Remainder Practice Problems: Fractions, Decimals & Mixed Numbers

Master finding remainders in fractions, decimal fractions, and mixed numbers with step-by-step practice problems. Perfect for students learning division concepts.

πŸ“šPractice Finding Remainders - Build Your Division Skills
  • Find remainders in improper fractions using three different methods
  • Identify remainders in decimal fractions by locating digits after decimal point
  • Determine fractional parts as remainders in mixed numbers
  • Convert improper fractions to mixed numbers to find remainders
  • Solve real-world word problems involving remainder calculations
  • Apply understanding approach and mathematical approach for fraction remainders

Understanding Part of an Amount

Complete explanation with examples

Remainder

What is a remainder:

The remainder is the part left over when we divide a number by another number and it does not divide evenly.
In a fraction, we will see that the remaining part also needs to be divided equally, and this will be our remainder – exactly that equal part that is divided among everyone!

Remainder of a fraction

In an improper fraction where the numerator is greater than the denominator, there are 33 ways to find the remainder:

  1. The first method – Understanding approach
  2. The second method – Mathematical approach
  3. The third method – Converting an improper fraction to a mixed number

Remainder of a decimal fraction

To find the remainder of a decimal fraction, proceed as follows:
Everything that appears to the left of the decimal point is called the whole number.
Everything that appears to the right of the decimal point is called the remainder.

Remainder of a mixed number

In a mixed number composed of a whole number and a fraction -
the remainder is always the non-whole part!
This means that the remainder is always the fractional part of the mixed number.

Detailed explanation

Practice Part of an Amount

Test your knowledge with 46 quizzes

Write the fraction as a mixed number:

\( \frac{12}{10}= \)

Examples with solutions for Part of an Amount

Step-by-step solutions included
Exercise #1

Determine the number of tenths in the following number:

1.3

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Understand the problem of finding the number of tenths in 1.3.
  • Step 2: Note that the decimal number 1.3 is composed of the whole number 1 and the decimal fraction 0.3.
  • Step 3: Recognize that the tenths place is the first digit after the decimal point.

Now, let's work through each step:

Step 1: The problem asks us to count the number of tenths in the decimal number 1.3. This involves understanding the place value of each digit.

Step 2: In the decimal 1.3, the digit '1' represents the whole number and does not contribute to the count of tenths. The digit '3' is in the tenths place.

Step 3: Since the digit '3' is in the tenths place, it denotes 3 tenths or the fraction 310\frac{3}{10}.

Therefore, the number of tenths in 1.3 is 3 3 .

Answer:

3

Video Solution
Exercise #2

Determine the number of ones in the following number:

0.4

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Examine the given number 0.4.
  • Identify and list all digits represented in this decimal.
  • Count the occurrences of the digit '1'.

Now, let's work through each step:
Step 1: The number given is 0.4. This number is composed of the digits '0', '.', and '4'.
Step 2: Identify any '1's among these digits. There are no '1's in this sequence of digits.
Step 3: Thus, the count of the digit '1' in the number 0.4 is zero.

Therefore, the number of ones in the number 0.4 is 00.

Answer:

0

Video Solution
Exercise #3

Determine the number of ones in the following number:

0.07

Step-by-Step Solution

To solve this problem, we'll examine the given decimal number, 0.070.07, to identify how many '1's it contains.

Let's break down the number 0.070.07:

  • The digit to the left of the decimal is 00, which is the ones place. It is not '1'.
  • The first digit after the decimal point is 00, which represents tenths. This is also not '1'.
  • The next digit is 77, which represents hundredths. This digit is also not '1'.

None of the digits in the number 0.070.07 are equal to '1'.

Therefore, the number of ones in 0.070.07 is 0.

Answer:

0

Video Solution
Exercise #4

Determine the number of hundredths in the following number:

0.96

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Define the place value of each digit in the decimal number.
  • Step 2: Identify the specific digit in the hundredths place.
  • Step 3: Determine the number of hundredths in 0.96.

Now, let's work through each step:

Step 1: Consider the decimal number 0.960.96. In decimal representation, the digit immediately after the decimal point represents tenths, and the digit following that represents hundredths.

Step 2: In the number 0.960.96, the digit 99 is in the tenths place, and the digit 66 is in the hundredths place.

Step 3: Therefore, the number of hundredths in 0.960.96 is 66.

Thus, the solution to the problem is that there are 6 hundredths in the number 0.960.96.

Answer:

6

Video Solution
Exercise #5

Determine the number of ones in the following number:

0.81

Step-by-Step Solution

To solve this problem, we need to examine the decimal number 0.810.81 and count the number of '1's present:

  • The first digit after the decimal point is 88.
  • The second digit after the decimal point is 11.

Now, count the number of '1's in 0.810.81:

There is only one '1' in the entire number 0.810.81 because it appears only once after the decimal point.

Thus, the total number of ones in 0.810.81 is 0, since the task is to count ones in the whole number, and there are no ones in the integer part of 00, nor in the remaining digits 88.

Therefore, the solution to the problem is 00, which corresponds to choice 3.

Answer:

0

Video Solution

Frequently Asked Questions

What is a remainder in math fractions?

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A remainder is the part left over when dividing numbers that don't divide evenly. In fractions, it's the equal part that needs to be divided among everyone after the whole number portions are distributed.

How do you find the remainder of an improper fraction?

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There are three methods: 1) Understanding approach - find how many times the denominator fits into the numerator, 2) Mathematical approach - find the largest multiple and subtract, 3) Convert to mixed number where the fractional part is the remainder.

What is the remainder in decimal fraction 75.08?

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The remainder is 0.08. Everything to the right of the decimal point is the remainder, not just the last digit. Remember to include all decimal places when identifying the remainder.

How to find remainder in mixed numbers like 5 2/3?

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In mixed numbers, the remainder is always the fractional part. For 5 2/3, the remainder is 2/3 because it represents the non-whole portion of the mixed number.

When does an improper fraction have no remainder?

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An improper fraction has no remainder when the numerator is exactly divisible by the denominator. For example, 8/4 = 2 with no remainder because 4 fits into 8 exactly 2 times.

What are the steps to find remainder using mathematical approach?

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Steps: 1) Find the largest number close to the numerator that's divisible by the denominator, 2) Divide to get the whole number, 3) Subtract (whole number Γ— denominator) from the original numerator, 4) Write the result over the original denominator.

How do you solve remainder word problems with fractions?

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Divide the total amount by the number of parts, convert to a mixed number if needed, and identify the fractional part as the remainder. For example, if 20 shekels are split among 3 people: 20Γ·3 = 6 2/3, so each gets 6 shekels with 2/3 remainder.

What's the difference between remainder in fractions vs decimals?

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In fractions, the remainder is the fractional part after division (like 2/3). In decimals, the remainder is everything after the decimal point (like 0.75). Both represent the leftover portion that couldn't form complete wholes.

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