Fractions and Decimals

Question 1

a part or a section of a whole

Answer 1

fractions

Question 2

A fraction consists of two parts

Answer 2

numerator and denominator

Question 3

the number you see in the upper part of the fraction. It tells you how many sections are represented in the fraction.

Answer 3

numerator

Question 4

the number you see in the lower part of the fraction. It tells you how many sections the whole is divided into.

Answer 4

denominator

Question 5

a fraction where the value of the numerator is less than the value of the denominator.

Answer 5

proper fraction

Question 6

a fraction where the value of the numerator is greater than or equal to the value of the denominator.

Answer 6

improper fractions

Question 7

a combination of a whole number and a proper fraction

Answer 7

Mixed number

Question 8

Here are the steps you need to follow so you can convert an improper fraction to a mixed number:

Answer 8

Divide the numerator by the denominator. To do this, put the numerator inside the division bracket while put the denominator outside the division bracket, then perform long division.
Designate the quotient as the whole number of the mixed number
Assign the remainder as the numerator of the proper fraction part of the mixed number.
Copy the denominator of the improper fraction and use it as the denominator of the mixed number.
Reduce the proper fraction part of the mixed number, if possible

Question 9

Here are the steps on how to transform a mixed number into an improper fraction:

Answer 9

Multiply the denominator of the mixed number by the whole number part then add the product to the numerator. The resulting number is the numerator of the improper fraction.
Copy the denominator of the proper fraction of the mixed number and use it as the denominator of the improper fraction.
Reduce the obtained fraction to its lowest terms, if possible.

Question 10

Example 1: Convert 4⁄3 to mixed number form.

Answer 10

1 1/3

Question 11

Example: Convert 2 3⁄5 to a mixed number.

Answer 11

Therefore, 2 3⁄5 = 13⁄5

Question 12

are fractions that have equal value. These fractions represent the same portion of the whole.

Answer 12

Equivalent fractions

Question 13

How To Determine an Equivalent Fraction to a Given Fraction

Answer 13

The easiest way to determine an equivalent fraction to a given fraction is to multiply the numerator and the denominator of the given fraction by the same number.

For example, if we want to find an equivalent fraction to 1⁄2, we can multiply its numerator and denominator by the same number. If we multiply both the numerator and the denominator of ½ by 2, we obtain an equivalent fraction to ½ which is 2⁄4.

Question 14

Example: Find three equivalent fractions to ⅗

Answer 14

To find the answers, let’s multiply the numerator and the denominator of ⅗ with the same numbers thrice.

3⁄5 x 2⁄2 = 6⁄10

            3⁄5 x 3⁄3 = 9⁄15

             3⁄5 x 4⁄4 = 12⁄20

Therefore, 6⁄10, 9⁄15, and 12⁄20 are equivalent fractions to ⅗.

Question 15

How To Determine if Two Fractions are Equivalent Fractions

Answer 15

One method you can use to determine if two fractions are equivalent is by using the cross-multiplication method.

To perform the cross-multiplication method, follow these steps:

Multiply the numerator of the first fraction by the denominator of the second fraction.
Multiply the denominator of the first fraction by the numerator of the second fraction.
If the products you have obtained from Steps 1 and 2 are equal, then the fractions are equivalent. Otherwise, the fractions are not equivalent.

Question 16

Example: Are ¼ and 3⁄12 equivalent fractions?

Answer 16

se the cross-multiplication method:

Multiply the numerator of the first fraction by the denominator of the second fraction.
1 x 12 = 12

Multiply the denominator of the first fraction by the numerator of the second fraction.
4 x 3 = 12

If the products you have obtained from Steps 1 and 2 are equal, then the fractions are equivalent.
We have obtained 12 both from Step 1 and Step 2. Hence, ¼ and 3⁄12 are equivalent fractions.

