Using Ratios ① Basics of Ratios and How to Simplify Them into Simple Integer Ratios
A “ratio” is a very useful way of showing how two or more quantities are related to each other.
Here, you will practice simplifying ratios into the simplest possible integer ratios and finding one value from the other.
What You Will Learn
Three basic rules for working with ratios:
① Dividing both terms by the same number gives a simpler integer ratio.
12：18 ＝ 2：3 (both terms were divided by 6)
② Multiplying both terms by the same number changes a ratio of fractions or decimals into an integer ratio.
1/2：2/3 ＝ 3：4 (both terms were multiplied by 6)
③ The value of the ratio “○：△” is ○ ÷ △ ＝ ○/△. For example, the value of the ratio 2：3 is 2/3.
Example Problem
Rewrite 0.4：0.6 and 2/5：3/5 as the simplest possible integer ratios. Also, if A：B ＝ 3：5 and A ＝ 120, what is B?
Solution:
①0.4：0.6 → (multiply both terms by 10) → 4：6 → (divide both terms by 2) → 2：3
②2/5：3/5 → (multiply both terms by 5) → 2：3
③When A：B ＝ 3：5, A ＝ 120 represents “3 parts.”
1 part ＝ 120 ÷ 3 ＝ 40. B ＝ 40 × 5 ＝ 200
Rewrite 0.4：0.6 and 2/5：3/5 as the simplest possible integer ratios. Also, if A：B ＝ 3：5 and A ＝ 120, what is B?
Solution:
①0.4：0.6 → (multiply both terms by 10) → 4：6 → (divide both terms by 2) → 2：3
②2/5：3/5 → (multiply both terms by 5) → 2：3
③When A：B ＝ 3：5, A ＝ 120 represents “3 parts.”
1 part ＝ 120 ÷ 3 ＝ 40. B ＝ 40 × 5 ＝ 200
Key Points
Remember
- For a ratio of fractions, multiply both terms by the least common multiple of the denominators to change it into an integer ratio.
- For a ratio of decimals, multiply by 10, 100, or another appropriate power of 10 to change it into an integer ratio.
- If one term of a ratio is known, the other term can always be found.
Practice Problems
- Rewrite the following ratios as the simplest possible integer ratios: ①36：48 ②0.3：0.8 ③2/3：3/4
- If A：B ＝ 4：7 and B ＝ 98, what is A?
- The ratio of the amount of money an older brother and his younger brother have is 5：3. If the older brother has 750 yen, how much money does the younger brother have?
Answers and Explanations
- Answer:① 3:4 ② 3:8 ③ 8:9
Explanation: ① 36:48 → divide by GCD=12 → 3:4. ② 0.3:0.8 → ×10 → 3:8. ③ 2/3:3/4 → multiply by the LCM of the denominators, 12 → (2/3)×12:(3/4)×12 = 8:9. - Answer:A = 56
Explanation: A:B=4:7 and B=98. 1 part=98÷7=14. A=14×4=56. - Answer:Younger brother's money = 450 yen
Explanation: Older brother:younger brother=5:3 and the older brother has 750 yen. 1 part=750÷5=150 yen. Younger brother=150×3=450 yen.