Fraction and Mixed-Number Sums - ISEE Middle Level: Mathematics Achievement

$2\ \frac{3}{4}$. $\frac{19}{6}-\frac{5}{12}$ with LCD 12: $\frac{38}{12}-\frac{5}{12}=\frac{33}{12}=\frac{11}{4}=2\frac{3}{4}$.

$3\ \frac{1}{6}$. As improper, $\frac{7}{3}+\frac{5}{6}$ with LCD 6: $\frac{14}{6}+\frac{5}{6}=\frac{19}{6}=3\frac{1}{6}$.

$1\ \frac{1}{24}$. LCD of 24: $\frac{22}{24}+\frac{3}{24}=\frac{25}{24}=1\frac{1}{24}$.

$1\ \frac{5}{8}$. Convert $1\frac{1}{4}$ to $1\frac{2}{8}$; since $\frac{7}{8}>\frac{2}{8}$, subtract to get $1\frac{5}{8}$.

$3\ \frac{1}{4}$. As improper fractions, $\frac{11}{2}-\frac{9}{4}$ with LCD 4: $\frac{22}{4}-\frac{9}{4}=\frac{13}{4}=3\frac{1}{4}$.

$4\ \frac{5}{6}$. Convert to improper fractions $\frac{11}{3}+\frac{7}{6}$, use LCD 6 for $\frac{22}{6}+\frac{7}{6}=\frac{29}{6}=4\frac{5}{6}$.

$4$. Summing whole numbers and fractions separately: $1+2=3$ and $\frac{1}{4}+\frac{3}{4}=1$, totaling $4$.

$\frac{9}{10}$. LCD of 10 converts $\frac{2}{5}$ to $\frac{4}{10}$ and $\frac{1}{2}$ to $\frac{5}{10}$, summing to $\frac{9}{10}$.

$\frac{7}{12}$. With LCD of 12, $\frac{5}{6}$ becomes $\frac{10}{12}$ minus $\frac{3}{12}$ equals $\frac{7}{12}$.

$\frac{1}{2}$. Using LCD of 6, convert $\frac{1}{3}$ to $\frac{2}{6}$ and add to $\frac{1}{6}$ for $\frac{3}{6}$, simplifying to $\frac{1}{2}$.

$\frac{2}{5}$. Subtracting numerators over the shared denominator of 10 gives $\frac{4}{10}$, reducing to $\frac{2}{5}$.

$\frac{1}{2}$. Adding numerators over the common denominator of 8 yields $\frac{4}{8}$, which simplifies to $\frac{1}{2}$.

Simplify the fraction and write improper results as mixed numbers if needed. Reducing to lowest terms ensures the simplest form, and converting improper fractions to mixed numbers improves readability when appropriate.

$\frac{ac+b}{c}$. Convert the mixed number by multiplying the whole part by the denominator and adding the numerator, placing over the original denominator.

$\frac{ad-bc}{bd}$ (then simplify if possible). With $bd$ as the common denominator, subtract the converted numerators and simplify the outcome for the difference.

$2$. Add fractions $\frac{3}{10}+\frac{7}{10}=\frac{10}{10}=1$, then plus whole 1 totals 2.

Rewrite both with a common denominator (often $\text{LCD}(b,d)$). To add fractions with unlike denominators, equivalent fractions must share a common denominator, ideally the least common one, before combining numerators.

$\frac{a+b}{n}$. When denominators are identical, numerators are added directly while retaining the shared denominator to form the sum.

$\frac{a-b}{n}$. For subtraction with matching denominators, subtract the numerators and keep the common denominator for the result.

$\text{LCD} = \text{LCM}(m,n)$. The least common denominator equals the least common multiple of the denominators, enabling equivalent fraction conversion for addition or subtraction.

$\frac{ad+bc}{bd}$ (then simplify if possible). Using $bd$ as the common denominator, convert each fraction and add numerators, then reduce the resulting fraction if possible.

$\frac{1}{2}$. Convert $\frac{2}{5}$ to $\frac{4}{10}$; subtract from $\frac{9}{10}$ to get $\frac{5}{10}$, simplifying to $\frac{1}{2}$.