: Add the two fractions

Now we add \( \frac{46}{10} \) and \( \frac{9}{10} \):

$$ \frac{46}{10} + \frac{9}{10} = \frac{46 + 9}{10} = \frac{55}{10} $$

Step 4: Simplify the result

We can simplify \( \frac{55}{10} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 5:

$$ \frac{55 \div 5}{10 \div 5} = \frac{11}{2} $$

We can also express this as a mixed number:

$$ \frac{11}{2} = 5\frac{1}{2} $$

So the sum of \( 4\frac{3}{5} \) and \( \frac{9}{10} \) is \( \frac{11}{2} \) or \( 5\frac{1}{2} \).