Estimation with Benchmarks
Compare to 0, 1/2 and 1 to judge fraction size quickly.
Key idea
Compare to 0, 1/2 and 1 to judge fraction size quickly.
In depth
Benchmarks like 0, 1/2 and 1 give quick sense of size. Compare a fraction to 1/2 to know if it is small or large, then do rough arithmetic.
Worked example
3/7 + 5/9: 3/7 is a bit under 1/2, 5/9 a bit over 1/2, so the sum is about 1.
Real-world uses
- Quickly judging whether 5/9 is more or less than half when comparing survey results
Common mistake
Using a benchmark that is too far away, which makes errors large.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Estimation with Benchmarks?
Compare to 0, 1/2 and 1 to judge fraction size quickly. It is a topic at the intermediate level in Arithmetic & Number Sense.
Where is Estimation with Benchmarks used in real life?
Real-world examples: Quickly judging whether 5/9 is more or less than half when comparing survey results.
What should I learn before Estimation with Benchmarks?
Make sure you are comfortable with Continued Fractions Intro, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Estimation with Benchmarks?
Using a benchmark that is too far away, which makes errors large.
How can I practise Estimation with Benchmarks?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Estimation with Benchmarks?
Move on to Number Sense Puzzles next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.