Penny Had A Piece Of String That Was 3 14 Yards Long

Penny Had A Piece Of String That Was 3 14 Yards Long She Wanted To C

Penny had a piece of string that was 3 1/4 yards long. She wanted to cut the string into strips that were 1 1/2 yards long. Use this information to answer the following questions.

Paper For Above instruction

Part A: To visualize how many strips Penny can cut, draw a rectangle representing the entire piece of string, labeled as 3 1/4 yards long. Divide this rectangle into segments each measuring 1 1/2 yards, either by drawing lines to indicate these divisions or by shading the sections. Count how many such 1 1/2-yard segments fit within the total length. This diagram helps illustrate the division of the total string into equal parts and provides a visual estimate of how many full strips she can obtain.

Part B: The number sentence representing the situation is: 3 1/4 ÷ 1 1/2 = ?

Part C: To find how many full strips Penny can cut, convert the mixed numbers to improper fractions:

  • 3 1/4 = 13/4
  • 1 1/2 = 3/2

Next, divide 13/4 by 3/2 by multiplying by the reciprocal:

13/4 ÷ 3/2 = 13/4 × 2/3 = (13×2)/(4×3) = 26/12

Simplify 26/12 to 13/6.

Convert 13/6 to a mixed number: 2 and 1/6 (because 6×2 = 12, with a remainder of 1).

Therefore, Penny can cut 2 full strips and have some string left over.

Answer Sentence: Penny can cut 2 full strips of 1 1/2 yards each from her 3 1/4-yard piece of string.

Part D: To find the remaining length of string, multiply the number of full strips by the length of each strip:

2 × 1 1/2 yards = 2 × 3/2 yards = 6/2 + 3/2 = 9/2 yards = 4 1/2 yards.

Subtract this from the total length:

3 1/4 yards = 13/4 yards

Remaining string = 13/4 - 9/2

Convert 9/2 to denominator 4: 18/4

Remaining string = 13/4 - 18/4 = -5/4

(which indicates more than the total length, so let's check carefully)

Alternatively, compute the leftover directly: total string is 3 1/4 yards, or 13/4 yards.

Used length for 2 strips: 2 × 1 1/2 = 2 × 3/2 = 3 yards.

Remaining length: 3 1/4 - 3 yards = (13/4) - (12/4) = 1/4 yard.

Answer Sentence: Penny has 1/4 yard of string left after cutting as many full strips as possible.

References

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