1.2. Solve and briefly explain each step to grade 5 mathematics learners the following multiplication, addition, and division calculations involving fractions. \( \begin{array}{ll}\text { 1.2.1. } 4 \frac{9}{3} \div \frac{12}{6} & \text { (6) } \\ \text { 1.2.2. } 6 \frac{12}{9} \times 5 \frac{3}{4} & \text { (6) } \\ \text { 1.2.3. } \frac{5}{17}+\frac{8}{4} & \text { (6) }\end{array} \)

Sure! Let's tackle each calculation step by step and keep it engaging for the learners. **1.2.1. \( 4 \frac{9}{3} \div \frac{12}{6} \)** First, we need to convert \(4 \frac{9}{3}\) into an improper fraction. Since \(9\) divided by \(3\) equals \(3\), we add that to \(4\): \[ 4 \times 3 + 3 = 15 \quad \text{so,} \quad 4 \frac{9}{3} = \frac{15}{1} \] Next, we simplify \(\frac{12}{6}\) to \(2\) because \(12\) divided by \(6\) is \(2\), or as a fraction \(\frac{2}{1}\). Now, we can perform the division: To divide fractions, we multiply by the reciprocal. So, \[ \frac{15}{1} \div \frac{2}{1} = \frac{15}{1} \times \frac{1}{2} = \frac{15 \times 1}{1 \times 2} = \frac{15}{2} \] This fraction means \(7.5\) or \(7 \frac{1}{2}\) when we convert it back into a mixed number! --- **1.2.2. \( 6 \frac{12}{9} \times 5 \frac{3}{4} \)** Convert both mixed numbers to improper fractions. For \(6 \frac{12}{9}\): First, simplify \( \frac{12}{9} \) to \( \frac{4}{3} \). Then: \[ 6 \times 3 + 4 = 22 \quad \text{so,} \quad 6 \frac{4}{3} = \frac{22}{3} \] Now for \(5 \frac{3}{4}\): \[ 5 \times 4 + 3 = 23 \quad \text{so,} \quad 5 \frac{3}{4} = \frac{23}{4} \] Now, multiply the two fractions: \[ \frac{22}{3} \times \frac{23}{4} = \frac{22 \times 23}{3 \times 4} = \frac{506}{12} \] Finally, we can simplify that fraction by dividing both the numerator and denominator by \(2\): \[ \frac{253}{6} \quad \text{or} \quad 42 \frac{1}{6} \, \text{as a mixed number.} \] --- **1.2.3. \( \frac{5}{17} + \frac{8}{4} \)** First, simplify \(\frac{8}{4}\) to \(2\). Now, to add fractions, they need a common denominator. The denominators of \(17\) and \(1\) (from \(2\)) have a common denominator of \(17\). So we convert \(2\) into a fraction with that denominator: \[ 2 = \frac{2 \times 17}{1 \times 17} = \frac{34}{17} \] Now we can add: \[ \frac{5}{17} + \frac{34}{17} = \frac{5 + 34}{17} = \frac{39}{17} \] And there we have it! This improper fraction can also be expressed as a mixed number: \[ 2 \frac{5}{17} \] Math can be fun when you can break it down step by step!