Reduce Fractions Practice Problems - Simplify & Expand

Master fraction reduction with step-by-step practice problems. Learn to simplify fractions by finding common factors and expand fractions efficiently.

πŸ“šPractice Reducing and Expanding Fractions Step by Step
  • Reduce fractions like 4/10 to 2/5 by dividing numerator and denominator
  • Find the greatest common factor to simplify fractions in one step
  • Practice multi-step reduction for complex fractions like 30/180 to 1/6
  • Expand fractions to equivalent forms with larger denominators
  • Master division techniques for faster fraction simplification
  • Build confidence with guided practice problems and instant feedback

Understanding How do you simplify fractions?

Complete explanation with examples
How do you simplify fractions? Or, how do you reduce fractions?

In most cases, when fractions are introduced to students as a new topic in the classroom, the initial reaction is: "Here's another complex subject we have to deal with." But then, reactions change and fractions are seen as a kind of enjoyable game that is more of a technical challenge. So, what's particularly important about fractions? Understanding their meaning, the division of roles between the numerator and the denominator, and how to reduce them. Is it difficult to reduce fractions? Not really.

So, when will you need to reduce the given fractions?

  • At the time it's required in an exercise/test.
  • In case you want to work with smaller fractions.
new example reduce_fractions

Detailed explanation

Practice How do you simplify fractions?

Test your knowledge with 17 quizzes

Increase the following fraction by a factor of 5:

\( \frac{6}{7}= \)

Examples with solutions for How do you simplify fractions?

Step-by-step solutions included
Exercise #1

Simplify the following fraction by a factor of 1:

310= \frac{3}{10}=

Step-by-Step Solution

We will reduce in the following way, divide the numerator by 1 and the denominator by 1:

3:110:1=310 \frac{3:1}{10:1}=\frac{3}{10}

Answer:

310 \frac{3}{10}

Video Solution
Exercise #2

Simplify the following fraction:

210= \frac{2}{10}=

Step-by-Step Solution

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

2:210:2=15 \frac{2:2}{10:2}=\frac{1}{5}

Answer:

15 \frac{1}{5}

Video Solution
Exercise #3

Simplify the following fraction by a factor of 4:

48= \frac{4}{8}=

Step-by-Step Solution

Let's simplify as follows, we'll divide both the numerator by 4 and the denominator by 4:

4:48:4=12 \frac{4:4}{8:4}=\frac{1}{2}

Answer:

12 \frac{1}{2}

Video Solution
Exercise #4

Simplify the following fraction:

416= \frac{4}{16}=

Step-by-Step Solution

We will reduce in the following way, divide the numerator by 4 and the denominator by 4:

4:416:4=14 \frac{4:4}{16:4}=\frac{1}{4}

Answer:

14 \frac{1}{4}

Video Solution
Exercise #5

Simplify the following fraction by a factor of 3:

36= \frac{3}{6}=

Step-by-Step Solution

We will reduce as follows, divide the numerator by 3 and the denominator by 3:

3:36:3=12 \frac{3:3}{6:3}=\frac{1}{2}

Answer:

12 \frac{1}{2}

Video Solution

Frequently Asked Questions

Everything you need to know about How do you simplify fractions?

How do you reduce fractions to lowest terms?

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To reduce fractions to lowest terms, divide both the numerator and denominator by their greatest common factor (GCF). For example, 4/10 reduces to 2/5 by dividing both by 2. Keep dividing until no common factors remain except 1.

What is the easiest way to simplify fractions?

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The easiest way is to find the largest number that divides evenly into both the numerator and denominator, then divide both by that number. Start by checking if both numbers are even (divisible by 2), then try 3, 5, and other common factors.

Can all fractions be reduced?

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No, not all fractions can be reduced. Fractions like 3/7 or 5/8 are already in lowest terms because their numerator and denominator share no common factors other than 1. These are called irreducible or simplified fractions.

What are the steps to reduce fractions?

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Follow these steps: 1) Find the greatest common factor (GCF) of the numerator and denominator, 2) Divide both the numerator and denominator by the GCF, 3) Check if the result can be reduced further, 4) Repeat until no common factors remain.

How do you expand fractions?

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To expand fractions, multiply both the numerator and denominator by the same number. For example, 1/3 can be expanded to 2/6 by multiplying both by 2, or to 5/15 by multiplying both by 5. This creates equivalent fractions.

Why is it important to reduce fractions?

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Reducing fractions makes them easier to work with in calculations, compare with other fractions, and understand visually. Simplified fractions like 1/2 are clearer than equivalent complex fractions like 50/100.

What's the difference between reducing and expanding fractions?

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Reducing fractions makes them simpler by dividing the numerator and denominator by a common factor. Expanding fractions makes them more complex by multiplying both parts by the same number. Both create equivalent fractions.

How do you know when a fraction is fully reduced?

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A fraction is fully reduced when the numerator and denominator have no common factors other than 1. You can check by finding the GCF - if it equals 1, the fraction cannot be reduced further.

More How do you simplify fractions? Questions

Click on any question to see the complete solution with step-by-step explanations

Reduce and Expand Simple Fractions

Simplify the Fraction 12/18 to an Equivalent Fraction with Denominator 9 Simplify the Fraction 6/24: Step-by-Step Reduction Guide Simplify 6/24: Converting to an Equivalent Fraction with Denominator 12 Simplify 5/50 to a Fraction with Denominator 10: Step-by-Step Simplify the Fraction 16/36: Finding the Reduction Factor

Continue Your Math Journey

Master How do you simplify fractions? first, then advance to these related topics that build on your fraction skills

Suggested Topics to Practice in Advance

A fraction as a divisorNumeratorDenominatorFractionsPart of a quantityRemainder of a fractionRemaindersPlacing Fractions on the Number LineCommon denominator

Topics Learned in Later Sections

Simplification and Expansion of Simple Fractions

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