Decimals percents and fractions worksheets: Fractions, decimals and percents worksheets

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Fractions, Decimals & Percents (Numeric)

For worksheet has 12 problems finding the missing value. Value can be either a fraction, decimal or Percent.

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50+ Converting Percents, Decimals, and Fractions worksheets for 5th Year on Quizizz

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Converting Percents, Decimals, and Fractions worksheets for Year 5 are essential tools for teachers who want to help their students develop a strong foundation in math. These worksheets focus on key concepts such as percents, ratios, and rates, which are crucial for understanding more complex mathematical topics in later grades. By using these worksheets, teachers can provide their students with ample practice opportunities to master the skills necessary for converting between percents, decimals, and fractions. Additionally, these Year 5 worksheets can be easily integrated into any math curriculum, allowing teachers to seamlessly incorporate them into their lesson plans. With a variety of exercises and problems, these worksheets cater to different learning styles and ensure that students have a comprehensive understanding of percents, decimals, and fractions.

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Decimal fractions — how to solve examples 5, 6 grade

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It turns out that learning to work with fractions is useful not only for school, but also to write a music track or make up a website. In this article, we deal with the theory and learn how to perform basic actions with fractions.

The concept of a decimal fraction

Before answering the question of how to find a decimal fraction, let’s look at the basic definitions, types of fractions and the difference between them.

The fraction is a number in mathematics, in which a and b are numbers or expressions. In fact, this is just one of the forms in which a number can be represented. There are two notation formats:

plain — ½ or a/b,
decimal — 0.5.

In an ordinary fraction, it is customary to write the dividend above the line, which becomes the numerator, and below the line there is always a divisor, which is called the denominator. The line between the numerator and denominator means division.

In decimal, the denominator is always 10, 100, 1000, 10000, etc. Basically, decimal is what you get when you divide the numerator by the denominator. The decimal fraction is written on a line separated by commas to separate the integer part from the fractional part. Like this:

0.8
7.42
9.932

End decimal is a fraction in which the number of digits after the decimal point is exactly defined.

Infinite decimal is when the number of digits after the decimal point is infinite. For convenience, mathematicians agreed to round these numbers to 1-3 after the decimal point.

Solve your math homework for 5.

Detailed solutions will help you understand the most difficult topic.

Properties of decimal fractions

The main property of decimal fraction is as follows: if one or more zeros are added to the decimal fraction on the right, its value will not change. This means that if your fraction has a lot of zeros, you can simply discard them. For example:

0.600 = 0.6
21.10200000 = 21.102

Basic features
The fraction has no value, provided that the divisor is zero. A fraction is zero if the numerator is zero and the denominator is not. Two fractions a/b and c/d are said to be equal if a * d = b * c. If the numerator and denominator are multiplied or divided by the same natural number, then the fraction equal to it will be

Common and decimal fractions are old friends. Here’s how they are related:

The integer part of the decimal is equal to the integer part of the mixed fraction. If the numerator is less than the denominator, then the integer part is equal to zero.
The fractional part of a decimal fraction contains the same digits as the numerator of the same fraction in ordinary form.
The number of digits after the decimal point depends on the number of zeros in the denominator of the common fraction. That is, 1 digit is a divisor of 10, 4 digits is a divisor of 10000.

Studying in mathematics courses is a great way to consolidate the acquired knowledge in practice and pull up complex topics.

How to write a decimal fraction

Let’s look at examples of how to write a decimal fraction. A small reminder: first we write the integer part, put a comma and then write down the numerator of the fractional part.

Example 1. Convert the common fraction 16/10 to decimal.

How we solve:

The denominator is 10 — this is one zero.
We count from right to left in the numerator of the fractional part one sign and put a comma.
In the resulting decimal fraction, the number 1 is the integer part, the number 6 is the fractional part.

Answer: 16/10 = 1.6.

Example 2. Convert 37/1000 to decimal.

