Simple Fraction Practice: Reduce and Expand Fractions

Master simplifying and expanding fractions with step-by-step practice problems. Learn to multiply and divide numerators and denominators while preserving values.

πŸ“šPractice Reducing and Expanding Simple Fractions
  • Expand fractions by multiplying numerator and denominator by the same number
  • Simplify fractions by dividing both parts by common factors
  • Find equivalent fractions with different numerators and denominators
  • Complete missing numbers in fraction expansion and reduction problems
  • Identify when fractions cannot be simplified further
  • Apply fraction concepts using real-world examples like pizza slices

Understanding Simplification and Expansion of Simple Fractions

Complete explanation with examples

Simplification and Expansiono f Simple Fractions

To amplify fractions

We will perform the same multiplication operation on the numerator and the denominator: the value of the fraction will be preserved.

You can expand as many times as you want and by any number.

To simplify fractions:

We will perform the same division operation on the numerator and the denominator: the value of the fraction will be preserved.

This can only be done with a number that is completely divisible by both the numerator and the denominator.

It is possible to simplify only until reaching a fraction in which it is not possible to find a number that divides without remainder both in the numerator and the denominator.

Step-by-step simplification of the fraction 24 over 16 to 6 over 4, and finally to 3 over 2 using division

Detailed explanation

Practice Simplification and Expansion of Simple Fractions

Test your knowledge with 17 quizzes

Increase the following fraction by a factor of 5:

\( \frac{3}{10}= \)

Examples with solutions for Simplification and Expansion of Simple Fractions

Step-by-step solutions included
Exercise #1

Simplify the following fraction:

124= \frac{12}{4}=

Step-by-Step Solution

Let's reduce as follows, divide the numerator by 4 and the denominator by 4:

12:44:4=31 \frac{12:4}{4:4}=\frac{3}{1}

Answer:

31 \frac{3}{1}

Video Solution
Exercise #2

Simplify the following fraction:

11= \frac{1}{1}=

Step-by-Step Solution

Let's reduce as follows, we'll divide both the numerator and denominator by 1:

1:11:1=11 \frac{1:1}{1:1}=\frac{1}{1}

Answer:

11 \frac{1}{1}

Video Solution
Exercise #3

Simplify the following fraction by a factor of 5:

1510= \frac{15}{10}=

Step-by-Step Solution

Let's reduce as follows, we'll divide both the numerator and denominator by 5:

15:510:5=32 \frac{15:5}{10:5}=\frac{3}{2}

Answer:

32 \frac{3}{2}

Video Solution
Exercise #4

Simplify the following fraction by a factor of 2:

128= \frac{12}{8}=

Step-by-Step Solution

Let's simplify as follows, we'll divide both the numerator by 2 and the denominator by 2:

12:28:2=64 \frac{12:2}{8:2}=\frac{6}{4}

Answer:

64 \frac{6}{4}

Video Solution
Exercise #5

Simplify the following fraction:

168= \frac{16}{8}=

Step-by-Step Solution

Let's simplify as follows, we'll divide both the numerator by 2 and the denominator by 2:

16:28:2=84 \frac{16:2}{8:2}=\frac{8}{4}

Answer:

84 \frac{8}{4}

Video Solution

Frequently Asked Questions

What does it mean to expand or amplify a fraction?

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Expanding a fraction means multiplying both the numerator and denominator by the same number. This creates an equivalent fraction that looks different but has the same value. For example, 1/2 expanded by 4 becomes 4/8.

How do you simplify a fraction step by step?

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To simplify a fraction: 1) Find a number that divides both numerator and denominator evenly, 2) Divide both parts by that number, 3) Repeat until no common factors remain. For example, 24/16 Γ· 8 = 3/2.

When can a fraction not be simplified anymore?

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A fraction cannot be simplified when there is no number (other than 1) that divides both the numerator and denominator without a remainder. For example, 3/5 cannot be simplified because 3 and 5 share no common factors.

Does expanding a fraction make it bigger?

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No, expanding a fraction does not change its actual value or make it bigger. The fraction only looks different with larger numbers, but represents the same amount. For instance, 1/2 = 4/8 = 8/16 all represent the same value.

What are equivalent fractions in simple terms?

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Equivalent fractions are different fractions that represent the same value. They are created by multiplying or dividing both the numerator and denominator by the same number. Examples include 2/4, 3/6, and 4/8, which all equal 1/2.

How do you find missing numbers in fraction problems?

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To find missing numbers: 1) Compare the known parts of both fractions, 2) Determine what number was used to multiply or divide, 3) Apply the same operation to the unknown part. If 2/8 = 4/β–‘, then 2Γ—2=4, so 8Γ—2=16.

What is the difference between simplifying and expanding fractions?

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Simplifying uses division to make fractions smaller and easier to work with, while expanding uses multiplication to create equivalent fractions with larger numbers. Both preserve the fraction's value but change its appearance.

Why is it important to learn fraction reduction and expansion?

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These skills are essential for adding, subtracting, and comparing fractions. They help solve math problems more easily and are used in real-life situations like cooking, measurements, and calculating proportions in recipes or construction projects.

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