These questions ask you to write, simplify or complete ratios while preserving what each term represents. Some comparisons have two terms, while others have three or more.
Build an equivalent ratio
Start by writing the quantities in the order named. If they are measurements, convert them to one unit before treating them as numbers. Then divide every term by a common factor; for simplest form, continue until the terms share no factor greater than one. For example, 27:45 becomes 3:5 after both terms are divided by 9.
| Signal | Method |
|---|---|
| A comparison names categories in sequence | Put their quantities in that same sequence; reversing the terms changes the meaning. |
| The quantities use different units | Convert first. For example, 75 cm and 1.5 m become 75:150, then 1:2. |
| An equivalent ratio is required | Use one multiplier or divisor on every term. If 7 becomes 21, multiply every other term by 3 as well. |
| A ratio has three or more terms | Preserve their order, scale every term together, and add the terms only when you need the total number of equal parts. |
To complete a missing term, find the multiplier that changes the known old term into its new value and apply that multiplier to the corresponding partner. Ratios are multiplicative comparisons: adding or subtracting the same amount from both terms usually changes the comparison.
Where mistakes happen
| Tempting route | How to reject it |
|---|---|
| Reverse the terms while keeping the original category names | Read the names aloud from left to right. A reversed pair answers the reversed comparison, not the one requested. |
| Stop at a ratio whose terms still share a factor | Check for a common divisor. A correct comparison can still fail the simplest-form instruction. |
| Compare the bare numbers from unlike measurement units | A metre value and a centimetre value cannot enter the ratio unchanged. Convert both measurements to the same unit first. |
| Use a part-to-whole comparison when two named parts are requested | Identify exactly what each side names. Adding all parts belongs in a denominator or total-parts calculation, not automatically in the ratio. |
| Scale only one term | Equivalent ratios require the same multiplication or division on every term. Check the multiplier term by term. |
Try it
Simplify 42:56 to 3:n. Enter the number that replaces n.
Green counters and yellow counters are in the ratio 24:36. Which ratio-notation statements are true? Select all that apply.
- Green to yellow simplifies to 2:3.
- Yellow to green simplifies to 3:2.
- Dividing both terms by 12 preserves the comparison.
- Green to yellow simplifies to 3:2.
- The ratio 24:12 is its simplest form.
A bead pattern has orange to violet beads in the ratio 4:7. If there are 28 orange beads, how many violet beads are there?
- 31
- 49
- 16
- 196