Let's solve the expression [tex]\( \frac{5}{8} + 1 \frac{3}{4} \)[/tex] step-by-step.
1. Convert the mixed number to an improper fraction:
The mixed number is [tex]\( 1 \frac{3}{4} \)[/tex]. To convert this to an improper fraction:
- Multiply the whole number part by the denominator: [tex]\( 1 \times 4 = 4 \)[/tex].
- Add the numerator to this product: [tex]\( 4 + 3 = 7 \)[/tex].
- So, [tex]\( 1 \frac{3}{4} \)[/tex] is equivalent to [tex]\( \frac{7}{4} \)[/tex] as an improper fraction.
2. Express both fractions with a common denominator:
We now have the fractions [tex]\( \frac{5}{8} \)[/tex] and [tex]\( \frac{7}{4} \)[/tex].
- The common denominator of 8 and 4 is 8.
- Convert [tex]\( \frac{7}{4} \)[/tex] to have the common denominator of 8:
[tex]\[
\frac{7}{4} \times \frac{2}{2} = \frac{14}{8}
\][/tex]
So, the fractions to be added are [tex]\( \frac{5}{8} \)[/tex] and [tex]\( \frac{14}{8} \)[/tex].
3. Add the fractions:
Since both fractions now have the common denominator, we can add their numerators:
[tex]\[
\frac{5}{8} + \frac{14}{8} = \frac{5 + 14}{8} = \frac{19}{8}
\][/tex]
4. Simplify the fraction (if needed):
- In this case, [tex]\( \frac{19}{8} \)[/tex] is already in its simplest form. However, we can express it as a mixed number if desired.
- Divide the numerator by the denominator: [tex]\( 19 \div 8 = 2 \)[/tex] remainder [tex]\( 3 \)[/tex].
- Thus, [tex]\( \frac{19}{8} \)[/tex] can be written as [tex]\( 2 \frac{3}{8} \)[/tex].
Putting it all together:
- The fractions in original form are [tex]\( \frac{5}{8} \)[/tex] and [tex]\( 1 \frac{3}{4} \)[/tex] which is [tex]\( \frac{7}{4} \)[/tex] as an improper fraction.
- Their sum is [tex]\( \frac{19}{8} \)[/tex], which can be expressed as [tex]\( 2 \frac{3}{8} \)[/tex] in mixed number form.
So, the final result is:
[tex]\( \frac{5}{8} + 1 \frac{3}{4} = \frac{19}{8} = 2 \frac{3}{8} \)[/tex].
