Kite Festival: Why Some Factors Make Products Larger

Explain how multiplying by a fraction greater than 1, less than 1, or equal to 1 changes a number.

Break apart the factor

Write the fraction as 1 plus a part or 1 minus a part. Then find the product.

Kenji's kite string is 40 m long. Sofia's kite string is 5/4 × 40 m long.

5/4 = 1 +
5/4 × 40 = 40 +
Sofia's string is m long, so it is longer than Kenji's string.

A big kite has a tail 24 inches long. A smaller kite has a tail 5/6 × 24 inches long.

5/6 = 1 −
5/6 × 24 = 24 −
The smaller kite's tail is inches long, so it is shorter than 24 inches.

Why is 7/3 × 15 greater than 15?

A. Because 7 is greater than 3, so you add 7 to 15.B. Because 7/3 is greater than 1, so the product is all of 15 plus 4/3 more of 15.C. Because multiplying always makes a number bigger.D. Because 15 is a whole number, and a whole number times a fraction is always bigger.

Why is 3/8 × 64 less than 64?

A. Because 8 is greater than 3, so you subtract 8 from 64.B. Because the product is 3/8, and 3/8 is less than 64.C. Because 3/8 is less than 1, so the product is only part of 64.D. Because multiplying by any fraction makes a number smaller.

Predict and explain

Do not multiply. Decide if each product is greater than, less than, or equal to the number, and tell why.

The practice kite flies on 60 m of string. Each team multiplies 60 m by a factor to get its string length. Circle every factor that gives a string longer than 60 m.

Three kite frames are 6/5 × 30 cm, 4/5 × 30 cm, and 5/5 × 30 cm long. Match each product to the sentence that explains its size.

The biggest kite at the festival has a frame 90 cm long. Lila builds a copy with a frame 7/6 × 90 cm long. Ben builds a copy with a frame 5/6 × 90 cm long. Without multiplying, whose frame is longer than 90 cm? Explain why.

Nina says that multiplying a number by a fraction always makes it smaller. Give an example that shows she is wrong, and explain why it works.

Multiplying by 1

Use fractions that equal 1 to make equivalent fractions.

Ava's kite is 2/3 of a meter wide. She multiplies 2/3 by 4/4.

4/4 =
2/3 × 4/4 = (2 × 4)/(3 × 4) = 8/

10.

Ava says 8/12 of a meter is wider than 2/3 of a meter because 8 and 12 are bigger numbers than 2 and 3. Which sentence explains why she is wrong?

A. 4/4 equals 1, and multiplying by 1 does not change a number, so 8/12 = 2/3.B. 4/4 is less than 1, so 8/12 is narrower than 2/3.C. 4/4 is greater than 1, so 8/12 is wider than 2/3.D. You must add 4/4 to 2/3, not multiply.

11.

The kite club writes each fraction in a new way. Each new fraction was made by multiplying by n/n, which equals 1. Find n.

3/5 × n/n = 9/15, so n =
7/8 × n/n = 14/16, so n =
5/6 × n/n = 25/30, so n =