Ratio shares and fraction operators · Foundation
| English | 中文 | Pinyin |
|---|---|---|
| ratio/ˈreɪʃɪəʊ/ | 比 | bǐ |
Which fraction describes the whole?
- A club shares 84 yuan between two teams in the ratio 2:5. Does the first team receive two fifths of the total?
- This lesson studies ratio 比: A comparison that states the relative numbers of equal-sized parts.
Choose the mathematical structure
- Add the ratio parts to find the whole: 2:5 has 7 equal parts. Divide the total by 7, then multiply by the required part count. A fraction acts as a multiplier; a percentage p acts as p/100. Keep part-to-part and part-to-whole comparisons separate.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines ratio?
A comparison that states the relative numbers of equal-sized parts.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
Each part is 84/7=12 yuan, giving shares 24 and 60. The first team has 2/7 of the whole, while its share is 2/5 of the other share. A 3/4 portion of 28 is 21. A 120% amount of 35 is 1.2×35=42, so percentages may exceed 100.
Ratio shares and fraction operators
Add the ratio parts to find the whole: 2:5 has 7 equal parts
Compare the model with the worked case and explain one change.
Find the smaller share of 84 in ratio 2:5.
There are 7 parts; 84/7×2=24.
Test a tempting shortcut
- A ratio 2:5 does not give the first share as 2/5 of the total. The total has 7 parts. A multiplier over 1 increases a positive quantity; it does not automatically mean a probability.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
For a 2:5 division, the first share is always 2/5 of the whole. This claim is false. Explain which definition or assumption it violates.
Find 3/4 of 28.
28/4×3=21.
For a 2:5 division, the first share is always 2/5 of the whole.
A ratio 2:5 does not give the first share as 2/5 of the total. The total has 7 parts. A multiplier over 1 increases a positive quantity; it does not automatically mean a probability.
Interpret a new situation
- AQA N11/N12 and R3–R8 link ratio parts to fractions and operators. Check the shares add to the stated total and simplify a ratio by dividing every part by the same positive factor.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Find 120% of 35.
120/100×35=42.
Match each part of a complete solution to its purpose.
An assumption justifies the model; a check tests the result; interpretation connects it to the question.
Use this in your course
- 8300 · Foundation · 3.1. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
A comparison that states the relative numbers of equal-sized parts. Choose the relationship, show the method, check its assumptions and interpret the result.