This answer key gives a full worked solution for each of the 10 ratios problems, with every step shown. Check each final answer in bold and compare your reasoning, especially the multiplication used to find equivalent ratios.
Problem 1: Writing a ratio
Apples to oranges: 4 apples and 7 oranges.
The ratio is 4 to 7, \(4:7\), or \(\frac{4}{7}\).
Problem 2: Part-to-whole ratio
Total players: \(9 + 6 = 15\).
Girls to all players: \(9:15\) (or \(3:5\) in simplest form).
Problem 3: Equivalent ratios
Multiply both numbers by the same value: \(2 \times 2 = 4\) and \(5 \times 2 = 10\); \(2 \times 3 = 6\) and \(5 \times 3 = 15\); \(2 \times 4 = 8\) and \(5 \times 4 = 20\).
Three equivalent ratios: \(4:10\), \(6:15\), \(8:20\). Other correct answers are possible.
Problem 4: Missing value
The first ratio is \(3:4\). To go from 3 to 12, multiply by 4 (\(3 \times 4 = 12\)).
Multiply the second number by 4 too: \(4 \times 4 = 16\).
The missing number is 16.
Problem 5: Simplest form
The greatest common factor of 18 and 24 is 6.
\(18 : 6 = 3\) and \(24 : 6 = 4\).
Simplest form: \(3:4\).
Problem 6: Ratio table
Each column keeps the ratio 5 pencils to 2 erasers.
15 pencils is \(5 \times 3\), so erasers are \(2 \times 3 = 6\).
8 erasers is \(2 \times 4\), so pencils are \(5 \times 4 = 20\).
25 pencils is \(5 \times 5\), so erasers are \(2 \times 5 = 10\).
Missing values in order: 20 pencils, 6 erasers, 10 erasers.
Problem 7: Comparing ratios
Mix A: \(3:5\). Since \(5 \times 3 = 15\), concentrate is \(3 \times 3 = 9\) cups.
Mix B: \(2:3\). Since \(3 \times 5 = 15\), concentrate is \(2 \times 5 = 10\) cups.
With the same 15 cups of water, Mix B has more concentrate (10 versus 9).
Mix B is stronger.
Problem 8: School store word problem
Pencils: \(7\) parts, and \(63 : 7 = 9\), so each part is 9.
Notebooks: \(3 \times 9 = 27\).
Total: \(63 + 27 = 90\).
27 notebooks, 90 items in all.
Problem 9: Mixing paint
Total parts: \(3 + 5 = 8\). Each part: \(40 : 8 = 5\) cups.
Blue: \(3 \times 5 = 15\) cups. Yellow: \(5 \times 5 = 25\) cups.
Check: \(15 + 25 = 40\).
15 cups of blue and 25 cups of yellow.
Problem 10: Farmers market
(a) Total parts: \(5 + 3 = 8\). Each part: \(96 : 8 = 12\).
Apples: \(5 \times 12 = 60\). Pears: \(3 \times 12 = 36\).
(b) After selling 12 apples: \(60 – 12 = 48\) apples, 36 pears. The ratio is \(48:36\). Divide both by 12: \(4:3\).
(a) 60 apples and 36 pears. (b) \(4:3\).
See every chapter on the Grade 6 math page.