Week 3 Review Answers and Solutions

These are the answers and solutions to the Week 3 Practice Exercises and Problems.

Solutions to Practice Exercise 1

a.) 2 1/5 + 3 2/5

We can add the whole numbers first, 2 + 1 = 3. Then, add the fractions: 1/5 + 2/5 = 3/5.
We then combine the whole number and the fraction, so the answer is 3 3/5.

b.) 8 1/4 + 2 3/4

We can add the whole numbers first, 8 + 2 = 10. Then, add the fractions: 1/4 + 3/4 = 4/4 = 1
We then add 10 + 1 = 11.

c.) 5 + 2 1/4

We can just add the whole numbers: 5 + 2 = 7. Then, we append the fraction. So the correct answer is 7 ¼.

d.) 5 1/2 + 1/5

We just add the fractions and combine the sum with the whole number 5 later. To add dissimilar fractions, we get the LCM of the denominators. The LCM of 2 and 5 is 10.

The equivalent fraction of ½ = 5/10.
The equivalent fraction of 1/5 = 2/10.
5/10 + 2/10 = 7/10

We now append 5. So, the correct answer is 5 7/10.

e.) 3 1/3 + 4 1/4 + 5 1/5

Just like in (d), we can separately add the whole numbers and then add the fractions.

Whole numbers: 3 + 4 + 5 = 12

To add dissimilar fractions, we get the LCM of the denominators. The LCM of 3, 4, and 5 is 60.

The equivalent fraction of 1/3 = 20/60.
The equivalent fraction of 1/4 = 15/60.
The equivalent fraction of 1/5 = 12/60.

20/60 + 15/60 +12/60 = 47/60

Appending the whole number, the final answer is 12 47/60.

Solutions to Practice Exercises 2

a.) 4 6/7 – 3/7

Solution

We just subtract the fractions and append the whole number. 6/7 – 3/7 = 3/7. So, the final answer is 4 3/7.

b.) 8 – 3/4

Solution

One strategy here is to borrow 1 from 8 and make the fraction 4/4. This means that 8 becomes 7 4/4.
So, 7 4/4 – ¾ = 7 ¼.

c.) 12 – 5 2/9

Solution

Our minuend is a whole number, so we can make a fraction out of it. To do this, we can borrow 1 from 12 and make the fraction 9/9. This means that 12 becomes 11 9/9.
So, 11 9/9 – 5 2/9 = 6 7/9.

d.) 7 3/10 – 7/10

We cannot subtract 3/10 – 7/10, so we borrow 1 from 7 and make the fraction 6 10/10. But since we already have 3/10, we add it to 6 10/10 making it 6 13/10.
So, 6 13/10 – 7/10 = 6 6/10 = 6 3/5.

e.) 6 1/5 – 3/4

Another strategy in subtracting fractions is to convert mixed fractions to improper fractions. The improper fraction equivalent of 6 1/5 is 31/5. Then, we find the LCM of 5 and 4 which is 20.

Now, the equivalent fraction of 31/5 is 124/20.
The equivalent fraction of 3/4 = 15/20.
124/20 – 15/20 = 109/20

Converting 109/20 to mixed fraction, we have 5 9/20.

f.) 9 3/8 – 4 5/7

9 3/8 – 4 5/7 = 8 3/8+8/8 – 4 5/7 = 8 11/8 – 4 5/7

The LCM of 8 and 7 is 56, so

4 77-40/56 = 4 37/56.

Solutions to Practice Problems

1.) 1 3/5 + 4/5 = 1 7/5 = 2 2/5

2.) Converting the improper fractions, we have
2 5/8= 21/8
1 5/6 = 11/6.

This means that we need to perform.
21/8-11/6.

Since they are dissimilar fractions, we get their LCM which is 48.
(126-88)/48= 38/48 reduce lowest term by dividing the numerator and denominator by 2, we get 19/24

3.) 2 5/6 – 17/8 = 17/6 – 17/8

LCD: 24
68/24 – 51/24 = 17/24

4.) 3/8 + 1/4
LCD: 8
3/8 + 2/8 = 5/8

Whole pizza – 5/8
8/8 – 5/8
= 3/8

5.) d = 3 4/15 + 5/8
d= 49/15 + 5/8
d= (49(8)+5(15))/120
d= (392+75)/120
d= 467/120
d=3 107/120

Practice Exercises on Subtracting Decimals

We have already learned how to add and subtract numbers with decimals. In this post, we practice subtracting decimals. Recall that in subtracting decimals, the decimal points should be aligned.

Practice Exercises

1.) 2.32 – 1.82
2.) 6.71 – 3.9
3.) 6 – 0.52
4.) 5.03 – 4.25
5.) 0.53 – 0.33
6.) 4 – 1.26
7.) 7.28 – 2.4
8.) 7.08 – 0.29
9.) 3 – 0.305
10.) 40 – 12.5

Answers

1.) 0.5
2.) 2.81
3.) 5.48
4.) 0.78
5.) 0.2
6.) 2.74
7.) 4.88
8.) 6.79
9.) 2.695
10.) 27.5

Enjoy learning!

