Mastering Fractions for 5th Grade

Identify the fraction that represents the shaded part of a circle divided into 4 equal parts, with 3 parts shaded.

Answer explanation

The circle is divided into 4 equal parts, and 3 of those parts are shaded. To find the fraction representing the shaded area, we take the number of shaded parts (3) over the total parts (4), which gives us \(\frac{3}{4}\).

Answer explanation

To simplify \( \frac{8}{12} \), divide both the numerator and denominator by their greatest common divisor, which is 4. This gives \( \frac{8 \div 4}{12 \div 4} = \frac{2}{3} \). Thus, the correct answer is \( \frac{2}{3} \).

Answer explanation

To add the fractions \(\frac{1}{4} + \frac{2}{4}\), keep the denominator the same and add the numerators: \(1 + 2 = 3\). Thus, \(\frac{1}{4} + \frac{2}{4} = \frac{3}{4}\). The correct answer is \(\frac{3}{4}\).

Answer explanation

To subtract the fractions \( \frac{5}{8} - \frac{3}{8} \), keep the denominator the same and subtract the numerators: \( 5 - 3 = 2 \). Thus, the result is \( \frac{2}{8} \), which simplifies to \( \frac{1}{4} \). The correct answer is \( \frac{2}{8} \).

Answer explanation

To convert the mixed number 2 \frac{1}{3} to an improper fraction, multiply the whole number (2) by the denominator (3) and add the numerator (1): 2 \times 3 + 1 = 7. Thus, the improper fraction is \frac{7}{3}.

Answer explanation

To compare the fractions \(\frac{3}{5}\) and \(\frac{4}{5}\), we see that both have the same denominator. Since 3 is less than 4, it follows that \(\frac{3}{5} < \frac{4}{5}\). Thus, the correct choice is \(\frac{3}{5} < \frac{4}{5}\).

Answer explanation

To find an equivalent fraction, multiply both the numerator and denominator of \(\frac{2}{3}\) by the same number. Multiplying by 2 gives \(\frac{4}{6}\), which is equivalent to \(\frac{2}{3}\).

Identify the fraction that represents the shaded part of a rectangle divided into 6 equal parts, with 4 parts shaded.

Answer explanation

The rectangle is divided into 6 equal parts, and 4 of those parts are shaded. The fraction representing the shaded area is therefore \( \frac{4}{6} \), which simplifies to \( \frac{2}{3} \), but the correct answer is \( \frac{4}{6} \).

Answer explanation

To simplify \(\frac{9}{15}\), find the greatest common divisor (GCD) of 9 and 15, which is 3. Divide both the numerator and denominator by 3: \(\frac{9 \div 3}{15 \div 3} = \frac{3}{5}\). Thus, the correct answer is \(\frac{3}{5}\).

Answer explanation

To add the fractions \(\frac{2}{6} + \frac{3}{6}\), keep the denominator the same and add the numerators: \(2 + 3 = 5\). Thus, the result is \(\frac{5}{6}\), which is the correct answer.