Fractions Introduction Lessons in the Third 228c9duwxgs - Mathematics - Exercises with solutions

Master fractions: identifying parts of a whole, comparing fractions, and equivalent fractions through these 10 detailed exercises.

Exercises 1 to 10
1 Identifying parts of a whole
Exercise 1
If a pizza is cut into 6 equal pieces and you eat 2 pieces, what fraction of the pizza did you eat?
Solution:

There are 6 total pieces and 2 pieces were eaten.

So the fraction eaten is 2 out of 6, or 2/6.

This can be simplified to 1/3 by dividing both numerator and denominator by 2.

Answer: 2/6 or 1/3
2 Comparing fractions
Exercise 2
Which is bigger: 1/3 or 1/5? Explain your answer.
Solution:

When comparing fractions with the same numerator (both have 1), the fraction with the smaller denominator is larger.

Since 3 is smaller than 5, 1/3 is larger than 1/5.

Think of it as: 1 piece of 3 is larger than 1 piece of 5.

Answer: 1/3 is bigger than 1/5
3 Equivalent fractions
Exercise 3
Show that 2/4 is the same as 1/2 using drawings.
Solution:

Draw two identical rectangles.

Divide the first into 4 equal parts and shade 2 parts (2/4).

Divide the second into 2 equal parts and shade 1 part (1/2).

Both rectangles have the same amount shaded, showing 2/4 = 1/2.

Answer: 2/4 and 1/2 are equivalent fractions
4 Fraction shapes
Exercise 4
A circle is divided into 8 equal parts. 5 parts are shaded. What fraction is shaded?
Solution:

The circle is divided into 8 equal parts.

5 parts are shaded.

So the fraction shaded is 5/8.

Answer: 5/8
5 Fraction word problems
Exercise 5
Tom has 10 marbles. He gives 3 marbles to his friend. What fraction of his marbles did he give away?
Solution:

Tom had 10 marbles total.

He gave away 3 marbles.

So the fraction given away is 3/10.

Answer: 3/10
6 More comparing fractions
Exercise 6
Which is bigger: 3/4 or 2/4? Explain why.
Solution:

Both fractions have the same denominator (4).

When denominators are the same, compare the numerators.

Since 3 is greater than 2, 3/4 is greater than 2/4.

Answer: 3/4 is bigger than 2/4
7 Fraction patterns
Exercise 7
Look at this pattern: 1/2, 2/4, 3/6, 4/8. What comes next? Explain the pattern.
Solution:

Each fraction in the sequence is equivalent to 1/2.

Numerator increases by 1, denominator increases by 2.

Next fraction: 5/10 (which also equals 1/2).

Answer: 5/10
8 Fraction pizzas
Exercise 8
A pizza is cut into 8 equal slices. Mom eats 1 slice, Dad eats 2 slices, and you eat 3 slices. What fraction of the pizza is left?
Solution:

Total slices: 8

Slices eaten: 1 + 2 + 3 = 6

Slices left: 8 - 6 = 2

Fraction left: 2/8 = 1/4

Answer: 2/8 or 1/4
9 Mixed fraction concepts
Exercise 9
Circle the largest fraction: 1/6, 1/3, 1/8, 1/4. Explain your answer.
Solution:

All fractions have numerator 1.

When numerators are the same, the fraction with the smallest denominator is largest.

Between 6, 3, 8, and 4, the smallest is 3.

So 1/3 is the largest fraction.

Answer: 1/3
10 Fraction review
Exercise 10
Draw a rectangle divided into 10 equal parts. Shade 4 parts. Write the fraction, find an equivalent fraction, and compare it to 1/2.
Solution:

Shaded fraction: 4/10

Equivalent fraction: 4/10 = 2/5 (divide by 2)

Compare to 1/2: 4/10 = 8/20, 1/2 = 10/20

So 4/10 is less than 1/2

Answer: 4/10, equivalent: 2/5, 4/10 < 1/2
Detailed Summary of Fraction Concepts
Key Definitions:

Fraction: A number representing a part of a whole, written as numerator/denominator

Numerator: The top number showing how many parts are taken

Denominator: The bottom number showing how many equal parts the whole is divided into

Equivalent Fractions: Different fractions that represent the same amount

Core Methods:
  1. Identifying Fractions: Count parts taken over total parts (shaded/total)
  2. Comparing Fractions:
    • Same numerator: smaller denominator = larger fraction
    • Same denominator: larger numerator = larger fraction
  3. Finding Equivalents: Multiply or divide both numerator and denominator by the same number
Tip 1: Always make sure parts are equal in size when working with fractions.
Tip 2: Draw pictures to visualize fractions when comparing them.
Tip 3: To simplify fractions, find the greatest common divisor of numerator and denominator.
Tip 4: Equivalent fractions represent the same portion of the whole.
Core Rule: The larger the denominator, the smaller each piece becomes when the numerator stays the same.
Memory Aid: Think of fractions like sharing food - more people (larger denominator) means smaller portions.
Essential Rules:

• Parts must be equal in size for fractions to be valid

• When comparing fractions with same numerator, smaller denominator = larger fraction

• When comparing fractions with same denominator, larger numerator = larger fraction

• Equivalent fractions: multiply/divide both parts by same number

• Always simplify fractions to lowest terms when possible

Examples:
  • Simple: 1/2 of a pizza (1 part of 2 equal parts)
  • Medium: 3/4 of a chocolate bar (3 parts of 4 equal parts)
  • Advanced: 5/8 of a pie (5 parts of 8 equal parts)
Common Pitfalls to Avoid:
  • Assuming unequal parts can form valid fractions
  • Confusing numerator with denominator
  • Forgetting to simplify fractions when possible
  • Comparing fractions without considering whether they refer to the same whole
Visual Fraction Reference
\(\frac{\text{part}}{\text{whole}}\)
Fraction Formula
Rule 1
Same Numerator
Smaller denominator = larger fraction
Rule 2
Same Denominator
Larger numerator = larger fraction
Rule 3
Equivalent Fractions
Multiply/divide both by same number

Key Takeaways

  • Fractions represent parts of a whole object or group
  • Numerator is the top number, denominator is the bottom number
  • Parts must be equal in size for fractions to work
  • Equivalent fractions represent the same amount
  • Comparing fractions requires special rules depending on numerators/denominators