How we solve:

The denominator is 1000, which is three zeros.
We count from right to left in the numerator of the fractional part three characters and put a comma.
Since there are only two digits in the numerator, we write zeros in empty places.
In the resulting decimal fraction, the number 0 is the integer part, 037 is the fractional part.

Answer: 37/1000 = 0.037.

How to read decimals

For the teacher to understand you correctly, it is important to read decimals correctly. First, we pronounce the integer part with the addition of the word «whole», and then the fractional part with the designation of the digit — it depends on the number of digits after the decimal point:

How many digits after the decimal point?	Reads like
one digit — tenths;	1.3 — one whole, three tenths;
two digits — hundredths	2.22 — two whole, twenty-two hundredths;
three digits — thousandths;	23.885 — twenty-three point eight hundred and eighty-five thousandths;
four digits — ten thousandths;	0.5712 — zero point five thousand seven hundred twelve ten thousandths;
etc.

Save a visual picture to remember faster.

Converting decimals

So that no task confuses you with its wording, it is important to know how to convert decimals to other types. Now let’s learn!

How to convert a decimal to a percentage

Already in the fifth grade, math problems hint that fractions are somehow related to percentages. And it’s true: percent is one hundredth of any number, denoted by the% sign.

1% \u003d 1/100 \u003d 0.01

To find out how to convert percentages to fractions, you need to remove the % sign and divide our number by 100, as in the example above.

And to convert decimal fraction to percent — multiply the fraction by 100 and add the% sign. Let’s use an example:

0.15 = 0.15 100% = 15%.

Expressing a fraction as a percentage is simple: first, turn it into a decimal fraction, and then apply the previous rule.

2/5 = 0.4
0.4 100% = 40%

8/25 = 0.32
0.32 100% = 32%

ratio of parts and whole. Visual plate is our helper friend:

Converting decimals

Quick reminder:

Decimal is a number with a remainder, where the remainder comes after the whole part and is separated by a comma.

Mixed shot is also a number with a remainder, but the remainder is written as a simple fraction (with a dash).

To convert decimals to mixed fractions, you do not need to memorize special algorithms. It is enough to understand the definitions and read the given fraction correctly — this is what schoolchildren do in the 5th grade. And now let’s practice!

Example 1. Convert 5.4 to a mixed number.

How we decide:

Read aloud: five point four. “Four tenths” suggests that there will be 4 in the numerator and 10 in the denominator. In mixed form, this fraction looks like this: 5 4/10.
And now let’s reduce the numerator and denominator by two (because we can) and get: 5 2/5.

Answer: 5.4 = 5 2/5.

Example 2. Convert 4.005 to a mixed number.

How we decide:

Read aloud: four point five thousandths. So 5 goes to the numerator, and 1000 goes to the denominator. In mixed form, it turns out like this: 4 5/1000. After reduction: 4 1/200.

Answer: 4.005 = 4 1/200.

Example 3. Convert 5.60 to a mixed number.

How we decide:

Read aloud: five point sixty hundredths. We send 60 to the numerator and 100 to the denominator. In mixed form, the fraction is as follows: 5 60/100.
Let’s reduce the fractional part by 10 and get 5 6/10. Or you can remember about the property of a decimal fraction and simply discard the zeros in the numerator and denominator.

Answer: 5.60 = 5 6/10.

How to convert a decimal to a common fraction

Let’s not invent a wheel and consider the easiest way to convert a decimal to a common fraction. Here’s how to do it:

Let’s rewrite the original fraction in a new form: put the original decimal fraction in the numerator, and one in the denominator. For example:
- 0.35 = 0.35/1
- 2.34 = 2.34/1
Multiply the numerator and denominator by 10 so many times that the comma disappears from the numerator. In this case, after each multiplication, the comma in the numerator is shifted to the right by one sign, and zeros are added to the denominator, respectively. An example is easier:
- 0.35 = 0.35/1 = 3.5/10 = 35/100
- 2.34 = 2.34/1 = 23.4/10 = 234/100
And now we reduce — that is, we divide the numerator and denominator into multiples of them:
- 0.35 \u003d 35/100, divide the numerator and denominator by five, we get 6/20, divide by 2 again, we get the final answer 3/10.
- 2.34 = 234/100 = 117/50 = 2 17/50.

