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Grade 7 Quiz: Ratios & Proportions — Easy Version 1
Grade 7 · MathSheets Name: ____________________ Date: __________
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.
How to solve
This quiz mixes questions from different lessons, like a real test. Read each question carefully: the lesson name in front tells you what kind of problem it is. Check your answers, then practise the lessons where you made mistakes.
Example
Proportional Relationships: Tables, Graphs & Equations: A bakery packs 4 muffins in each box. Let x be the boxes and y the muffins. What number goes in the blank in the x column?
| x | y |
|---|---|
| 1 | 4 |
| 2 | 8 |
| 3 | 12 |
| 4 | 16 |
Not quite. The answer is
💡 An hour is 2 times as long as 12 of an hour, so in a full hour the runner goes 2 times as far: 8 ÷ 12 = 8 × 2 = 16. The speed is 16 miles per hour.
✓ Correct!
Not quite. The answer is
💡 An hour is 2 times as long as 12 of an hour, so in a full hour the runner goes 2 times as far: 8 ÷ 12 = 8 × 2 = 16. The speed is 16 miles per hour.
💡 How to solve: Unit Rates & Complex Fractions
Unit rate = distance ÷ time. When the time is a fraction of an hour, dividing by a fraction means multiplying by its reciprocal, so dividing by 12 is the same as multiplying by 2.
Try a similar one
A car travels 10 miles in 5 hours. What is its speed in miles per hour (unit rate)?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The constant of proportionality is the unit rate, pages per minute: divide 10 by 2. k = 10 ÷ 2 = 5 pages per minute.
✓ Correct!
Not quite. The answer is
💡 The constant of proportionality is the unit rate, pages per minute: divide 10 by 2. k = 10 ÷ 2 = 5 pages per minute.
💡 How to solve: Constant of Proportionality
In a proportional relationship y = kx, the constant of proportionality is k = yx — the unit rate. Pick any pair (x, y) with x not 0, divide y by x, and simplify. For an equation like 4y = 12x, solve for y first: y = 3x, so k = 3.
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The table shows a proportional relationship between x and y. What is the constant of proportionality k?
| x | y |
|---|---|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 y = 6.5x has the form y = kx with k = 6.5 and nothing added. Yes, it is proportional.
✓ Correct!
Not quite. The answer is
💡 y = 6.5x has the form y = kx with k = 6.5 and nothing added. Yes, it is proportional.
💡 How to solve: Identifying Proportional Relationships
A relationship is proportional when yx is the same for every pair. In a table, divide each y by its x and check that all the ratios match. A graph is proportional only if it is a straight line through the origin (0, 0). An equation is proportional only if it has the form y = kx, with no number added or subtracted.
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Is the relationship shown in the table proportional?
| x | y |
|---|---|
| 1 | 2 |
| 3 | 6 |
| 4 | 8 |
| 5 | 10 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The top went from 4 to 8: 8 ÷ 4 = 2, so the top was multiplied by 2. Multiply the bottom by 2 too: 4 × 2 = 8. Check: 44 = 88. So x = 8.
✓ Correct!
Not quite. The answer is
💡 The top went from 4 to 8: 8 ÷ 4 = 2, so the top was multiplied by 2. Multiply the bottom by 2 too: 4 × 2 = 8. Check: 44 = 88. So x = 8.
💡 How to solve: Proportional Relationships
Cross-multiply: in ab = cx, a × x = b × c, so x = (b × c) ÷ a. You can also find what the first numerator was multiplied by to get the second and multiply the denominator by the same number.
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12 = 2x, x = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Each inch on the drawing stands for 4 feet, so divide to find how many inches: 8 ÷ 4 = 2. Check: 2 × 4 = 8. The wall is 2 inches long on the drawing.
✓ Correct!
Not quite. The answer is
💡 Each inch on the drawing stands for 4 feet, so divide to find how many inches: 8 ÷ 4 = 2. Check: 2 × 4 = 8. The wall is 2 inches long on the drawing.
💡 How to solve: Scale Drawings & Scale Factor
Use the scale: to find the actual length, multiply the drawing length by the number of feet per inch. To find the drawing length, divide the actual length by the number of feet per inch.
