Unit 2 Day 3: Comparing Fraction Sizes

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Unit 2: Understanding Fractions

Day 3: Which is Bigger?

Today's Objectives

Vocabulary Focus

The > symbol means "greater than". (Think of an alligator mouth eating the bigger number!)

The < symbol means "less than".

The Big Idea: The Butterfly Method

When denominators are different, it's hard to compare. The Butterfly Method is a quick trick!

a

b

c

d

Multiply diagonally: a x d and c x b. The bigger product is on the side of the bigger fraction!

I Do: Comparing \(\frac{2}{3}\) and \(\frac{3}{4}\)

8

\(\frac{\color{#3b82f6}{2}}{\color{#8b5cf6}{3}}\)

9

\(\frac{\color{#8b5cf6}{3}}{\color{#3b82f6}{4}}\)

Since 9 is bigger than 8, \(\frac{3}{4}\) is the bigger fraction. So, \(\frac{2}{3} < \frac{3}{4}\).

I Do: Comparing \(\frac{5}{6}\) and \(\frac{3}{4}\)

20

\(\frac{\color{#3b82f6}{5}}{\color{#8b5cf6}{6}}\)

18

\(\frac{\color{#8b5cf6}{3}}{\color{#3b82f6}{4}}\)

Since 20 is bigger than 18, \(\frac{5}{6}\) is the bigger fraction. So, \(\frac{5}{6} > \frac{3}{4}\).

We Do: Let's Try Together

Let's compare \(\frac{5}{8}\) and \(\frac{1}{2}\).

First, we multiply 5 x 2 to get ___?

Next, we multiply 1 x 8 to get ___?

Since 10 is greater than 8, the fraction ___? is greater.

We Do: Let's Try Together

Let's compare \(\frac{2}{5}\) and \(\frac{3}{7}\).

The first product is 2 x 7 = ___?

The second product is 3 x 5 = ___?

So, \(\frac{2}{5}\) is ___? \(\frac{3}{7}\).

You Do: Practice Time!

Work on the problems on your notes sheet.

Problem 1:

Which is greater? Use <, >, or =.

\(\frac{5}{6} \quad ? \quad \frac{4}{5}\)

Problem 2:

Which is smaller? Use <, >, or =.

\(\frac{3}{8} \quad ? \quad \frac{2}{5}\)

Independent Practice

Try these problems on your own.

Green Level

Compare \(\frac{1}{4}\) and \(\frac{3}{4}\).

Yellow Level

Compare \(\frac{2}{3}\) and \(\frac{5}{8}\).

Red Level

Tim ate \(\frac{3}{5}\) of his candy bar. Sara ate \(\frac{4}{7}\) of hers. Who ate more?

Exit Ticket

On a piece of paper, compare the fractions \(\frac{4}{9}\) and \(\frac{3}{7}\) using <, >, or =.

Unit 2: Understanding Fractions

Day 3: Which is Bigger?

Today's Objectives

Vocabulary Focus

The > symbol means "".

The < symbol means "".

I Do: Comparing \(\frac{2}{3}\) and \(\frac{3}{4}\)

1. Multiply diagonally: 2 x 4 = 8 and 3 x 3 = 9.

2. Since 9 is bigger than 8, \(\frac{3}{4}\) is bigger. So, \(\frac{2}{3}\) \(\frac{3}{4}\).

I Do: Comparing \(\frac{5}{6}\) and \(\frac{3}{4}\)

1. Multiply diagonally: 5 x 4 = 20 and 3 x 6 = 18.

2. Since 20 is bigger than 18, \(\frac{5}{6}\) is bigger. So, \(\frac{5}{6}\) \(\frac{3}{4}\).

We Do: Let's Try Together

Problem 1: Let's compare \(\frac{5}{8}\) and \(\frac{1}{2}\).

First, we multiply 5 x 2 to get .

Next, we multiply 1 x 8 to get .

The fraction is greater.

Problem 2: Let's compare \(\frac{2}{5}\) and \(\frac{3}{7}\).

The first product is 2 x 7 = .

The second product is 3 x 5 = .

So, \(\frac{2}{5}\) is \(\frac{3}{7}\).

You Do: Practice Time!

Problem 1: Which is greater? \(\frac{5}{6} \quad \_\_\_ \quad \frac{4}{5}\)

Problem 2: Which is smaller? \(\frac{3}{8} \quad \_\_\_ \quad \frac{2}{5}\)

Independent Practice

Green: Compare \(\frac{1}{4}\) and \(\frac{3}{4}\).

Yellow: Compare \(\frac{2}{3}\) and \(\frac{5}{8}\).

Red: Tim ate \(\frac{3}{5}\) of his candy bar. Sara ate \(\frac{4}{7}\) of hers. Who ate more?

Exit Ticket

Compare the fractions \(\frac{4}{9}\) and \(\frac{3}{7}\) using <, >, or =.