## Math 6 Chapter 3 Lesson 13: Mixed Numbers Decimals and Percents

## 1. Summary of theory Tóm

### 1.1. Mixed numbers

– If a positive fraction is greater than 1, we can write it as a mixed number by: dividing the numerator by the denominator, the resulting quotient is the integer part of the mixed number, the remainder is the numerator of the attached fraction, and the denominator is still given sample.

**Example 1:** \(\dfrac{5}{4} = 1\dfrac{1}{4}\)

– To write a mixed number as a fraction, we multiply the integer part by the denominator and add the numerator, the result is the numerator of the fraction, and the denominator is still the given denominator.

**Example 2:** \(2\dfrac{1}{4} = \dfrac{{1.4 + 1}}{4} = \dfrac{5}{4}\)

**Attention:**

– For mixed numbers with a “-” sign in front, we just need to change its opposite according to the usual rules and then write a “-” sign in front of the found fraction, absolutely do not take the negative integer part. with the denominator and then add the numerator.

**Example 3: **\( – 3\dfrac{4}{7} = – \dfrac{{3.7 + 4}}{7} = – \dfrac{{25}}{7}\)

– When writing a negative fraction as a mixed number, we just need to write its opposite as a mixed number and put a “-” sign in front of the result.

**Example 4: **\(\dfrac{{ – 11}}{9} = – \dfrac{{11}}{9} = – 1\dfrac{2}{9}\)

### 1.2. Decimal fraction. Decimal.

A decimal fraction is a fraction whose denominator is a power of 10.

**Example 5: **\(\dfrac{{ – 3}}{{10}};\,\,\,\dfrac{{17}}{{100}} = \dfrac{{17}}{{{{10}^2) }}};\dfrac{{2021}}{{1000}} = \dfrac{{2021}}{{{{10}^3}}};…\)

– Decimal fractions can be written as decimals.

**Example 6:** \(\dfrac{{ – 3}}{{10}} = – 0.3;\,\,\,\dfrac{{17}}{{100}} = 0.17;\dfrac{{2021} }{{1000}} = 2,021;…\)

– Decimal has two parts:

- The integer part to the left of the comma;
- The decimal is written to the right of the comma.

The number of decimal places is equal to the number of zeros in the denominator of the decimal fraction.

### 1.3. Percent

– Fractions with denominator 100 are written as a percentage, i.e. the form consisting of the numerator of the given fraction with the symbol %.

**Example 7:** \(\dfrac{25}{{100}} = 25\% ;\,\,\dfrac{{120}}{{100}} = 120\% \)

## 2. Illustrated exercise

**Question 1: **Write the following fractions as mixed numbers: \(\displaystyle {{17} \over 4};{{21} \over 5}\)

– We have:

Derive: \(\displaystyle {{17} \over 4} = 4 + {1 \over 4} = 4{1 \over 4}\)

– We have:

Derive: \(\displaystyle {{21} \over 5} = 4 + {1 \over 5} = 4{1 \over 5}\)

**Verse 2:** Write mixed numbers as fractions: \(\displaystyle 2{4 \over 7};\,4{3 \over 5}\)

**Solution guide**

We have: \( \displaystyle 2{4 \over 7} = {{2.7 + 4} \over 7} = {{18} \over 7}\)

\( \displaystyle 4{3 \over 5} = {{4.5 + 3} \over 5} = {{23} \over 5}\)

**Question 3: **Write the following fractions as decimals

\(\dfrac{{27}}{{100}};\,\,\,\dfrac{{ – 13}}{{1000}};\,\,\dfrac{{261}}{{100000} }\)

**Solution guide**

We have \(\dfrac{{27}}{{100}} = 0.27;\,\,\,\dfrac{{ – 13}}{{1000}} = – 0.013;\)\(\dfrac) {{261}}{{100000}} = 0.00261\)

**Question 4: **Write the following decimals as decimal fractions

\(1.21\,\,;\,\,0.07\,\,;\,\, – 2.013\)

**Solution guide**

\(1,21 = \dfrac{{121}}{{100}}\,\,;\,\,0.07 = \dfrac{7}{{100}};\)\( – 2.013 = \ dfrac{{ – 2013}}{{1000}}\)

## 3. Practice

### 3.1. Essay exercises

**Question 1:** Write the fractions \(\dfrac{7}{{10}},\dfrac{{10}}{{21}},\dfrac{7}{8}\) as the sum of fractions whose numerator is 1 and different models.

**Verse 2:** Calculate reasonably

\(\dfrac{{\dfrac{5}{{22}} + \dfrac{3}{{13}} – \dfrac{1}{2}}}{{\dfrac{4}{{13}} – \dfrac{2}{{11}} + \dfrac{3}{2}}}\)

**Question 3: **Find the simplest fractions knowing that: Product of numerator and denominator is 220; the simplest fraction that can be represented by a decimal.

**Question 4: **Compare \(A = \dfrac{{{{20}^{10}} + 1}}{{{{20}^{10}} – 1}}\) and \(B = \dfrac{{{) {20}^{10}} – 1}}{{{{20}^{10}} – 3}}\)

### 3.2. Multiple choice exercises Bài

**Question 1:** Write the decimal 0.25 in fraction form, we get

A. \(\dfrac{1}{4}\)

B. \(\dfrac{5}{2}\)

C. \(\dfrac{1}{5}\)

D. \(\dfrac{3}{4}\)

**Verse 2:** The fraction \(\dfrac{{47}}{{100}}\) written as a percentage is

A. 4.7%

B. 47%

C. 0.47%

D. 470%

**Question 3: **Select the correct answers

A. \(\dfrac{{19.20}}{{19 + 20}} = \dfrac{1}{{19}} + \dfrac{1}{{20}}\)

B. \(6\dfrac{{23}}{{11}} = \dfrac{{6.23 + 11}}{{11}}\)

C. \(a\dfrac{a}{{99}} = \dfrac{{100{\rm{a}}}}{{99}}\,\,\left( {a \in {N^*) }} \right)\)

D. \(\dfrac{{15}}{{23}} = \dfrac{{1.23}}{{15}}\)

**Question 4: **Mixed numbers \( – 2\dfrac{3}{4}\) written as a fraction is

A. \( – \dfrac{{5}}{4}\)

B. \( – \dfrac{{11}}{4}\)

C. \( – \dfrac{{11}}{6}\)

D. \( – \dfrac{{21}}{4}\)

**Question 5:** Writing the fraction \(\dfrac{{131}}{{1000}}\) as a decimal we get:

A. 0.131

B. 0.1311

C. 1.31

D. 0.0131

## 4. Conclusion

Through this lesson, you should understand the following main topics:

- Know the concept of mixed numbers, decimals, percentages.
- Do some related exercises.

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