Lesson 6: What is Ratio?

§Text Passage

1Summary 重點摘要

Ratio compares two quantities. For example, 20 boys and 30 girls, the ratio is 20:30, simplified to 2:3. Learn how to write, read and simplify ratios.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Block 1: How to Write a RatioWhen writing a ratio, be clear about which quantity comes first and which comes second; the order cannot be swapped freely. Example: with 20 boys and 30 girls, the ratio of boys to girls is 20:30; writing 30:20 means the opposite, girls to boys. Read carefully which two quantities the question asks about. Another example: a basket holds 5 apples and 8 oranges, so the ratio of apples to oranges is 5:8; if the question asks for oranges to apples, write 8:5. The same basket yields two different ratios because the question differs.
2. Block 2: How to Read a RatioThe colon ':' in a ratio is read as 'to'. Example: 2:3 is read 'two to three' and 10:5 is read 'ten to five'. Although a ratio is related to division and fractions, it is not read as 'divided by' and is not named like a fraction; a ratio shows how many times one quantity is of another. Another example: 25:4 is read 'twenty-five to four'; in writing and reading a ratio, the first term, the colon and the second term are all indispensable and their order cannot be swapped — the two numbers on either side of the colon are called the terms.
3. Block 3: Simplifying RatiosSimplifying a ratio works like simplifying a fraction: find the greatest common factor of both terms, then divide both by it. Example: for 12:18, the GCF of 12 and 18 is 6; 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so 12:18 = 2:3. A ratio is in simplest form when its terms share no factor except 1. Another example: 25:15 — divide both terms by 5 to get 5:3; check by scaling back: 5 and 3 multiplied by 5 return exactly 25 and 15, so the simplification is sound.
4. Block 4: Units Must Be the SameBefore writing a ratio, make sure both quantities use the same unit; convert first if they do not. Example: compare 1 metre with 50 centimetres by writing 1 m as 100 cm, giving 100:50, which simplifies to 2:1. Writing 1:50 directly would be wrong, because the two numbers would use different units. Another example: the ratio of 2 hours to 40 minutes — convert to minutes first: 2 hours = 120 minutes, giving 120:40, which simplifies to 3:1; time units are the ones most often left unconverted, so take extra care.
5. Block 5: Ratio and FractionA ratio can be written in fraction form: 2:3 = 23, with the first term as numerator and the second as denominator. The reading is different, though: 23 is read as 'two-thirds' while 2:3 is read 'two to three'. A fraction names one number and a ratio relates two quantities, so choose the form the question asks for. Another example: 3:5 in fraction form is 35; if a question asks what part of the whole class the boys form, use the part-to-whole ratio, for instance 20:50 = 25, which differs from comparing two parts with each other.
6. Block 6: Ratio ValueThe ratio value is the quotient of the first term divided by the second. Example: the ratio value of 2:3 is 2 ÷ 3 = 23. It is a single number, which can be a fraction, a decimal or a whole number, such as 4:2 giving 2. Two ratios with equal values form a proportion, which is a key way to test proportion. Another example: the ratio value of 6:4 is 6 ÷ 4 = 1.5, a decimal; 3:2 has the same value 1.5, so 6:4 and 3:2 form a proportion — showing exactly that they are two forms of one ratio.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Ratio compares two quantities, symbol is :
• First term is before :, second term is after :
• Simplify ratio same as fractions: divide by GCF
• Different units: convert first
• Ratio value = first term ÷ second term