What is a ratio? A ratio is a comparison of two quantities by division. A ratio actually compares one thing happening to another. Ratios compares two or more amounts and are often expressed as fractions in simplest form or as decimals. Ratio can be written in three different ways:-
1. Using a colon like 3:2
2. Using a fraction like 3/2
3. Using the word “ to” like 3 to 2
Ratio Example: - Sam has 4 apples and 9 bananas. What is the ratio of his apples to bananas?
Solution: - Total numbers of apples are 4 and bananas are 9. SO the ratio will be 4:9.
Multiplying and dividing any ratio by same non- zero number makes no difference to the ratio. For example, the ratio 3:9 is equal to 1:3.
Two ratios that name the same number are equivalent ratios. Equivalent ratios can be calculated by multiplying or dividing each term of the ratio by the same non - zero number.
For example: - If we have a ratio 2:7, multiplying both terms by 3 gives a new ratio 6:21
Hence, 2:7 and 6:21 are equivalent ratios.
If we have 12:3, if we reduce this fraction, we get 4:1
Hence 12:3 and 4:1 are equivalent ratios.
Now let us learn about ratio and rates. A rate is a ratio involving two quantities in different units. The rate 225 heartbeat/ 3minutes compare heartbeat to minutes. If the denominator is 1 then it is known as the unit rate. Therefore,
225 heartbeat/3 minutes = 75 heartbeat / 1 minute.
Hence, the unit rate is 75 heartbeats per minute.
Equivalent rates have the same value but use different measurements. We use equivalent rates to help us with unit conversions.
For example: - A jet flies 540 miles per hour. What is the rate in miles per minute?
Solution: - 540 miles/ 1 hour = 1hour/60 min
After simplifying, we get 9 miles per minute.
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| Example of a ratio |
2. Using a fraction like 3/2
3. Using the word “ to” like 3 to 2
Ratio Example: - Sam has 4 apples and 9 bananas. What is the ratio of his apples to bananas?
Solution: - Total numbers of apples are 4 and bananas are 9. SO the ratio will be 4:9.
Multiplying and dividing any ratio by same non- zero number makes no difference to the ratio. For example, the ratio 3:9 is equal to 1:3.
Two ratios that name the same number are equivalent ratios. Equivalent ratios can be calculated by multiplying or dividing each term of the ratio by the same non - zero number.
For example: - If we have a ratio 2:7, multiplying both terms by 3 gives a new ratio 6:21
Hence, 2:7 and 6:21 are equivalent ratios.
If we have 12:3, if we reduce this fraction, we get 4:1
Hence 12:3 and 4:1 are equivalent ratios.
Now let us learn about ratio and rates. A rate is a ratio involving two quantities in different units. The rate 225 heartbeat/ 3minutes compare heartbeat to minutes. If the denominator is 1 then it is known as the unit rate. Therefore,
225 heartbeat/3 minutes = 75 heartbeat / 1 minute.
Hence, the unit rate is 75 heartbeats per minute.
Equivalent rates have the same value but use different measurements. We use equivalent rates to help us with unit conversions.
For example: - A jet flies 540 miles per hour. What is the rate in miles per minute?
Solution: - 540 miles/ 1 hour = 1hour/60 min
After simplifying, we get 9 miles per minute.