Question 17

The lowest term of a fraction is also known as its

Answer 17

simplest form

Question 18

How To Reduce a Fraction to Its Lowest Term

Answer 18

Reducing or simplifying a fraction to its lowest term is the process of transforming a fraction to its simplest form.

For example, 15⁄20 is a fraction that is not in its lowest term. We can transform 15⁄20 into an equivalent fraction that is in the lowest term. The lowest term of 15⁄20 is 3⁄4. We will discuss in the next section how to reduce a fraction into its lowest terms.

It is important to note that the original fraction and its lowest term are equivalent fractions. Therefore, 15⁄20 and its simplified form 34, are equivalent fractions.

Question 19

The most reliable way to transform a fraction into its lowest term is using the Greatest Common Factor (GCF) of the numerator and the denominator. To transform a given fraction to its lowest terms:

Answer 19

Determine the GCF of the numerator and the denominator.
Divide both the numerator and the denominator by the GCF, the resulting fraction is the fraction reduced into lowest terms.

Question 20

Example 1: What is 8⁄10 in its lowest terms?

Answer 20

Determine the GCF of the numerator and the denominator.
Determine the GCF of 8 and 10. Using the prime factorization method, the GCF of 8 and 10 is 2.

Divide the numerator and the denominator by the GCF.
8⁄10 ÷ 2⁄2 = 4⁄5

The resulting fraction is ⅘. Hence, ⅘ is the lowest term of 8⁄10.

Question 21

Example 2: Simplify 45⁄225.

Answer 21

Determine the GCF of the numerator and the denominator.
Determine the GCF of 45 and 225. Using the prime factorization method, the GCF of 45 and 225 is 45.

Divide the numerator and the denominator by the GCF.
45⁄225 ÷ 45⁄45 = 1⁄5

The resulting fraction is ⅕. Hence, ⅕ is the lowest term of 45⁄225.

Question 22

fractions with the same denominators. For example, 2⁄3 and 1⁄3

Answer 22

similar fractions

Question 23

are fractions with unlike denominators. For example, 2⁄5 and 1⁄3

Answer 23

dissimilar fractions

Question 24

Dissimilar fractions can be transformed into equivalent similar fractions using

Answer 24

least common multilpe

Question 25

What Are Decimals?

Answer 25

numbers that combine a whole number and a fraction together

Question 26

numbers that combine a whole number and a fraction together

Answer 26

decimals

Question 27

Let’s use the decimal number 18.945 as an example.

We know that 18 is the whole number part of the decimal number. We also know the corresponding place value of the digits of 18; 8 is in the ones digit while 1 is in the tens digit. However, once we step to the right of the decimal point, we will encounter a new system for the place values of the digits of the decimal number.

Answer 27

The first digit on the right of the decimal point is the digit in the tenths place. Hence, 9 is in tenth place. Its value is 0.9.

The second digit on the right of the decimal point is the digit in the hundredths place. Hence, 4 is in the hundredths place. Its value is 0.04

The third digit on the right of the decimal point is the digit in the thousandths place. Hence, 5 is in the thousandths place. Its value is 0.005.

As you move to the left of the decimal number, the place value of the digits becomes 10 times larger. Therefore, the tenths place is 10 times larger than the hundredths place, the hundredths place is ten times larger than the thousandths place, and so on.

Question 28

These are the decimal numbers where the digits of the fractional part are finite or have an end. This means that the digits after the decimal point are countable.

Answer 28

terminating decimal

Question 29

These are the opposite of terminating decimals. The number of digits on the right of the decimal point is infinite or has no end. This means that the digits after the decimal point are uncountable.

Answer 29

non-terminating decimals

Question 30

These are terminating decimal numbers where the digits on the right of the decimal point are repeating but have an end.

Answer 30

Terminating and Repeating (Recurring) Decimal Numbers

Question 31

These are non-terminating decimal numbers where the digits on the right of the decimal point are repeating but have no end.

