Mixed-Number Word Problems - ISEE Lower Level Mathematics Achievement

1. What is $2\ \frac{1}{4}+3\ \frac{2}{4}$?

   $5\ \frac{3}{4}$. Add the whole numbers $2+3=5$ and the fractions $\frac{1}{4}+\frac{2}{4}=\frac{3}{4}$ to combine the mixed numbers with a common denominator.

2. What is the remaining water if you have $3\ \frac{3}{4}$ gal and pour out $1\ \frac{2}{5}$ gal?

   $2\ \frac{7}{20}$ gal. Subtract the mixed numbers with LCD 20, borrowing to get $2\ \frac{7}{20}$ gallons remaining.

3. What is the change in temperature if it rises from $-1\ \frac{1}{2}$ to $2\ \frac{1}{4}$ degrees?

   $3\ \frac{3}{4}$ degrees. Subtract $-1\ \frac{1}{2}$ from $2\ \frac{1}{4}$ with LCD 4 to find the temperature rise of $3\ \frac{3}{4}$ degrees.

4. What is the total weight of $2\ \frac{3}{8}$ lb of apples and $1\ \frac{5}{8}$ lb of pears?

   $4$ lb. Add the mixed numbers $2\ \frac{3}{8}+1\ \frac{5}{8}=4$ to determine the total weight.

5. What is the total time if you read $1\ \frac{2}{3}$ hr on Monday and $2\ \frac{1}{6}$ hr on Tuesday?

   $3\ \frac{5}{6}$ hr. Add the mixed numbers with LCD 6 to combine the reading times, resulting in $3\ \frac{5}{6}$ hours total.

6. What is the total length if one ribbon is $1\ \frac{3}{4}$ ft and another is $2\ \frac{1}{4}$ ft?

   $4$ ft. Add the mixed numbers $1\ \frac{3}{4}+2\ \frac{1}{4}=4$ to find the combined length.

7. What is the difference between $9\ \frac{1}{8}$ and $4\ \frac{5}{8}$?

   $4\ \frac{1}{2}$. Subtract the mixed numbers, borrowing to get $4\ \frac{4}{8}$, then simplify to $4\ \frac{1}{2}$.

8. What is $5\ \frac{1}{6}-2\ \frac{5}{6}$?

   $2\ \frac{1}{3}$. Borrow 1 from the whole number to subtract $\frac{7}{6}-\frac{5}{6}=\frac{2}{6}$, then simplify to $\frac{1}{3}$.

9. What is the total number of yards in $1\ \frac{3}{5}$ yd plus $2\ \frac{4}{15}$ yd?

   $3\ \frac{13}{15}$ yd. Add the mixed numbers with LCD 15 to combine the lengths, resulting in $3\ \frac{13}{15}$ yards total.

10. What is the difference in distance between $6\ \frac{1}{5}$ mi and $2\ \frac{4}{5}$ mi?

    $3\ \frac{2}{5}$ mi. Subtract the mixed numbers with a common denominator of 5 to find the distance difference of $3\ \frac{2}{5}$ miles.

11. What is $7\ \frac{2}{3}-3\ \frac{1}{6}$ in simplest form?

    $4\ \frac{1}{2}$. Convert to a common denominator of 6, subtract to get $4\ \frac{3}{6}$, then simplify to $4\ \frac{1}{2}$.

12. What is $6\ \frac{3}{8}+1\ \frac{7}{8}$ in simplest mixed-number form?

    $8\ \frac{1}{4}$. Add to get $8\ \frac{2}{8}$, then simplify by reducing $\frac{2}{8}$ to $\frac{1}{4}$.

13. What is left if a tank has $5\ \frac{1}{2}$ gal and you use $2\ \frac{3}{4}$ gal?

    $2\ \frac{3}{4}$ gal. Subtract the mixed numbers with LCD 4, borrowing to get $2\ \frac{3}{4}$ gallons remaining.

14. What is $4\ \frac{3}{5}-1\ \frac{1}{5}$?

    $3\ \frac{2}{5}$. Subtract the whole numbers $4-1=3$ and the fractions $\frac{3}{5}-\frac{1}{5}=\frac{2}{5}$ since the denominators match.

15. What is the least common denominator (LCD) used for when adding or subtracting mixed numbers?

    It makes the fractional denominators match so you can combine numerators. The LCD ensures equivalent fractions with identical denominators, enabling direct addition or subtraction of the numerators.

16. What is the remaining fabric if you start with $8\ \frac{1}{3}$ yd and use $3\ \frac{5}{6}$ yd?

    $4\ \frac{1}{2}$ yd. Subtract the mixed numbers with LCD 6, borrowing to get $4\ \frac{1}{2}$ yards of fabric left.

17. What is left to run if you planned $5\ \frac{3}{4}$ mi and already ran $2\ \frac{1}{2}$ mi?

    $3\ \frac{1}{4}$ mi. Subtract the mixed numbers with LCD 4 to find $3\ \frac{1}{4}$ miles remaining to run.

18. What is $3\ \frac{1}{2}+2\ \frac{1}{4}$ in simplest form?

    $5\ \frac{3}{4}$. Convert to a common denominator of 4, add to get $5\ \frac{3}{4}$, which is already simplified.

19. What is the total height if one plant is $1\ \frac{7}{10}$ ft and another is $2\ \frac{9}{10}$ ft?

    $4\ \frac{3}{5}$ ft. Add the mixed numbers to get $4\ \frac{6}{10}$, then simplify to $4\ \frac{3}{5}$ feet total height.

20. What is the total amount of juice in $1\ \frac{1}{2}$ L plus $2\ \frac{2}{3}$ L?

    $4\ \frac{1}{6}$ L. Add the mixed numbers with LCD 6 to get $3\ \frac{7}{6}$, then convert to $4\ \frac{1}{6}$ liters total.

21. What is the total distance if you walk $2\ \frac{5}{6}$ mi and then $1\ \frac{1}{3}$ mi?

    $4\ \frac{1}{6}$ mi. Add the mixed numbers with LCD 6 to get $3\ \frac{7}{6}$, then convert to $4\ \frac{1}{6}$ miles total.

Study these flashcards