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Math  /  Numbers & Operations

Question6. Ivey has 1 yard of yarn to make mini plush animals. Different animals require different amounts of yarn as shown below. \begin{tabular}{|l|l|l} FROG & FOX & PANDA \\ \hline59\frac{5}{9} yard & 49\frac{4}{9} yard & PIG \\ \hline & 13\frac{1}{3} yard & 58\frac{5}{8} yard \\ \hline \end{tabular} a. Which two animals would Ivey not be able to make? Explain. b. Ivey wants to make a pig, fox, and panda. She plans to add 29+49+19\frac{2}{9}+\frac{4}{9}+\frac{1}{9}. Did Ivey rename the fractions correctly? If not, correct her work. Then determine if Ivey has enough yarn to make the 3 animals. OManeuvering the Middle LLC, 202

Studdy Solution

STEP 1

1. Ivey has a total of 11 yard of yarn.
2. The yarn required for each animal is given in fractions of a yard.
3. We need to determine which two animals cannot be made with the available yarn.
4. We need to verify if Ivey's addition of fractions is correct and if she has enough yarn to make a pig, fox, and panda.

STEP 2

1. Determine the yarn required for each animal.
2. Identify the two animals that cannot be made.
3. Verify the addition of fractions.
4. Determine if Ivey has enough yarn for the pig, fox, and panda.

STEP 3

List the yarn required for each animal: - Frog: 59\frac{5}{9} yard - Fox: 49\frac{4}{9} yard - Panda: 13\frac{1}{3} yard - Pig: 58\frac{5}{8} yard

STEP 4

Identify the two animals that cannot be made with 1 yard of yarn: - Calculate the sum of yarn required for each pair of animals and compare to 1 yard.

STEP 5

Calculate the yarn required for each pair: - Frog and Fox: 59+49=99=1\frac{5}{9} + \frac{4}{9} = \frac{9}{9} = 1 yard - Frog and Panda: 59+13=59+39=89\frac{5}{9} + \frac{1}{3} = \frac{5}{9} + \frac{3}{9} = \frac{8}{9} yard - Frog and Pig: 59+58=4072+4572=8572\frac{5}{9} + \frac{5}{8} = \frac{40}{72} + \frac{45}{72} = \frac{85}{72} yard - Fox and Panda: 49+13=49+39=79\frac{4}{9} + \frac{1}{3} = \frac{4}{9} + \frac{3}{9} = \frac{7}{9} yard - Fox and Pig: 49+58=3272+4572=7772\frac{4}{9} + \frac{5}{8} = \frac{32}{72} + \frac{45}{72} = \frac{77}{72} yard - Panda and Pig: 13+58=824+1524=2324\frac{1}{3} + \frac{5}{8} = \frac{8}{24} + \frac{15}{24} = \frac{23}{24} yard

STEP 6

Conclusion: The two animals that cannot be made are Frog and Pig, and Fox and Pig, as both pairs require more than 1 yard.

STEP 7

Verify Ivey's addition of fractions for pig, fox, and panda: - Ivey's addition: 29+49+19=79\frac{2}{9} + \frac{4}{9} + \frac{1}{9} = \frac{7}{9} - Correct fractions: Pig 58\frac{5}{8}, Fox 49\frac{4}{9}, Panda 13\frac{1}{3}

STEP 8

Correct the addition of fractions: - Convert 13\frac{1}{3} to 39\frac{3}{9} for common denominator - Correct addition: 58+49+39\frac{5}{8} + \frac{4}{9} + \frac{3}{9}

STEP 9

Determine if Ivey has enough yarn: - Calculate total yarn required: 58+49+39=4572+3272+2472=10172\frac{5}{8} + \frac{4}{9} + \frac{3}{9} = \frac{45}{72} + \frac{32}{72} + \frac{24}{72} = \frac{101}{72} - 10172>1\frac{101}{72} > 1, so Ivey does not have enough yarn.
Conclusion: Ivey cannot make a pig, fox, and panda with 1 yard of yarn. The fractions were not renamed correctly.

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