Reducing Fractions to Lowest Terms

Consider the following two fractions: 1/2 and 2/4. These fractions are equivalent fractions. They both represent the same amount. One half of an orange is equal to two quarters of an orange. However, only one of these fractions is written in lowest terms. A fraction is in lowest terms when the numerator and denominator have no common factor other than 1.

The factors of 2 are 1 and 2. The factors of 4 are 1, 2, and 4. 2 and 4 share a common factor: 2. We can reduce this fraction by dividing both the numerator and denominator by their common factor, 2. 2 ÷ 2/4 ÷ 2 = 1/2. 1 and 2 have no common factor other than 1, so the fraction is in lowest terms.

Task 12

A Visit to a Concert

A lady was late ____1___ the concert. When she __2__ the concert ___3___. She entered ____4___ the hall and ___5___ her seat. The orchestra ___6___ some music. She had listened for a while before she ___7___ her neighbor: "What ___8___ ? "___9___ symphony", he answered. "Oh, dear! I ___10___ the first eight!" exclaimed the lady.

1. a. to 2. a. come

b. for b. comes

c. at c. came

d. in  d. had come

3. a. is already beginning 4. a. in

b. is already begun b. into

c. had begun yet c. to

d. had already begun  d. ---

5. a. finded 6. a. was playing

b. found b. was played

c. founded c. had played

d. was found  d. has been playing

7. a. had asked 8. a. do the play

b. asked b. they are playing

c. would ask c. they have played

d. ask d. are they playing

9. a. the nine 10. a. have missed

b. ninth b. had missed

c. the ninth c. was missed

d. a ninth  d. am missing

Enjoy yourself!

– Why did the student do multiplication problems on the floor?

– The teacher told her not to use tables!

– If you had 8 apples in one hand and 5 apples in the other, what would you have?

– Really big hands!

– What does the zero say to the the eight?

– Nice belt!

How old is my daughter?

My daughter is twice as old as my son and half as old as I am. In twenty-two years my son will be half my age. How old is my daughter?

Think a bit. Now think once more!

If you don’t know the answer read further.

Let us assume my daughter is age x. We are told my daughter is twice as old as my son, so that my son must be age x/2. We are also told that I am twice as old as my daughter so my age is 2x. In 22 years time my son will be (x/2 + 22) and I will be (2x + 22). Since he will be half of my age at that time x/2 + 22 = 1/2 (2x+22). Multiplying both sides by 2 we get x + 44 = 2x + 22 or x = 22. My daughter is 22 years old.

Self-assessment

Be ready to speak on the topic "Properties of rational numbers" using the following as a plan:

1. Why does the equation 2n=7 have no solution?

2. When do we say that a problem has no solution?

3. What should we do to find a multiplier?

4. What is a rational number?

5. What does the denominator denote?

6. What does the numerator denote?

7. What is a proper fraction?

8. What fraction do we call improper?

9. What is a mixed fraction?

10. What’s the difference between proper and improper fraction?

11. What’s an equivalent fraction?

12. How can we transform equivalent fractions?

13. What is the simplest fraction?

14. How to reduce a fraction?

15. Explain what is the greatest common factor?

16. When do we say that a number is relatively prime?

17. How do we add and subtract two simple fractions?

18. How do we multiply fractions?

19. How can we divide a fraction by another one?

20. Do mathematical concepts work in the case of rational numbers or integers?

Check your active vocabulary on the topic:

less than greater than proper fraction improper fraction mixed fraction equivalent fraction whole part fractional part to change to higher (lower) terms relatively prime the simplest fraction to reduce a fraction both

property to solve the problem twice as many as to translate into equation to represent to express to allow to have no solution to find the result to denote equal parts to divide into parts value

to determine the greatest common factor as well as to perform an arithmetic operation to bring to common denominator to draw a conclusion valid in the case of

Translate into English and be ready to give illustrative examples:

позначати знайти результат представити не має розв’язку у випадку з відносно простий дійти висновку виконати арифметичну операцію дробова частина в двічі більше, ніж дозволяти

вірний, правильний обидва нескоротний дріб скоротити (піднести) скоротити дріб так само, як привести до спільного знаменника найбільший спільний множник визначити, встановити більше, ніж

поділити на частини еквівалентний дріб властивість виражати правильний дріб ціла частина розв’язати задачу величина менше, ніж неправильний дріб мішаний дріб перевести у рівняння рівні частини

Fill in the gaps using a word from the list:

Multiplier Denominator mixed fractions

Solution Numerator Improper fractions The greatest common factor

Quotient Proper fractions Equivalent fractions

1. If we are allowed to use only integers, the equation 2n = 7 has no … .

2. If we try to solve the equation 2n = 7 we will find that n = 7/2 as to find a multiplier you should divide the product 7 by the … 2.

3. A rational number is a … of two integers p/q where q is not equal to 0.

4. The … denotes the number of equal parts into which the whole is divided.

5. The … denotes how many of these parts are taken.

6. Fractions representing values less than 1, like 2/3 for example are called ….

7. Fractions which name a number equal or greater than 1, like 2/3 or 3/2, are called ….

8. Numbers like 1 ½ which name a whole number and a fractional number are called ….

9. Fractions which represent the same fractional numbers like 1/2, 2/4, 4/8 and so on are called ….

10. … is the largest possible integer by which the numerator as well as denominator is divisible.

M ODULE 5