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On a scale drawing, 1 inch = 6 feet. If a wall measures 3 inches on the drawing, what is its actual length in feet?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 1 | 3 |
| 2 | ___ |
| ___ | 9 |
| 4 | 12 |
Not quite. The answer is
💡 A proportional relationship has the equation y = kx. k is the unit rate, the dollars for x = 1. The story gives it: k = 3. The equation is y = 3x.
✓ Correct!
Not quite. The answer is
💡 A proportional relationship has the equation y = kx. k is the unit rate, the dollars for x = 1. The story gives it: k = 3. The equation is y = 3x.
💡 How to solve: Proportional Relationships: Tables, Graphs & Equations
A proportional relationship has the equation y = kx, where k is the unit rate (the y-value when x = 1). Find k by dividing any y by its x. To fill a missing y, multiply its x by k; to fill a missing x, divide its y by k. Each pair (x, y) is a point on the graph, and the points line up on a straight line through (0, 0). Example: 4 pages every minute gives y = 4x, so 3 minutes → 12 pages and 20 pages → 5 minutes.
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Maya earns $5.00 for each hour she babysits. Let x be the hours and y the dollars. Write the equation for this relationship.
| x | y |
|---|---|
| 1 | 5 |
| 2 | ___ |
| ___ | 15 |
| 4 | 20 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Divide each new side by the matching old side: 1 ÷ 2 = 12 and 2 ÷ 4 = 12. Both sides are multiplied by the same scale factor, 12, so yes.
✓ Correct!
Not quite. The answer is
💡 Divide each new side by the matching old side: 1 ÷ 2 = 12 and 2 ÷ 4 = 12. Both sides are multiplied by the same scale factor, 12, so yes.
💡 How to solve: Scaled Copies: Scale Factor, Angles & Area
In a scaled copy every length is multiplied by the same scale factor. Scale factor = copy length ÷ original length. Angles do not change. Area is multiplied by the scale factor twice: with scale factor 3, a 2-by-4 rectangle (area 8) becomes 6-by-12 (area 72 = 8 × 9). A scale like 1 to 50,000 means 1 cm on the map is 50,000 cm (500 m) in real life.
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A rectangle is 2 cm by 4 cm. A scaled copy is 1 cm by 2 cm. What is the scale factor?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Put in the numbers: 26 = 13 × t. Divide both sides by 13: t = 26 ÷ 13 = 2. Check: 13 × 2 = 26. So t = 2.
✓ Correct!
Not quite. The answer is
💡 Put in the numbers: 26 = 13 × t. Divide both sides by 13: t = 26 ÷ 13 = 2. Check: 13 × 2 = 26. So t = 2.
💡 How to solve: Formulas: Distance, Rate & Time
Use d = r × t. To find distance, multiply rate by time; to find rate, r = d ÷ t; to find time, t = d ÷ r. For perimeter P = 2l + 2w, subtract the known doubled side from P and divide by 2, for example l = (P - 2w) ÷ 2.
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Using d = rt, find the distance d when r = 17 and t = 2.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Speed is miles ÷ hours: 40 ÷ 10 = 4. The car goes 4 miles per hour.
✓ Correct!
Not quite. The answer is
💡 Speed is miles ÷ hours: 40 ÷ 10 = 4. The car goes 4 miles per hour.
💡 How to solve: Unit Rates & Complex Fractions
Unit rate = distance ÷ time. When the time is a fraction of an hour, dividing by a fraction means multiplying by its reciprocal, so dividing by 12 is the same as multiplying by 2.
Try a similar one
A car travels 35 miles in 5 hours. What is its speed in miles per hour (unit rate)?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| x | y |
|---|---|
| 1 | 6 |
| 2 | 12 |
| 3 | 18 |
| 4 | 24 |
Not quite. The answer is
💡 In y = kx, k = y ÷ x for every pair. Use the first row, (1, 6): k = 6 ÷ 1 = 6.
✓ Correct!
Not quite. The answer is
💡 In y = kx, k = y ÷ x for every pair. Use the first row, (1, 6): k = 6 ÷ 1 = 6.
💡 How to solve: Constant of Proportionality
In a proportional relationship y = kx, the constant of proportionality is k = yx — the unit rate. Pick any pair (x, y) with x not 0, divide y by x, and simplify. For an equation like 4y = 12x, solve for y first: y = 3x, so k = 3.
Try a similar one
The table shows a proportional relationship between x and y. What is the constant of proportionality k?
| x | y |
|---|---|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Grade 7 Quiz: Ratios & Proportions — Easy Version 1
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.