Answer 31

Non-terminating and Repeating (Recurring) Decimal Numbers

Question 32

If you have a half (½) of a peso, this also means you have 0.5 pesos. Therefore, ½ is equivalent to 0.5. However, how am I able to convert ½ into 0.5? How did I convert a fraction into its decimal form?

Answer 32

The easiest way to convert fractions into their decimal form is, of course, by using a calculator. However, knowing how to convert fractions into their decimal form manually gives you an edge during an examination where calculators are not allowed.

Question 33

Here are the steps to convert a proper fraction into its decimal form:

Answer 33

Divide the numerator by the denominator. Use the numerator as the dividend while use the denominator as the divisor.
Put a zero with a decimal point above the division bracket then add a decimal point and a zero after the number inside the division bracket.
Apply long division.

Question 34

Convert ½ to its decimal form.

Answer 34

Step 1: Divide the numerator by the denominator. Use the numerator as the dividend while use the denominator as the divisor.

We put 1 inside the division bracket since it is the numerator of the fraction. Meanwhile, we put 2 outside the division bracket since it is the denominator of the fraction.

fractions and decimals 10
Step 2: Put a zero with a decimal point above the division bracket then add a decimal point and a zero after the number inside the division bracket.

fractions and decimals 11
As we add a decimal point and a zero to the number inside the division bracket, 1 becomes 10. Now, we can divide 10 by 2 and proceed with the normal division process.

Step 3: Apply long division.

We may now perform division with whole numbers:

fractions and decimals 12
Therefore, the decimal form of ½ is 0.5

Question 35

Convert ⅓ to its decimal form.

Answer 35

Step 1: Divide the numerator by the denominator. Use the numerator as the dividend while use the denominator as the divisor.

We put 1 inside the division bracket since it is the numerator of the fraction. Meanwhile, we put 3 outside the division bracket since it is the denominator of the fraction.

fractions and decimals 13
Step 2: Put a zero with a decimal point above the division bracket then add a decimal point and a zero after the number inside the division bracket.

fractions and decimals 14
Step 3: Apply long division.

fractions and decimals 15
Continue adding 0 to the remainder in case it is smaller than the divisor so that you can continue the division process.

fractions and decimals 16
Since the division process is never-ending and we will never arrive at a remainder of 0, then the decimal form of the fraction is a non-terminating decimal. Furthermore, since the digits of the decimal are repeating or recurring, then it means that the decimal number we obtained is a non-terminating and repeating decimal.

Therefore, the decimal form of ⅓ is 0.333…

Question 36

Here are the steps to convert an improper fraction into its decimal form:

Answer 36

Divide the numerator by the denominator. Use the numerator as the dividend while use the denominator as the divisor.
Divide the whole numbers.
If there’s a remainder, add a decimal point and a zero to the right of the number inside the division bracket and add a zero also to the right of the remainder.
Apply long division and put a decimal point to the final answer.

Question 37

Convert 8⁄5 to its decimal form

Answer 37

Divide the numerator by the denominator. Use the numerator as the dividend while use the denominator as the divisor.
fractions and decimals 17
Divide the whole numbers.
fractions and decimals 18
If there’s a remainder, add a decimal point and a zero to the right of the number inside the division bracket and add a zero also to the right of the remainder.
fractions and decimals 19
Apply long division and put a decimal point to the final answer.
fractions and decimals 20

Question 38

There are only two steps you must keep in your mind so you will be able to convert a mixed number to its decimal form:

Answer 38

Use the whole number part of the mixed number as the whole number part of the decimal form
Convert the proper fraction part of the mixed number into its decimal form. The obtained result is the fractional part of the decimal form

Question 39

Convert 2 2⁄5 to its decimal form.

Answer 39

Use the whole number part of the mixed number as the whole number part of the decimal form.
The whole number part in 2 2⁄5 is 2. Therefore, this is also the whole number part of its decimal form.

