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Your friend says that the quotient 3/8 divided by 1/8 is 1/3 what is the correct quotient? What mistake did you friend likely make?

11 answers

To find the correct quotient of \(\frac{3}{8}\) divided by \(\frac{1}{8}\), we can use the rule that dividing by a fraction is the same as multiplying by its reciprocal.

So, we can calculate:

\[ \frac{3}{8} \div \frac{1}{8} = \frac{3}{8} \times \frac{8}{1} \]

Now we can perform the multiplication:

\[ \frac{3 \times 8}{8 \times 1} = \frac{24}{8} = 3 \]

Thus, the correct quotient is \(3\).

Your friend likely made a mistake by misunderstanding the operation of division with fractions, perhaps treating it incorrectly as subtraction or mixing up the fractions when calculating. Instead of multiplying the top and the bottom of the fractions, they might have miscalculated without fully inverting the second fraction.

-2 1/2 divided by 1/4

To divide \(-2 \frac{1}{2}\) by \(\frac{1}{4}\), we first need to convert \(-2 \frac{1}{2}\) into an improper fraction.

  1. Convert \(-2 \frac{1}{2}\) to an improper fraction: \[ -2 \frac{1}{2} = -\left(2 \times 2 + 1\right)/2 = -\left(4 + 1\right)/2 = -\frac{5}{2} \]

  2. Now we need to divide \(-\frac{5}{2}\) by \(\frac{1}{4}\): \[ -\frac{5}{2} \div \frac{1}{4} = -\frac{5}{2} \times \frac{4}{1} \]

  3. Multiply: \[ -\frac{5 \times 4}{2 \times 1} = -\frac{20}{2} = -10 \]

Thus, \(-2 \frac{1}{2}\) divided by \(\frac{1}{4}\) equals \(-10\).

-5/6 divided by 5/7

To divide \(-\frac{5}{6}\) by \(\frac{5}{7}\), we will multiply by the reciprocal of the second fraction.

The reciprocal of \(\frac{5}{7}\) is \(\frac{7}{5}\).

Now, we can perform the division as follows:

\[ -\frac{5}{6} \div \frac{5}{7} = -\frac{5}{6} \times \frac{7}{5} \]

When multiplying, the \(5\) in the numerator of the first fraction and the \(5\) in the denominator of the second fraction cancel out:

\[ -\frac{5 \times 7}{6 \times 5} = -\frac{7}{6} \]

So, \(-\frac{5}{6}\) divided by \(\frac{5}{7}\) equals \(-\frac{7}{6}\).

-5 2/3* -1 1/2

To multiply \(-5 \frac{2}{3}\) by \(-1 \frac{1}{2}\), we first convert both mixed numbers into improper fractions.

  1. Convert \(-5 \frac{2}{3}\) to an improper fraction: \[ -5 \frac{2}{3} = -\left(5 \times 3 + 2\right)/3 = -\left(15 + 2\right)/3 = -\frac{17}{3} \]

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

Now we can multiply the two improper fractions:

\[ -\frac{17}{3} \times -\frac{3}{2} \]

When multiplying two negative numbers, the result will be positive:

\[ \frac{17 \times 3}{3 \times 2} \]

Now simplifying:

  1. The \(3\) in the numerator and the \(3\) in the denominator cancel out: \[ \frac{17}{2} \]

Thus, the product of \(-5 \frac{2}{3}\) and \(-1 \frac{1}{2}\) is \(\frac{17}{2}\).

If desired, you can convert \(\frac{17}{2}\) back to a mixed number: \[ \frac{17}{2} = 8 \frac{1}{2} \]

So the final answer is \(\frac{17}{2}\) or \(8 \frac{1}{2}\).

do it without canciling out

Certainly! Let's multiply \(-5 \frac{2}{3}\) by \(-1 \frac{1}{2}\) without canceling out any factors during the process.

  1. Convert \(-5 \frac{2}{3}\) to an improper fraction: \[ -5 \frac{2}{3} = -\left(5 \times 3 + 2\right)/3 = -\left(15 + 2\right)/3 = -\frac{17}{3} \]

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

  3. Now multiply the two improper fractions: \[ -\frac{17}{3} \times -\frac{3}{2} \]

Since both fractions are negative, the product will be positive:

\[ \frac{17 \times 3}{3 \times 2} \]

Calculating the numerator:

  • \(17 \times 3 = 51\)

Calculating the denominator:

  • \(3 \times 2 = 6\)

So we have: \[ \frac{51}{6} \]

  1. Convert \(\frac{51}{6}\) to a mixed number:
    • Dividing \(51\) by \(6\) gives \(8\) remainder \(3\):

Thus, we can express this as: \[ 8 \frac{3}{6} \]

And simplify \(\frac{3}{6}\) to \(\frac{1}{2}\): \[ 8 \frac{1}{2} \]

The final answer, without canceling out, is \(\frac{51}{6}\) or expressed as a mixed number \(8 \frac{1}{2}\).

all fractions equal to -4/9

To find fractions that are equal to \(-\frac{4}{9}\), we can multiply both the numerator and the denominator of \(-\frac{4}{9}\) by the same non-zero integer. Here are some examples using different integers:

  1. Multiply by \(2\): \[ -\frac{4 \times 2}{9 \times 2} = -\frac{8}{18} \]

  2. Multiply by \(3\): \[ -\frac{4 \times 3}{9 \times 3} = -\frac{12}{27} \]

  3. Multiply by \(4\): \[ -\frac{4 \times 4}{9 \times 4} = -\frac{16}{36} \]

  4. Multiply by \(-1\): \[ -\frac{4 \times (-1)}{9 \times (-1)} = \frac{4}{9} \]

  5. Multiply by \(-2\): \[ -\frac{4 \times (-2)}{9 \times (-2)} = \frac{8}{18} \]

  6. Multiply by \(-3\): \[ -\frac{4 \times (-3)}{9 \times (-3)} = \frac{12}{27} \]

In general, any fraction of the form \(-\frac{4k}{9k}\), where \(k\) is any non-zero integer, will be equal to \(-\frac{4}{9}\).

Summary of Some Equivalent Fractions

  1. \(-\frac{8}{18}\)
  2. \(-\frac{12}{27}\)
  3. \(-\frac{16}{36}\)
  4. \(-\frac{20}{45}\)
  5. \(-\frac{28}{63}\)
  6. \(-\frac{32}{72}\)

All of these fractions are equal to \(-\frac{4}{9}\).