Learn on PengiSaxon Math, Course 1Chapter 6: Geometry and Number Operations

Lesson 56: Common Denominators, Part 2

New Concept To add, subtract, or compare fractions with unlike denominators, we must rename them to have a common denominator, often using their least common multiple. <br <br To rename a fraction, we multiply it by a fraction equal to 1. What’s next This is the core technique for handling unlike fractions. Next, you’ll apply this concept through worked examples on addition, subtraction, and comparison problems.

Section 1

📘 Common Denominators, Part 2

New Concept

To add, subtract, or compare fractions with unlike denominators, we must rename them to have a common denominator, often using their least common multiple.
<br><br>
To rename a fraction, we multiply it by a fraction equal to 1.

What’s next

This is the core technique for handling unlike fractions. Next, you’ll apply this concept through worked examples on addition, subtraction, and comparison problems.

Section 2

Finding a Common Denominator

Property

To add or subtract fractions with different denominators, you must first rename them to have a common denominator. This is typically the least common multiple (LCM) of the original denominators.

Examples

12+13=1323+1232=36+26=56 \frac{1}{2} + \frac{1}{3} = \frac{1 \cdot 3}{2 \cdot 3} + \frac{1 \cdot 2}{3 \cdot 2} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}
3423=33432434=912812=112 \frac{3}{4} - \frac{2}{3} = \frac{3 \cdot 3}{4 \cdot 3} - \frac{2 \cdot 4}{3 \cdot 4} = \frac{9}{12} - \frac{8}{12} = \frac{1}{12}
23+14=2434+1343=812+312=1112 \frac{2}{3} + \frac{1}{4} = \frac{2 \cdot 4}{3 \cdot 4} + \frac{1 \cdot 3}{4 \cdot 3} = \frac{8}{12} + \frac{3}{12} = \frac{11}{12}

Explanation

Imagine trying to add half a pizza to a third of another pizza. The slices are different sizes, making it a mess! To fix this, you must recut both pizzas into slices of the same size, like sixths. Now you can simply count the new, identical slices to find your total. It’s the secret to making fraction math easy!

Section 3

Renaming a Fraction

Property

To rename a fraction, we multiply it by a fraction equal to 1.

Examples

12=1244=48 \frac{1}{2} = \frac{1}{2} \cdot \frac{4}{4} = \frac{4}{8}
23=2355=1015 \frac{2}{3} = \frac{2}{3} \cdot \frac{5}{5} = \frac{10}{15}
35=3522=610 \frac{3}{5} = \frac{3}{5} \cdot \frac{2}{2} = \frac{6}{10}

Explanation

Think of renaming a fraction as putting it in a clever disguise that doesn't actually change its value. When you multiply a fraction by something like 44\frac{4}{4}, you're just multiplying by 1. The fraction's value stays the same, but it's now cut into more, smaller pieces, which is perfect for adding it to or comparing it with other fractions.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 6: Geometry and Number Operations

  1. Lesson 1

    Lesson 51: Rounding Decimal Numbers

  2. Lesson 2

    Lesson 52: Mentally Dividing Decimal Numbers by 10 and by 100

  3. Lesson 3

    Lesson 53: Decimals Chart

  4. Lesson 4

    Lesson 54: Reducing by Grouping Factors Equal to 1

  5. Lesson 5

    Lesson 55: Common Denominators, Part 1

  6. Lesson 6Current

    Lesson 56: Common Denominators, Part 2

  7. Lesson 7

    Lesson 57: Adding and Subtracting Fractions: Three Steps

  8. Lesson 8

    Lesson 58: Probability and Chance

  9. Lesson 9

    Lesson 59: Adding Mixed Numbers

  10. Lesson 10

    Lesson 60: Polygons

  11. Lesson 11

    Investigation 6: Attributes of Geometric Solids

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Common Denominators, Part 2

New Concept

To add, subtract, or compare fractions with unlike denominators, we must rename them to have a common denominator, often using their least common multiple.
<br><br>
To rename a fraction, we multiply it by a fraction equal to 1.

What’s next

This is the core technique for handling unlike fractions. Next, you’ll apply this concept through worked examples on addition, subtraction, and comparison problems.

Section 2

Finding a Common Denominator

Property

To add or subtract fractions with different denominators, you must first rename them to have a common denominator. This is typically the least common multiple (LCM) of the original denominators.

Examples

12+13=1323+1232=36+26=56 \frac{1}{2} + \frac{1}{3} = \frac{1 \cdot 3}{2 \cdot 3} + \frac{1 \cdot 2}{3 \cdot 2} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}
3423=33432434=912812=112 \frac{3}{4} - \frac{2}{3} = \frac{3 \cdot 3}{4 \cdot 3} - \frac{2 \cdot 4}{3 \cdot 4} = \frac{9}{12} - \frac{8}{12} = \frac{1}{12}
23+14=2434+1343=812+312=1112 \frac{2}{3} + \frac{1}{4} = \frac{2 \cdot 4}{3 \cdot 4} + \frac{1 \cdot 3}{4 \cdot 3} = \frac{8}{12} + \frac{3}{12} = \frac{11}{12}

Explanation

Imagine trying to add half a pizza to a third of another pizza. The slices are different sizes, making it a mess! To fix this, you must recut both pizzas into slices of the same size, like sixths. Now you can simply count the new, identical slices to find your total. It’s the secret to making fraction math easy!

Section 3

Renaming a Fraction

Property

To rename a fraction, we multiply it by a fraction equal to 1.

Examples

12=1244=48 \frac{1}{2} = \frac{1}{2} \cdot \frac{4}{4} = \frac{4}{8}
23=2355=1015 \frac{2}{3} = \frac{2}{3} \cdot \frac{5}{5} = \frac{10}{15}
35=3522=610 \frac{3}{5} = \frac{3}{5} \cdot \frac{2}{2} = \frac{6}{10}

Explanation

Think of renaming a fraction as putting it in a clever disguise that doesn't actually change its value. When you multiply a fraction by something like 44\frac{4}{4}, you're just multiplying by 1. The fraction's value stays the same, but it's now cut into more, smaller pieces, which is perfect for adding it to or comparing it with other fractions.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 6: Geometry and Number Operations

  1. Lesson 1

    Lesson 51: Rounding Decimal Numbers

  2. Lesson 2

    Lesson 52: Mentally Dividing Decimal Numbers by 10 and by 100

  3. Lesson 3

    Lesson 53: Decimals Chart

  4. Lesson 4

    Lesson 54: Reducing by Grouping Factors Equal to 1

  5. Lesson 5

    Lesson 55: Common Denominators, Part 1

  6. Lesson 6Current

    Lesson 56: Common Denominators, Part 2

  7. Lesson 7

    Lesson 57: Adding and Subtracting Fractions: Three Steps

  8. Lesson 8

    Lesson 58: Probability and Chance

  9. Lesson 9

    Lesson 59: Adding Mixed Numbers

  10. Lesson 10

    Lesson 60: Polygons

  11. Lesson 11

    Investigation 6: Attributes of Geometric Solids