Practice Quiz on Converting Decimals to Percent

We have already learned how to convert decimals to percent. Recall that to do this, we have to multiply the decimal by 100 in order to get its percentage. For example, 0.125 in decimals is equal to 12.5%. Now, let’s do some practice exercises.

Practice Quiz: Converting Decimals to Percent

1.) 0.2

2.) 0.5

3.) 1.3

4.) 0.06

5.) 0.0082

6.) 0.75

7.) 0.2315

8.) 0.62

9.) 0.02

10.) 0.34

Answer Key

1.) 20%

2.) 50%

3.) 130%

4.) 6%

5.) 0.82%

6.) 75%

7.) 23.15%

8.) 62%

9.) 2%

10.) 34%

Practice Quiz on Converting Percent to Decimals

We have already learned how to convert percent to decimals. In this post, we are going to practice how to convert percent to decimals. Recall that in converting percent to decimals, you just have to divided the percentage by 100.

Practice Quiz: Converting Percent to Decimals

1.) 20%

2.) 80%

3.) 25%

4.) 7%

5.) 150%

6.) 9.7%

7.) 0.35%

8.)12.17%

9.) 100%

10.) 420%

Answer Key

1.) 0.2

2.) 0.8

3.) 0.25

4.) 0.07

5.) 1.5

6.) 0.097

7.) 0.0035

8.) 0.1217

9.) 1

10.) 4.2

Practice Quiz on Converting Percent to Fraction

We have already learned how to convert percent to fraction. This post allows you to practice what you have already learned.

Practice Quiz: Converting Percent to Fraction

Convert the following percent to their equivalent fractions

1.) 25%

2.) 80%

3.) 2.5%

4.) 20%

5.) 5%   » Read more

Practice Quiz on Converting Fraction to Percent

After learning converting fraction to percent, let’s practice by answering the following questions. There are different methods in converting fraction to percent. One method is to convert the fraction to decimal first, then multiply by the result by 100. However, in the solutions below, we will mostly use equivalent fractions. That is, since we want a% means a/100, we will convert the fraction to its equivalent fraction with denominator 100. We can do this by multiplying the numerator and the denominator  by the same number.

Practice Quiz: Converting Fraction to Percent

1.) 3/4

2.) 5/8

3) 9/10

4.) 1/4

5.) 7/10

6.) 3/5

7.) 3/8

8.) 7/20

9.) 1/5

10.) 7/50

Solutions and Answers

1). We can make 3/4 as 100 by multiplying the denominator by 25. In effect,

\displaystyle \frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100}.

 Therefore, 3/4 is equal to 75%.

2.) What number should we multiply to 8 to get 100? That is, 100/8 or 12.5.

\displaystyle \frac{5}{8} = \frac{5 \times 12.5}{8 \times 12.5} = \frac{62.5}{100}.

Therefore, 5/8 is equal to 62.5%.

3.) This is a bit easy. What will you multiply to 10 to get 100? Of course, it’s 10.  So,

\displaystyle \frac{9}{10} = \frac{9 \times 10}{10 \times 10} = \frac{90}{100}.

 Therefore, 9/10 is equal to 90%.

4.) What should you multiply by 4 to get 100? It’s 25.

\displaystyle \frac{1}{4} = \frac{1 \times 25}{4 \times 25} = \frac{25}{100}

 So, 1/4 is equal to 25%.

5.) To make the denominator 100, we should multiply by 10 (similar to number 3). So,

\displaystyle \frac{7}{10} = \frac{7 \times 10}{10 \times 10} = \frac{70}{100}.

So, 7/10 is equal to 70%.

6.) What should we multiply by 5 to get 100? It’s 20. So,

\displaystyle \frac{3}{5} = \frac{3 \times 20}{5 \times 20} = \frac{60}{100}

So, 3/5 is equal to 60%.

7.) As discussed in number 2, we should multiply 8 by 12.5 in order to get 100. Therefore,

\displaystyle \frac{3}{8} = \frac{3 \times 12.5}{8 \times 12.5} = \frac{37.5}{100}.

So, 3/8 is equal to 37.5%.

8.) What should be multiplied by 20 to get 100? It’s 5. So,

\displaystyle \frac{7}{20} = \frac{7 \times 5}{20 \times 5} = \frac{35}{100}.

So, 7/20 is equal to 35%.

9.) What should be multiplied by 5 to get 100? It’s 20. So,

\displaystyle \frac{1}{5} = \frac{1 \times 20}{5 \times 20} = \frac{20}{100}

Therefore, 1/5 is equal to 20%.

