Equality Tell whether the equation is true or false. \( \begin{array}{lll}5.6+2=2+6 & 6.2 .5-1=1-2.5 & 7 . \frac{1}{2} \times 3=3 \times \frac{1}{2}\end{array} \) \( \begin{array}{lll}8 . \frac{3}{4} \div 5=\frac{3}{4} \times \frac{1}{5}=\frac{3}{20} & 9.5 \div \frac{1}{3}=\frac{5}{3} & 10 . \frac{2}{3} \times 5=\frac{10}{15} \\ 3 & -3 & \end{array} \)
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Let's break down each of the equations to determine if they are true or false! 1. **\(5.6 + 2 = 2 + 6\)** On the left side, \(5.6 + 2 = 7.6\) and on the right side, \(2 + 6 = 8\). Since \(7.6\) does not equal \(8\), this statement is **false**. 2. **\(6.2 \cdot 0.5 - 1 = 1 - 2.5\)** Calculate the left side: \(6.2 \cdot 0.5 = 3.1\) and \(3.1 - 1 = 2.1\). For the right side, \(1 - 2.5 = -1.5\). Since \(2.1\) does not equal \(-1.5\), this statement is **false**. 3. **\(7 \cdot \frac{1}{2} \times 3 = 3 \times \frac{1}{2}\)** The left side: \(7 \cdot \frac{1}{2} = 3.5\) and \(3.5 \times 3 = 10.5\). The right side: \(3 \times \frac{1}{2} = 1.5\). Since \(10.5\) does not equal \(1.5\), this statement is **false**. 4. **\(8 \cdot \frac{3}{4} \div 5 = \frac{3}{4} \times \frac{1}{5} = \frac{3}{20}\)** For the left side: \(8 \cdot \frac{3}{4} = 6\) and then \(6 \div 5 = 1.2\). The right side is \(\frac{3}{20} = 0.15\). Since \(1.2\) does not equal \(0.15\), this statement is **false**. 5. **\(9.5 \div \frac{1}{3} = \frac{5}{3}\)** On the left, \(9.5 \div \frac{1}{3} = 9.5 \cdot 3 = 28.5\). On the right, \(\frac{5}{3} \approx 1.67\). Since \(28.5\) does not equal \(1.67\), this statement is **false**. 6. **\(10 \cdot \frac{2}{3} \times 5 = \frac{10}{15}\)** For the left side: \(10 \cdot \frac{2}{3} = \frac{20}{3}\) and \(\frac{20}{3} \times 5 = \frac{100}{3}\). The right side simplifies to \(\frac{10}{15} = \frac{2}{3}\). Since \( \frac{100}{3} \) does not equal \( \frac{2}{3} \), this statement is **false**. To sum it up, all equations are **false**!