11.3 Explain Fraction Equivalence Using Visual Models

11.3 Explain Fraction Equivalence Using Visual Models

I can use a visual model to show that two fractions are equivalent and explain why they are equivalent.

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Equivalent fractions (video) | Fractions | Khan Academy

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Launch

We're going to do a few problems to practice before we start.

Multiple Choice

Colton says the diagrams below represent equivalent fractions. Is he correct?

• yes

• no

Fill in the Blanks

The rectangle below has a length of 1. What fraction does the shaded part represent?

Spark your learning

Compare Jason’s and Kym’s turns. Whose turn is closer to being a full turn? Use the visual model of each turn to explain.

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Multiple Choice

Whose turn is closer to being a full turn?

• Jason's turn is closer to being a full turn.

• Kym's turn is closer to being a full turn.

• Neither turn is closer to being a full turn.

Neither is closer to a full turn.

Neither turn is closer because the turns are the same, or equal. The circles that represent both turns are the same size, and the amount of shading in both circles is the same. They represent the same part of a full turn.

Build Understanding

Sam wants to paint a skateboard ramp with a cool design. He has just enough paint to cover half of the ramp.

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Multiple Choice

The size of one part in 3/6​​ of a rectangle is _______ the size of one part in 1/2 of a rectangle of the same size.

• larger than

• the same size as

• smaller than

Multiple Choice

One part in 1/2​​ is ____ three parts in 3/6​.

• larger than

• the same size as

• smaller than

A rectangle that is divided into 6 equal parts has smaller parts than a same-sized rectangle that is divided into 2 equal parts. One part in 1/2​

​ is the same size as three parts in 3/6​​ .

REMINDER!

Two or more fractions that name the same amount are called equivalent fractions.

There are other ways we can write 3/6 in visual models.

Here is one of them.

Fill in the Blanks

How can you use multiplication to describe the relationship between the numerators? The numerator 3 is

times as many as the numerator 1.

Fill in the Blanks

How can you use multiplication to describe the relationship between the denominators? The denominator 6 is

times as many as the denominator 2.

To write an equivalent fraction, multiply the numerator and denominator of the fraction by the same number.

When you compared the numerators, you found that 3 parts is 3 times as many as 1 part. When you compared the denominators, you found that 6 parts is 3 times as many as 2 parts. You can multiply the numerator by 3, and you can multiply the denominator by 3.