What is the difference of 3 1/2

Question

and 1 2/3
(1 point)
Responses

1 5/6
1 Start Fraction 5 over 6 End Fraction

2 5/6
2 Start Fraction 5 over 6 End Fraction

5 1/6
5 Start Fraction 1 over 6 End Fraction

1 4/9

Answer 1

To find the difference between \( 3 \frac{1}{2} \) and \( 1 \frac{2}{3} \), we first convert both mixed numbers to improper fractions.

1. Convert \( 3 \frac{1}{2} \) to an improper fraction: \[ 3 \frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2} \]

2. Convert \( 1 \frac{2}{3} \) to an improper fraction: \[ 1 \frac{2}{3} = \frac{(1 \times 3) + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3} \]

Now we need to find the difference: \[ \frac{7}{2} - \frac{5}{3} \]

To subtract these fractions, we need a common denominator. The least common multiple of 2 and 3 is 6.

Convert both fractions to have a denominator of 6: \[ \frac{7}{2} = \frac{7 \times 3}{2 \times 3} = \frac{21}{6} \] \[ \frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6} \]

Now, perform the subtraction: \[ \frac{21}{6} - \frac{10}{6} = \frac{21 - 10}{6} = \frac{11}{6} \]

Finally, convert \( \frac{11}{6} \) back to a mixed number: \[ \frac{11}{6} = 1 \frac{5}{6} \]

Therefore, the difference of \( 3 \frac{1}{2} \) and \( 1 \frac{2}{3} \) is: \[ 1 \frac{5}{6} \]

The correct response is \( 1 \frac{5}{6} \).

Answer 2

THanks! moving on.
Unit 8 Lesson 8
Solve Problems with Mixed Numbers Quick Check
1 of 51 of 5 Items
Question
Solve the following problem: Asia walks 2 1/4
miles to the park and then another 1 6/8
miles to her friend’s house. How many miles does she walk in all?(1 point)
Responses

4

1/2

3 7/8
3 Start Fraction 7 over 8 End Fraction

3

Answer 3

To find the total distance Asia walks, we need to add the two mixed numbers: \(2 \frac{1}{4}\) miles and \(1 \frac{6}{8}\) miles.

1. Convert both mixed numbers to improper fractions:

   • Convert \(2 \frac{1}{4}\): \[ 2 \frac{1}{4} = \frac{(2 \times 4) + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \]

   • Convert \(1 \frac{6}{8}\): \[ 1 \frac{6}{8} = \frac{(1 \times 8) + 6}{8} = \frac{8 + 6}{8} = \frac{14}{8} \]

2. Now we can add the two improper fractions: \[ \frac{9}{4} + \frac{14}{8} \]

3. Find a common denominator: The least common multiple of 4 and 8 is 8.

   Convert \( \frac{9}{4} \) to have a denominator of 8: \[ \frac{9}{4} = \frac{9 \times 2}{4 \times 2} = \frac{18}{8} \]

4. Now, add the two fractions: \[ \frac{18}{8} + \frac{14}{8} = \frac{18 + 14}{8} = \frac{32}{8} \]

5. Simplify the fraction: \[ \frac{32}{8} = 4 \]

So, Asia walks a total of 4 miles.

The correct response is 4.

Answer 4

Lucy saws a wooden rod into two pieces. The larger piece is 7 3/4
inches long. The original rod was 9 1/8
inches long. How many inches long is the resulting smaller piece?(1 point)
Responses

2

1 3/8

2 5/8

16 7/8

Answer 5

To find the length of the smaller piece of wood that Lucy sawed, we need to subtract the length of the larger piece from the original length of the rod.

1. Identify the lengths:

   • Original rod length: \(9 \frac{1}{8}\) inches
   • Larger piece length: \(7 \frac{3}{4}\) inches

2. Convert both mixed numbers to improper fractions:

   • Convert \(9 \frac{1}{8}\): \[ 9 \frac{1}{8} = \frac{(9 \times 8) + 1}{8} = \frac{72 + 1}{8} = \frac{73}{8} \]

   • Convert \(7 \frac{3}{4}\): \[ 7 \frac{3}{4} = \frac{(7 \times 4) + 3}{4} = \frac{28 + 3}{4} = \frac{31}{4} \]

3. To subtract these fractions, we need a common denominator. The least common multiple of 8 and 4 is 8.

   Convert \( \frac{31}{4} \) to have a denominator of 8: \[ \frac{31}{4} = \frac{31 \times 2}{4 \times 2} = \frac{62}{8} \]

4. Now subtract the lengths: \[ \frac{73}{8} - \frac{62}{8} = \frac{73 - 62}{8} = \frac{11}{8} \]

5. Convert \( \frac{11}{8} \) back to a mixed number: \[ \frac{11}{8} = 1 \frac{3}{8} \]

Thus, the length of the resulting smaller piece is 1 \(\frac{3}{8}\) inches.

The correct response is 1 \(\frac{3}{8}\).

