Tóm tắt nội dung bài viết

**Vocabulary**

**Fraction:** Phân số

**Numerator: **Tử số

**Denominator: **Mẫu số

In the fraction 8/13, the numerator is 8 and the denominator is 13.

**Equivalent fractions: **Phân số tương đương (2/3; 4/6;…)

**The lowest common denominator: **Mẫu số chung nhỏ nhất

**Common factor:** Nhân tử chung

**Add:** Cộng

**Minus: **Trừ

**Multiply:** Nhân

**Divide:** Chia; * divisible:* Có thể chia được; Có thể chia hết.

**Times: **Nhân; lần

**Equal to; Equals; is: **Bằng

**Decimal:** Số thập phân

**Percent:** Phần trăm

**Sign: **Ký hiệu

**Odd:** Số lẻ

**Even:** Số chẵn

**Largest number: **Số lớn nhất

**Smallest number:** Số nhỏ nhất

**Obtain:** Đạt được; thu được

**Convert:** Chuyển

**Reduce: **Đơn giản; giản lược

**Drop:** Loại bỏ, xóa bỏ

**Carry out:** Thực hiện; Tính toán

**Procedure:** Thủ tục (thường được sử dụng trong chương trình, *còn gọi là chương trình con,* tương tự như **Funtion**).

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**Change the fraction**

*– To change a fraction to a decimal, divide the numerator of the fraction by its denominator.*

**Example:**

Express 5/6 as a decimal. We divide 5 by 6, obtaining 0.83.

*– To convert a decimal to a fraction, delete
the decimal point and divide by whatever unit of 10 the number of decimal
places represents.*

**Example:**

Convert 0.83 to a fraction.

+ First, delete the decimal point.

+ Second,
two decimal places represent hundredths, so divide 83 by 100: 83/100

0.83 = 83/100

*– To change a fraction to a percent, find
its decimal form, multiply by 100, and add a percent sign.*

**Example:**

Express 3/8 as a percent.

To convert 3/8 to a decimal, divide 3 by 8, which gives us 0.375. Multiplying 0.375 by 100 gives us 37.5%.

*– To change a percent to a fraction, drop the percent sign and divide the number by 100.*

**Example:**

Express 17% as a fraction.

Dropping the % sign gives us 17, and dividing by 100 gives us 17/100

*– To reduce a fraction, divide the numerator
and denominator by the largest number that divides them both evenly.*

**Example 1:**

Reduce 10/15 .

Dividing both the numerator and denominator by 5 gives us 2/3

**Example 2:**

Reduce 12/36

The largest number that divides into both 12 and 36 is 12.

Reducing the fraction, we have 1/3.

**Note:** In both examples, the reduced
fraction is exactly equal to the original fraction: 2/3 = 10/15 and 12/36 = 1/3

**Add fractions**

*– To add fractions with like denominators,
add the numerators of the fractions, keeping the same denominator.*

**Example:** 1/7 + 2/7 + 3/7 = 6/7

*– To add fractions with different
denominators, you must first change all of the fractions to equivalent
fractions with the same denominators.*

**STEP 1**. Find the lowest (or least)
common denominator, the smallest number divisible by all of the denominators.

**Example:**

If the fractions to be added are 1/3, 1/4 and 5/6, then the lowest common denominator is 12, because 12 is the smallest number that is divisible by 3, 4, and 6.

**STEP 2**. Convert all of the fractions to equivalent fractions, each having the lowest common denominator as its denominator.

To do this, multiply the numerator of each fraction by the number of times that its denominator goes into the lowest common denominator.

The product of this multiplication will be the new numerator.

The denominator of the equivalent fractions will be the lowest common denominator. (See Step 1 above.)

**Example:**

The lowest common denominator of are 1/3, 1/4 and 5/6 is 12.

Thus, 1/3 = 4/12 because 12 divided by 3 is 4, and 4 times 1 = 4. 1/4 = 3/12, because 12 divided by 4 is 3, and 3 times 1 = 3. 5/6 = 10/12, because 12 divided by 6 is 2, and 2 times 5 = 10.

**STEP 3**. Now add all of the equivalent fractions by adding the numerators.

**Example:**

4/12 + 3/12 + 10/12 = 17/12

**STEP 4**. Reduce the fraction if possible.

**Example:**

Add 4/5, 2/3, and 8/15.

The lowest common denominator is 15, because 15 is the smallest number that is divisible by 5, 3, and 15.

Then, 4/5 is equivalent to 12/15; 2/3 is equivalent to 10/15; and 8/15remains as 8/15.

Adding these numbers gives us 12/15 + 10/15 + 8/15 = 30/15.

Both 30 and 15 are divisible by 15, giving us 2/1, or 2.

**Multiply fractions**

*To multiply fractions, follow this procedure:*

**STEP 1**. To find the numerator of the
product, multiply all the numerators of the fractions being multiplied.

**STEP 2**. To find the denominator of the
product, multiply all of the denominators of the fractions being multiplied.

**STEP 3**. Reduce the product.

**Example:**

5/7 x 2/15 = 1/7 x 2/3 = 2/21.

We reduced by dividing both the numerator and denominator by 5, the common factor.

**Divide fractions**

*To divide fractions, follow this procedure:*

**STEP 1**. Invert the divisor. That is,
switch the positions of the numerator and denominator in the fraction you are
dividing by.

**STEP 2**. Replace the division sign with
a multiplication sign.

**STEP 3**. Carry out the multiplication
indicated.

**STEP 4**. Reduce the product.

**Example:**

Find 3/4 : 7/8.

Inverting 7/8, the divisor, gives us 8/7.

Replacing the division sign with a multiplication sign gives us 3/4 x 8/7. Carrying out the multiplication gives us 3/4 x 8/7 = 24/28.

The fraction 24/28 may then be reduced to 6/7 by dividing both the numerator and the denominator by 4.