Operations with Fractions Practice Problems & Solutions

Let us solve the problem of multiplying the two fractions $\frac{2}{3}$ and $\frac{5}{7}$.

• Step 1: Identify the numerators and denominators. Here, the numerators are $2$ and $5$, and the denominators are $3$ and $7$.
• Step 2: Multiply the numerators: $2 \times 5 = 10$.
• Step 3: Multiply the denominators: $3 \times 7 = 21$.
• Step 4: Put the results together in a new fraction: $\frac{10}{21}$.
• Step 5: Simplify the fraction if needed. In this case, $\frac{10}{21}$ is already in its simplest form as $10$ and $21$ have no common factors besides $1$.

Therefore, the solution to the problem $\frac{2}{3} \times \frac{5}{7}$ is $\frac{10}{21}$.

The problem involves adding the fractions $\frac{1}{3}$ and $\frac{4}{9}$.

Step 1: Identify the Least Common Denominator (LCD).

• The denominators are 3 and 9. The least common multiple of 3 and 9 is 9. Thus, the LCD is 9.

Step 2: Convert the fractions to have the common denominator.

• The fraction $\frac{1}{3}$ must be converted to have the denominator of 9. Multiply both the numerator and denominator by 3:
• $\frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}$
• The fraction $\frac{4}{9}$ already has the denominator of 9, so it remains unchanged.

Step 3: Add the equivalent fractions.

• Add the numerators together, keeping the denominator:
• $\frac{3}{9} + \frac{4}{9} = \frac{3+4}{9} = \frac{7}{9}$

Step 4: Simplify the result, if necessary.

• The fraction $\frac{7}{9}$ is already in simplest form.

Therefore, the solution to the problem is $\frac{7}{9}$.

To find the result of dividing $\frac{2}{4}$ by $\frac{4}{3}$, follow these steps:

• Step 1: Simplify the fraction $\frac{2}{4}$. This becomes $\frac{1}{2}$ because both the numerator and the denominator can be divided by 2.
• Step 2: Find the reciprocal of the fraction $\frac{4}{3}$. The reciprocal is $\frac{3}{4}$ because it exchanges the numerator and the denominator.
• Step 3: Multiply $\frac{1}{2}$ by $\frac{3}{4}$. $\frac{1}{2} \times \frac{3}{4} = \frac{1 \times 3}{2 \times 4} = \frac{3}{8}$
• Step 4: The result is $\frac{3}{8}$, which is already in its simplest form.

Therefore, the solution to the problem $\frac{2}{4}:\frac{4}{3}$ is $\frac{3}{8}$.

To find the sum $\frac{1}{4} + \frac{7}{8}$, follow these steps:

• Step 1: Identify the least common denominator (LCD) of the fractions. The denominators 4 and 8 have an LCD of 8.
• Step 2: Convert $\frac{1}{4}$ to an equivalent fraction with a denominator of 8. Multiply both the numerator and the denominator by 2: $\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$.
• Step 3: The second fraction, $\frac{7}{8}$, already has the correct denominator. Therefore, it remains $\frac{7}{8}$.
• Step 4: Add the numerators of the two fractions: $\frac{2}{8} + \frac{7}{8} = \frac{2+7}{8} = \frac{9}{8}$.

Therefore, the sum of $\frac{1}{4}$ and $\frac{7}{8}$ is $\frac{9}{8}$.

To multiply fractions, we multiply numerator by numerator and denominator by denominator

1*4 = 4

4*5 = 20

4/20

Note that we can simplify this fraction by 4

4/20 = 1/5