Year 7 Chapter 3B & 3C T2 Week 2

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 \(\frac{2}{3}\).

Answer explanation

To simplify \( \frac{12}{18} \), find the greatest common divisor (GCD) of 12 and 18, which is 6. Divide both the numerator and denominator by 6: \( \frac{12 \div 6}{18 \div 6} = \frac{2}{3} \). Thus, the correct answer is \( \frac{2}{3} \).

Answer explanation

To find an equivalent fraction, multiply both the numerator and denominator of \(\frac{5}{8}\) by the same number. Multiplying by 2 gives \(\frac{10}{16}\), which is equivalent. The other options do not simplify to \(\frac{5}{8}\).

Answer explanation

To convert the mixed number 2\frac{3}{5} to an improper fraction, multiply the whole number (2) by the denominator (5) and add the numerator (3): 2 \times 5 + 3 = 10 + 3 = 13. Thus, the improper fraction is \frac{13}{5}.

Answer explanation

To convert the improper fraction \( \frac{17}{4} \) to a mixed number, divide 17 by 4. The quotient is 4 and the remainder is 1. Thus, it can be expressed as \( 4 \frac{1}{4} \), which is the correct answer.

Answer explanation

To simplify \( \frac{18}{24} \), divide both the numerator and denominator by their greatest common divisor, which is 6. This gives \( \frac{18 \div 6}{24 \div 6} = \frac{3}{4} \). Thus, the simplest form is \( \frac{3}{4} \).

Answer explanation

To convert the mixed number 5\frac{2}{7} to an improper fraction, multiply the whole number (5) by the denominator (7) and add the numerator (2): 5 \times 7 + 2 = 35 + 2 = 37. Thus, the improper fraction is \frac{37}{7}.

Answer explanation

To convert the improper fraction \(\frac{22}{5}\) to a mixed number, divide 22 by 5. The quotient is 4 and the remainder is 2. Thus, it can be expressed as \(4\frac{2}{5}\), making \(4\frac{2}{5}\) the correct answer.

Answer explanation

To simplify \( \frac{36}{54} \), divide both the numerator and denominator by their greatest common divisor, which is 18. This gives \( \frac{36 \div 18}{54 \div 18} = \frac{2}{3} \). Thus, the simplest form is \( \frac{2}{3} \).

Answer explanation

To find an equivalent fraction to \( \frac{3}{5} \), multiply both the numerator and denominator by the same number. Multiplying by 2 gives \( \frac{6}{10} \), which is equivalent. The other options do not represent the same value.