Do not forget about minus in the answer if the example was about a negative number. Very annoying mistake!

Operations with decimals

You can do the same things with decimals as with any other numbers. Let’s consider the most common ones with simple examples.

How to divide a decimal by a natural number

Divide the integer part of a decimal by this number.
Put a comma in the quotient and continue the calculation as in normal division.

Example 1. Divide 4.8 by 2.

How to solve:

Write down the division by a corner.
Divide an integer part by two. Write the result in a quotient and put a comma.
Multiply the quotient by the divisor, write down, look at the remainder of the division. But we haven’t finished yet, so we don’t write down the remainder «zero». We demolish 8 and divide it by 2.
Dividing again. We write the resulting 4 in the quotient and multiply it by the divisor:

Answer: 4.8 : 2 = 2.4.

Example 2. Divide 183.06 by 45.

How do we solve:

Record the angle division.
Divide the integer part of 183 by 45. Write down the result, put a comma in the quotient.
Write difference result of 183 and 180. Demolish 0. Write 0 to quotient to demolish 6.
Write down the result of the difference between 306 and 270. 36 is not divisible by 45, so add zero and produce the difference.

Answer: 183.06 : 45 = 4.068.

How to divide a decimal by a common fraction

To divide a decimal by a common or mixed fraction, you need to represent the decimal fraction as a common fraction, and write the mixed number as an improper fraction.

Example 1. Divide 0.25 by 3/4.

How to solve:

Write 0.25 as a fraction: 0.25 = 25/100.
Divide a fraction according to the rules:

Answer: 0.25: 3/4 = 1/3.

Example 2 Divide 2. 55 by 1 1/3.

How to solve:

Write 2.55 as a fraction: 2.55 = 255/1000.
Write 1 1/3 as a fraction: 1 1/3 = 4/3.
Divide a fraction according to the rules:

Answer: 2.55: 1 1/3 = 1 73/80.

How to multiply a decimal by a common fraction

To multiply a decimal by a common or mixed fraction, two rules for 6th grade are used. At the first, we reduce the decimal fraction to the form of an ordinary fraction and then multiply by the desired number. In the second case, we convert an ordinary or mixed fraction to a decimal and then multiply.

Example 1. Multiply 2/5 by 0.8.

How to solve:

Write 0.8 as a fraction: 0.8 = 8/10.
Multiply according to the rules: 2/5 ∗ 8/10 = 2/5 ∗ 4/5 = 8/25 = 0. 32.

Answer: 2/5 ∗ 0.8 = 0.32.

Example 2. Multiply 0.28 by 6 1/4.

How to solve:

Write 6 1/4 as a decimal: 6 1/4 = 6.25.
Multiply according to the rules: 0.28 ∗ 6.25 = 0.8.

Answer: 0.28 ∗ 6 1/4 = 0.8.

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Fractions, Decimals & Percents (Numeric) Worksheet Download

50+ Converting Percents, Decimals, and Fractions worksheets for 5th Year on Quizizz

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Explore printable Converting Percents, Decimals, and Fractions worksheets for 5th Year

Decimal fractions — how to solve examples 5, 6 grade

The concept of a decimal fraction

Properties of decimal fractions

How to write a decimal fraction

How to read decimals

Converting decimals

How to convert a decimal to a percentage

Converting decimals

How to convert a decimal to a common fraction

Operations with decimals

How to divide a decimal by a natural number

How to divide a decimal by a common fraction

How to multiply a decimal by a common fraction

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