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Mary ate 4 1/2 pears and Carmie ate 7 2/4 pears. If they finished all the pears in a box, how many pears were in the box?(1 point)

Responses

11 1/4
11 Start Fraction 1 over 4 End Fraction

12
12

11 3/6
11 Start Fraction 3 over 6 End Fraction

11

7 answers

To find out how many pears were in the box, we need to add the number of pears Mary ate and the number of pears Carmie ate.

Mary ate \(4 \frac{1}{2}\) pears, which can be converted to an improper fraction:

\[ 4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2} \]

Carmie ate \(7 \frac{2}{4}\) pears, which simplifies to \(7 \frac{1}{2}\), and can also be converted to an improper fraction:

\[ 7 \frac{2}{4} = 7 \frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2} \]

Now, we add the two amounts:

\[ \frac{9}{2} + \frac{15}{2} = \frac{9 + 15}{2} = \frac{24}{2} = 12 \]

Therefore, the total number of pears in the box is \(12\).

The correct response is:

12

What is the fractional equivalent of 2.125?(1 point)
Responses

216
2 Start Fraction 1 over 6 End Fraction

238
2 Start Fraction 3 over 8 End Fraction

218
2 Start Fraction 1 over 8 End Fraction

128
1 Start Fraction 2 over 8 End Fraction

To convert the decimal \(2.125\) into a fractional form, we can break it down as follows:

  1. The whole number part is \(2\).
  2. The decimal part is \(0.125\).

Next, we can convert \(0.125\) into a fraction.

Since \(0.125\) can be expressed as \(\frac{125}{1000}\):

\[ 0.125 = \frac{125}{1000} \]

Now, we can simplify \(\frac{125}{1000}\):

\[ \frac{125 \div 125}{1000 \div 125} = \frac{1}{8} \]

So, we have:

\[ 2.125 = 2 + 0.125 = 2 + \frac{1}{8} \]

To express this as a single fraction, we can convert the whole number \(2\) into a fraction with a denominator of \(8\):

\[ 2 = \frac{16}{8} \]

Now, we can add the two fractions together:

\[ 2.125 = \frac{16}{8} + \frac{1}{8} = \frac{16 + 1}{8} = \frac{17}{8} \]

However, since that specific option isn't given, we also re-check whether any of the options could correspond correctly.

Based on the provided options, the only equivalent form is to check which represents \(2.125\):

Evaluating the provided options:

  1. 216 (not a valid fraction)
  2. 2 Start Fraction 1 over 6 End Fraction which translates to \(2 \frac{1}{6} \approx 2.1667\) (not equivalent)
  3. 238 (not a valid fraction)
  4. 2 Start Fraction 3 over 8 End Fraction translates to \(2 \frac{3}{8} = 2.375\) (not equivalent)
  5. 218 (not a valid fraction)
  6. 2 Start Fraction 1 over 8 End Fraction translates to \(2 \frac{1}{8} = 2.125\) (equivalent!)
  7. 128 (not a valid fraction)
  8. 1 Start Fraction 2 over 8 End Fraction (equivalent to \(1 \frac{1}{4}\), or 1.25, not equivalent)

Thus, the correct fractional equivalent to \(2.125\) is:

2 Start Fraction 1 over 8 End Fraction

Fernando spent $20 of his $50 weekly allowance on snacks. What percent of his weekly allowance did he spend on snacks?(1 point)
__%

To find out what percent of his weekly allowance Fernando spent on snacks, we can use the formula for percentage:

\[ \text{Percentage} = \left(\frac{\text{Amount spent}}{\text{Total amount}}\right) \times 100 \]

In this case, the amount spent on snacks is $20, and the total weekly allowance is $50.

Now, substituting the values:

\[ \text{Percentage} = \left(\frac{20}{50}\right) \times 100 \]

First, calculate \(\frac{20}{50}\):

\[ \frac{20}{50} = 0.4 \]

Now multiply by 100 to convert it to a percentage:

\[ 0.4 \times 100 = 40 \]

Therefore, Fernando spent 40% of his weekly allowance on snacks.

Kim made three quiches for a party: cheese, spinach, and mushroom. The cheese quiche was cut into 8 equal pieces, the spinach quiche was cut into 16 equal pieces, and the mushroom quiche was cut into 4 equal pieces. At the party, people ate 5 pieces of the cheese, 9 pieces of the spinach, and 2 pieces of the mushroom. Which quiche did people eat the most of? Identify the fractions in numerical order from greatest to least.(1 point)
Responses

58
, 916
, 24
: The cheese quiche was eaten the most.
Start Fraction 5 over 8 End Fraction , Start Fraction 9 over 16 End Fraction , Start Fraction 2 over 4 End Fraction : The cheese quiche was eaten the most.

16, 8, 4: The cheese quiche was eaten the most.
16, 8, 4: The cheese quiche was eaten the most.

1016
, 816
, 916
: The cheese quiche was eaten the most.
Start Fraction 10 over 16 End Fraction , Start Fraction 8 over 16 End Fraction , Start Fraction 9 over 16 End Fraction : The cheese quiche was eaten the most.

916
, 58
, 24
: The spinach quiche was eaten the most.
Start Fraction 9 over 16 End Fraction , Start Fraction 5 over 8 End Fraction , Start Fraction 2 over 4 End Fraction : The spinach quiche was eaten the most.

To identify which quiche was eaten the most and express the amounts eaten in proper fractions, we start with the amount of each quiche and the number of pieces eaten.

Quiche Details:

  1. Cheese Quiche:

    • Cut into 8 equal pieces.
    • Pieces eaten: 5
    • Fraction eaten: \[ \text{Fraction of cheese quiche eaten} = \frac{5}{8} \]

  2. Spinach Quiche:

    • Cut into 16 equal pieces.
    • Pieces eaten: 9
    • Fraction eaten: \[ \text{Fraction of spinach quiche eaten} = \frac{9}{16} \]

  3. Mushroom Quiche:

    • Cut into 4 equal pieces.
    • Pieces eaten: 2
    • Fraction eaten: \[ \text{Fraction of mushroom quiche eaten} = \frac{2}{4} = \frac{1}{2} \]

Comparison of Fractions:

Now we need to compare the fractions \(\frac{5}{8}\), \(\frac{9}{16}\), and \(\frac{1}{2}\).

For ease of comparison, we convert all fractions to have a common denominator. The least common denominator for \(8\), \(16\), and \(2\) is \(16\).

  1. Convert \(\frac{5}{8}\): \[ \frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{10}{16} \]

  2. \(\frac{9}{16}\) remains the same.

  3. Convert \(\frac{1}{2}\): \[ \frac{1}{2} = \frac{1 \times 8}{2 \times 8} = \frac{8}{16} \]

Now we have the following fractions:

  • Cheese: \(\frac{10}{16}\)
  • Spinach: \(\frac{9}{16}\)
  • Mushroom: \(\frac{8}{16}\)

Order from Greatest to Least:

  1. Cheese: \(\frac{10}{16}\)
  2. Spinach: \(\frac{9}{16}\)
  3. Mushroom: \(\frac{8}{16}\)

Conclusion:

  • The cheese quiche was eaten the most.
  • The fractions in numerical order from greatest to least are:
    • \(\frac{10}{16}, \frac{9}{16}, \frac{8}{16}\)

Based on the available choices, the option: Start Fraction 10 over 16 End Fraction , Start Fraction 9 over 16 End Fraction , Start Fraction 2 over 4 End Fraction : The cheese quiche was eaten the most. is correct.