Friends smiling around a table at a fun pizza party

Whose Pizza Wins?

Maya ate 3/4 of her pizza. Leo ate 2/3 of his. The pizzas are the same size. Who ate more?

4th Grade Math

Step 1: Analyze the Models

Maya: 3/4

Leo: 2/3

Both bars show the same whole, so we can analyze them fairly. Which bar shows more shaded?

Maya's bar is missing only 1/4. Leo's bar is missing 1/3, a bigger piece. Since less is missing, 3/4 shows more.

Step 2: Make Equal-Size Parts

Fourths and thirds are different sizes. Multiply the numerator and denominator of 3/4 by 3 to make an equivalent fraction in twelfths.

3/4 = ?/12

3 x 3 = 9 and 4 x 3 = 12, so 3/4 = 9/12. Leo's 2/3 = 8/12. Since 9/12 > 8/12, Maya ate more!

Let's Remember

Three Ways to Compare Fractions

          1. Rewrite both with a common denominator.

          2. Compare both to the benchmark 1/2.

          3. If numerators match, bigger parts win.

First, check that both fractions describe the same whole. Then justify your answer with the symbols >, <, or =.

Step 3: Use the Benchmark 1/2

3/8

5/6

Half of 8 is 4, and 3 < 4, so 3/8 is less than 1/2. Half of 6 is 3, and 5 > 3, so 5/6 is more than 1/2.

Which symbol makes this true? 3/8 ○ 5/6

3/8 is below 1/2 and 5/6 is above 1/2. So 3/8 < 5/6. The benchmark did all the work!

Watch Out!

3/4

5/8

A bigger denominator does NOT mean a bigger fraction!

          Jae said 5/8 > 3/4 because 8 > 4. But 3/4 = 6/8, and 6/8 > 5/8.
          More parts means each part is smaller.
        

Solve It!

2/5 ○ 2/3

Which symbol makes this true?

The numerators match, so compare part sizes. Thirds are bigger pieces than fifths. Two big pieces beat two small pieces, so 2/5 < 2/3.

Word Problem

Zara ran 3/4 of a mile. Ben ran 5/8 of a mile. Who ran farther?

Rewrite 3/4 as eighths: 3/4 = 6/8. Since 6/8 > 5/8, Zara ran farther.

What Goes in the Blank?

3/4 > ?/8

Which number makes this comparison true?

3/4 = 6/8. So 3/4 > 5/8 is true. With 6, the fractions would be equal. With 7, the right side would be greater.

Benchmark Check

Which fraction is greater than 1/2?

Half of 9 is 4 and a half. Since 5 > 4.5, 5/9 > 1/2. Both 3/8 and 4/10 fall below one half.

Read the Models

3/5

7/10

Which symbol makes this true? 3/5 ○ 7/10

3/5 = 6/10. Since 6/10 < 7/10, we write 3/5 < 7/10. The models show the same result.

Challenge!

Compare 7/12 and 5/8. Both are close to 1/2, so the benchmark cannot decide this one. You will need a common denominator.

A common denominator is 24. 7/12 = 14/24 and 5/8 = 15/24. Since 14/24 < 15/24, 7/12 < 5/8.

Why must two fractions describe the same whole before you compare them? Could 1/2 of a small pizza be less than 1/4 of a giant one?

Great Work!

0/9

correct

analyze numerator denominator equivalent fraction justify