Which is greater: 4/7 or 4/9?
Give me a hint
The numerator is the same. Which denominator makes larger pieces?
Compare a worked response
4/7
Four sevenths contains four larger pieces than four ninths of the same whole.
Compare & order fractions
Use the size of the parts, a benchmark or equal units—not the size of the digits alone.
Your learning goal
Compare and order positive fractions and connect exact fractions to decimals.
Understand the idea
Start with the same whole
A comparison of fraction numbers assumes a common unit whole. Three quarters is greater than two thirds as a number, but three quarters of a small pizza could be less food than two thirds of a large pizza. State which comparison you are making.
Words worth knowing
- Benchmark
- A familiar reference value, such as 0, 1/2 or 1.
- Common denominator
- A shared denominator used to name equal-sized parts.
- Equivalent decimal
- A decimal naming the same number as a fraction; some decimals repeat.
Make it visible
Compare equal wholes, not just digits.
Predict a result, change a value, and use the diagram to explain your reasoning.
Predict before changing a value. Every whole in a bar diagram uses the same size. The models use non-negative amounts up to two wholes per input.
Use what is already alike
With the same denominator, more equal parts means a greater number: 5/8 > 3/8. With the same positive numerator, fewer parts per whole means larger parts: 3/5 > 3/7. These are different situations; choose a reason, not a digit shortcut.
Benchmarks can avoid large calculations
Compare each fraction with 1/2 or 1. Since 4/9 < 1/2 and 5/8 > 1/2, 4/9 < 5/8. If both fractions are close to 1, compare their missing amounts: 7/8 is missing 1/8, while 5/6 is missing 1/6.
Rename with equal units when needed
To compare 5/6 and 7/9, use eighteenths: 15/18 > 14/18. Alternatively divide numerator by denominator. Remember that 1/3 = 0.333… exactly; 0.33 is only an approximation and is slightly less than 1/3.
Follow the reasoning
One decision at a time.
Work out the next step before opening the explanation.
Compare 7/8 and 5/6
- Both numbers are close to 1. The gaps are 1/8 and 1/6.
- 1/8 is smaller than 1/6, so 7/8 is closer to 1 from below.
- Therefore 7/8 > 5/6. A common denominator confirms 21/24 > 20/24.
Order 0.6, 2/3 and 5/8
- Write exact common units: 0.6 = 3/5 = 72/120.
- 5/8 = 75/120 and 2/3 = 80/120.
- Least to greatest: 0.6 < 5/8 < 2/3.
Try with support
Make your thinking visible.
Use paper or a whiteboard. Show the equal parts, calculation and explanation before comparing your response.
Compare 3/8 and 5/12 using twenty-fourths.
Give me a hint
Multiply both integers in each fraction to make the denominator 24.
Compare a worked response
3/8 < 5/12
3/8 = 9/24 and 5/12 = 10/24.
Independent practice
Build a strategy you can explain.
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
0 of 8 questions completed
This round saves on this device. It is practice, not a school mark.
Check the concepts, too.
What does the answer mean?
Two bottle fill levels can be compared as proportions. To compare the actual amount of water, you also need the capacities.