Answer 6

Henry has a pot with 6 3/10
liters of water. He pours out 3 1/5
liters of water. How many liters of water remain in the pot?(1 point)
Responses

2 9/10

3 1/5

9 1/2

3 1/10

Answer 7

To find out how much water remains in the pot after Henry pours out some water, we need to subtract the amount he poured out from the original amount of water he had.

1. Identify the amounts:

   • Original amount of water: \(6 \frac{3}{10}\) liters
   • Amount poured out: \(3 \frac{1}{5}\) liters

2. Convert both mixed numbers to improper fractions:

   • Convert \(6 \frac{3}{10}\): \[ 6 \frac{3}{10} = \frac{(6 \times 10) + 3}{10} = \frac{60 + 3}{10} = \frac{63}{10} \]

   • Convert \(3 \frac{1}{5}\): \[ 3 \frac{1}{5} = \frac{(3 \times 5) + 1}{5} = \frac{15 + 1}{5} = \frac{16}{5} \]

3. To subtract these fractions, we need a common denominator. The least common multiple of 10 and 5 is 10.

   Convert \( \frac{16}{5} \) to have a denominator of 10: \[ \frac{16}{5} = \frac{16 \times 2}{5 \times 2} = \frac{32}{10} \]

4. Now subtract the amounts: \[ \frac{63}{10} - \frac{32}{10} = \frac{63 - 32}{10} = \frac{31}{10} \]

5. Convert \( \frac{31}{10} \) back to a mixed number: \[ \frac{31}{10} = 3 \frac{1}{10} \]

Thus, the amount of water remaining in the pot is 3 \(\frac{1}{10}\) liters.

The correct response is 3 \(\frac{1}{10}\).

Answer 8

Gary is 834
years old. His brother is 3712
years younger than he is. How many years old is Gary’s brother?(1 point)
Responses

1158
11 Start Fraction 5 over 8 End Fraction

456
4 Start Fraction 5 over 6 End Fraction

516
5 Start Fraction 1 over 6 End Fraction

1213
12 Start Fraction 1 over 3 End Fraction

Answer 9

To find out how old Gary's brother is, we need to subtract the age difference from Gary's age.

1. Identify Gary's age and the age difference:

   • Gary's age: \(834\) years
   • Age difference: \(3712\) years younger

2. Calculate Gary's brother's age: \[ \text{Brother's age} = \text{Gary's age} - \text{Age difference} \] \[ \text{Brother's age} = 834 - 3712 \]

3. Now, perform the subtraction: \[ 834 - 3712 = -2878 \]

Since a negative age does not make sense in this context, it seems there might be an error in the problem as presented.

However, if we consider the absolute values and understand why one might think of an age difference larger than an individual's age, it suggests needing further clarification on the question.

Regardless, the calculation indicates the resulting age is not reasonable.

If we consider the intention was to convey the age of Gary's brother effectively, we would reinterpret with realistic numbers. If you meant something different or intended a different calculation, please verify the initial numbers.

If we’re continuing with Gary's age as realistic and finding a plausible missing age related to him, please review the specifics:

If it was meant to say "Gary's brother is younger by \(112\)” or smaller values, we can adjust accordingly.

In case the numbers presented were unclear, I would be glad to assist with recalibrating!

Answer 10

Gary is 8 3/4 years old. His brother is 3 7/12 years younger than he is. How many years old is Gary’s brother?(1 point)
Responses

11 5/8

4 5/6

5 1/6

12 1/3

Answer 11

To determine how old Gary's brother is, we need to subtract the age difference from Gary's age. Let's break it down step by step:

1. Identify Gary's age and the age difference:

   • Gary's age: \(8 \frac{3}{4}\) years
   • Age difference: \(3 \frac{7}{12}\) years

2. Convert the mixed numbers to improper fractions:

   • Convert \(8 \frac{3}{4}\): \[ 8 \frac{3}{4} = \frac{(8 \times 4) + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4} \]

   • Convert \(3 \frac{7}{12}\): \[ 3 \frac{7}{12} = \frac{(3 \times 12) + 7}{12} = \frac{36 + 7}{12} = \frac{43}{12} \]

3. Now we need to subtract these fractions. To do this, we need a common denominator. The least common multiple of 4 and 12 is 12.

   • Convert \( \frac{35}{4} \) to have a denominator of 12: \[ \frac{35}{4} = \frac{35 \times 3}{4 \times 3} = \frac{105}{12} \]

4. Subtract the two fractions: \[ \frac{105}{12} - \frac{43}{12} = \frac{105 - 43}{12} = \frac{62}{12} \]

5. Simplify \(\frac{62}{12}\): \[ \frac{62}{12} = \frac{31}{6} \]

6. Convert \(\frac{31}{6}\) back to a mixed number:

   • Divide 31 by 6:
     • 31 divided by 6 is 5 (whole number)
     • The remainder is 1

   Thus, \[ \frac{31}{6} = 5 \frac{1}{6} \]

Therefore, Gary’s brother is 5 \(\frac{1}{6}\) years old.

The correct response is 5 \(\frac{1}{6}\).