Convert the proper fraction part of the mixed number into its decimal form. The obtained result is the fractional part of the decimal form.
Using the steps on converting a proper fraction into its decimal form (you can review the steps in the section above), ⅖ is equal to 0.4.

Therefore, the decimal form of 2 2⁄5 is 2.4

Question 40

How To Convert Decimals into Fractions

Answer 40

If we can convert fractions into decimals, of course, we can also perform the opposite. We can convert a decimal into a fraction form.

However, take note that not all decimals can be converted into fractions. Again, non-terminating decimals are irrational numbers which means they cannot be expressed as fractions.

Let’s now proceed to the steps on how to convert decimals into fractions:

Use the numbers on the right of the decimal point as the numerator of the fraction. Do not write the zeros that appear immediately after the decimal point and before the nonzero digit.
If there is one digit on the right of the decimal point, use 10 as the denominator. If there are two digits on the right of the decimal point, use 100 as the denominator. If there are three digits on the right of the decimal point, use 1000 as the denominator and so on.
Reduce the fraction you have obtained from Step 1 and Step 2 into its lowest terms.

Question 41

Convert 0.2 to its fraction form.

Answer 41

Use the numbers on the right of the decimal point as the numerator of the fraction. Do not write the zeros that appear immediately after the decimal point and before the nonzero digit.
The number on the right of the decimal point is 2. Therefore, the numerator of the fraction form is 2.

If there is one digit on the right of the decimal point, use 10 as the denominator. If there are two digits on the right of the decimal point, use 100 as the denominator. If there are three digits on the right of the decimal point, use 1000 as the denominator and so on.
Since there’s only one digit on the right of the decimal point (which is 2), we will use 10 as the denominator. This means that we have 2⁄10.

Reduce the fraction you have obtained from Step 1 and Step 2 into its lowest terms.
The Greatest Common Factor (GCF) of 2 and 10 is 2. Dividing both the numerator and the denominator of 2⁄10 by 2:

2⁄10 ÷ 2⁄2 = 1⁄5

Therefore, the fraction form of 0.2 is ⅕

Question 42

Convert 0.008 to fraction.

Answer 42

1. Use the numbers on the right of the decimal point as the numerator of the fraction. Do not write the zeros that appear immediately after the decimal point and before the nonzero digit.

The number on the right of the decimal point is 008. However, we will not consider those numbers on the left of 8 because they immediately appear after the decimal point and before the nonzero digit. This means that the numerator of our fraction is 8.

2. If there is one digit on the right of the decimal point, use 10 as the denominator. If there are two digits on the right of the decimal point, use 100 as the denominator. If there are three digits on the right of the decimal point, use 1000 as the denominator, and so on.

There are three digits on the right of the decimal point (i.e., 008). Hence, we will use 1000 as the denominator. This means we have 8⁄1000.

3. Reduce the fraction you have obtained from Step 1 and Step 2 into its lowest terms.

The Greatest Common Factor (GCF) of 8 and 1000 is 8. Dividing both the numerator and the denominator of 8⁄1000 by 8:

8⁄1000 ÷ 8⁄8 = 1⁄125

Therefore, 0.008 is equal to 1⁄125

Question 43

1) Reduce to lowest terms.
27
81
a)
1
3
b)
1
2
c)
7
9
d)
2
5

Answer 43

A

Question 44

2) Transform 4 into an improper fraction.
2
3
a)
15
3
b)
24
3
c)
14
3
d)
9
3

Answer 44

C

Question 45

3) Which digit of 0.43201 is in the hundredths place?
a) 4
b) 3
c) 2
d) 0

Answer 45

B

Question 46

4) Which of the following is an equivalent fraction to ?
5
6
a)
10
13
b)
9
10
c)
35
36
d)
25
30

Answer 46

D

Question 47

5) Convert 0.12 to fraction form
a)
3
25
b)
4
5
c)
2
15
d) None of the above

Answer 47

A