Equivalent ratios and simplest form

1. Simplify $12:20$.

   2 marks
2. Simplify $42:18$.

   2 marks
3. Complete $3:7=12:x$.

   2 marks
4. Simplify $15:25:35$.

   2 marks
5. Simplify $2\text{m}:50\text{cm}$.

   3 marks
6. A student says $4:6$ and $7:9$ are equivalent because 3 was added to each entry. Explain the error.

   3 marks

Equivalent correct methods earn the corresponding marks. Include units where asked.

1. Simplify $12:20$.

   2 marks

   Divide both entries by 4.

   $3:5$.
2. Simplify $42:18$.

   2 marks

   Divide both entries by 6.

   $7:3$.
3. Complete $3:7=12:x$.

   2 marks

   The first entry is multiplied by 4, so multiply 7 by 4.

   $x=28$.
4. Simplify $15:25:35$.

   2 marks

   Divide all three entries by 5.

   $3:5:7$.
5. Simplify $2\text{m}:50\text{cm}$.

   3 marks

   Convert 2 m to 200 cm.

   Divide both entries of $200:50$ by 50.

   $4:1$.
6. A student says $4:6$ and $7:9$ are equivalent because 3 was added to each entry. Explain the error.

   3 marks

   $4:6$ simplifies to $2:3$.

   To scale 4 to 7 requires multiplying by $\frac{7}{4}$; that would change 6 to 10.5, not 9.

   The same addition does not preserve a ratio.