10. What should be multiplied by 50 to get 100? It’s 2. So,

\displaystyle \frac{7}{50} = \frac{7 \times 2}{50 \times 2} = \frac{14}{100}.

So, 7/50 is equal to 14%.

Practice Quiz on Converting Decimals to Fractions

We have already learned how to convert decimals to fractions. The idea as we have discussed in the preceding link is to find the place value of the rightmost significant digit. The decimals whose place values are tenths, hundredths, thousandths and so on are multiplied by 1/10, 1/100, 1/1000 and so on respectively. After performing multiplication, the fraction must be reduced to lowest terms.

Practice Quiz: Converting Decimals to Fractions

Convert the following decimals to fractions.

1. ) 0.4

2.) 0.8

3.) 0.18

4.) 0.25

5.) 0.75

6.) 0.35

7.) 0.125

8.) 0.9

9.) 0.05

10.) 0.016

Complete Solutions and Answers

1.) 0.4 is the same as 4 tenths or 4 \times \frac{1}{10} = \frac{4}{10}.

We reduce to lowest terms by dividing both the numerator and denominator by 2. That is,

\displaystyle \frac{4 \div 2}{10 \div 2} = \frac{2}{5}.

Answer: \frac{2}{5}

2.) 0.8 is the same as 8 tenths or  8 \times \frac{1}{10} = \frac{8}{10}.

We reduce to lowest terms by dividing both the numerator and denominator by 2. That is,

\displaystyle \frac{8 \div 2}{10 \div 2} = \frac{4}{5}.

Answer: \frac{4}{5}

3.) 0.18 is the same as 18 hundredths or  18 \times \frac{1}{100} = \frac{18}{100}.

We reduce to lowest terms by dividing both the numerator and denominator by 2. That is,

\displaystyle \frac{18 \div 2}{100 \div 2} = \frac{9}{50}.

Answer: \frac{9}{50}

4.) 0.25 is the same as 25 hundredths or  25 \times \frac{1}{100} = \frac{25}{100}.

We reduce to lowest terms by dividing both the numerator and denominator by 25. That is,

\displaystyle \frac{25 \div 25}{100 \div 25} = \frac{1}{4}.

Answer: \frac{1}{4}

5.) 0.75 is the same as 75 hundredths or  75 \times \frac{1}{100} = \frac{75}{100}

We reduce to lowest terms by dividing both the numerator and denominator by 25. That is,

\displaystyle \frac{75 \div 25}{100 \div 25} = \frac{3}{4}.

Answer: \frac{3}{4}

6.) 0.35 is the same as 35 hundredths or  75 \times \frac{1}{100} = \frac{35}{100}

We reduce to lowest terms by dividing both the numerator and denominator by 5. That is,

\displaystyle \frac{35 \div 5}{100 \div 5} = \frac{7}{20}.

Answer: \frac{7}{20}

7.) 0.125 is the same as 125 thousandths or  125 \times \frac{1}{1000} = \frac{125}{1000}

We reduce to lowest terms by dividing both the numerator and denominator by 125. That is,

\displaystyle \frac{125 \div 125}{1000 \div 125} = \frac{1}{8}.

Answer: \frac{1}{8}

8.) 0.9 is the same as 9 tenths or 9 \times \frac{1}{10} = \frac{9}{10}.

Answer: \frac{9}{10}

9.) 0.05 is the same as 5 hundredths or  5 \times \frac{1}{100} = \frac{5}{100}

We reduce to lowest terms by dividing both the numerator and denominator by 5. That is,

\displaystyle \frac{5 \div 5}{100 \div 5} = \frac{1}{20}.

Answer: \frac{1}{20}

10.) 0.016 is the same as 16 thousandths or  16 \times \frac{1}{1000} = \frac{16}{1000}

We reduce to lowest terms by dividing both the numerator and denominator by 8. That is,

\displaystyle \frac{16 \div 8}{1000 \div 8} = \frac{2}{125}.

Answer: \frac{2}{125}

Practice Quiz on Converting Fractions to Decimals

In the previous post, we have learned how to convert fractions to decimals. Now, let’s see what you have learned in converting fractions to decimals by answering the following quiz.

Convert the following fractions to decimals.

1.) 1/5

2.) 3/4

3.) 2/3

4.) 3/8

5.) 5/6

6.) 7/10

7.) 7/15

8.) 5/8

9.) 5/7

10.) 9/20

11.) 8 \frac{3}{4}

12.) 12 \frac{7}{9}

Answer key

1.) 0.2

2.) 0.75

3.) 0.666… (repeating never ending 6’s) or 0.67 if rounded to nearest hundredths

4.) 0.375

5.) 0.8333… (repeating never ending 3’s)

6.) 0.7

7.) 0.4666 (repeating never ending 6’s)

8.) 0.625

9.) 0.714285714285 (repeating never ending 714285’s)

10.) 0.45

11.) 8.75

12) 12.777… (repeating never ending 7’s)

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