Question

2 find the value of the following ratios. write ○ in the parentheses for those with the same value as the left and right ratios. (1) 2:3 ⇨ ( ) 4:6 ⇨ ( ) (2) 4:1 ⇨ ( ) 3:1 ⇨ ( ) (3) 6:10 ⇨ ( ) 10:15 ⇨ ( ) (4) 10:2 ⇨ ( ) 5:1 ⇨ ( ) (5) 6:2 ⇨ ( ) 3:1 ⇨ ( ) (6) 1:3 ⇨ ( ) 4:8 ⇨ ( ) 3 circle the value of ratios from the parentheses. some questions will have two or more answers. (1) \\(\frac{1}{3}\\) ( 2:4 · 2:6 · 2:8 · 9:3 · 6:3 · 6:2 (2) 2 ( 6:3 · 8:4 · 2:4 · 5:10 · 8:16 · 10:5 (3) 3 ( 3:9 · 6:12 · 6:2 · 15:5 · 4:12 · 1:3 (4) 0.5 ( 2:4 · 4:6 · 5:10 · 8:4 · 10:5 · 1:2 (5) \\(\frac{3}{2}\\) ( 10:15 · 6:9 · 6:4 · 8:12 · 9:18 · 3:2 (6) \\(\frac{4}{5}\\) ( 10:8 · 10:15 · 12:15 · 6:10 · 4:5 · 15:20

Explanation:

Step1: Calculate the value of each ratio

• For \(2:3\), the value is \(\frac{2}{3}\approx0.67\).
• For \(4:6\), simplify to \(2:3\), value is \(\frac{2}{3}\approx0.67\).
• For \(4:1\), value is \(\frac{4}{1} = 4\).
• For \(3:1\), value is \(\frac{3}{1}=3\).
• For \(6:10\), simplify to \(3:5\), value is \(\frac{3}{5} = 0.6\).
• For \(10:15\), simplify to \(2:3\), value is \(\frac{2}{3}\approx0.67\).
• For \(10:2\), simplify to \(5:1\), value is \(\frac{5}{1}=5\).
• For \(5:1\), value is \(\frac{5}{1}=5\).
• For \(6:2\), simplify to \(3:1\), value is \(\frac{3}{1}=3\).
• For \(3:1\), value is \(\frac{3}{1}=3\).
• For \(1:3\), value is \(\frac{1}{3}\approx0.33\).
• For \(4:8\), simplify to \(1:2\), value is \(\frac{1}{2}=0.5\).

Step2: Compare the values

• In (1), \(2:3\) and \(4:6\) have the same value.
• In (2), \(4:1\) and \(3:1\) have different values.
• In (3), \(6:10\) and \(10:15\) have different values.
• In (4), \(10:2\) and \(5:1\) have the same value.
• In (5), \(6:2\) and \(3:1\) have the same value.
• In (6), \(1:3\) and \(4:8\) have different values.

Step3: Circle the correct ratios for question 3

• For \(\frac{1}{3}\):
• \(2:6=\frac{2}{6}=\frac{1}{3}\).
• For \(2\):
• \(6:3 = 2\), \(8:4=2\), \(10:5 = 2\).
• For \(3\):
• \(6:2=3\), \(15:5 = 3\).
• For \(0.5\):
• \(2:4 = 0.5\), \(5:10=0.5\), \(1:2 = 0.5\).
• For \(\frac{3}{2}\):
• \(6:4=\frac{3}{2}\), \(3:2=\frac{3}{2}\).
• For \(\frac{4}{5}\):
• \(12:15=\frac{4}{5}\), \(4:5=\frac{4}{5}\).

Answer:

1. (1) \(2:3\) (\(4:6\)) [\(\bigcirc\)]; (2) \(4:1\) ( ); \(3:1\) ( ) [ ]; (3) \(6:10\) ( ); \(10:15\) ( ) [ ]; (4) \(10:2\) (\(5:1\)) [\(\bigcirc\)]; (5) \(6:2\) (\(3:1\)) [\(\bigcirc\)]; (6) \(1:3\) ( ); \(4:8\) ( ) [ ]
2. (1) \(2:6\); (2) \(6:3\), \(8:4\), \(10:5\); (3) \(6:2\), \(15:5\); (4) \(2:4\), \(5:10\), \(1:2\); (5) \(6:4\), \(3:2\); (6) \(12:15\), \(4:5\)