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QuestionFind three fractions equivalent to −712\frac{-7}{12}. What is the numerator for −712=□24\frac{-7}{12}=\frac{\square}{24}?

Studdy Solution

STEP 1

Assumptions1. We are looking for a fraction equivalent to −712\frac{-7}{12} . The new denominator is243. The new fraction must be simplified

STEP 2

To find an equivalent fraction, we multiply both the numerator and the denominator of the original fraction by the same number. The number we choose is determined by the new denominator. In this case, we need to find a number that when multiplied by12 gives24.
−712=−7×n12×n\frac{-7}{12} = \frac{-7 \times n}{12 \times n}

STEP 3

Now, we determine the value of n by dividing the new denominator by the original denominator.
n=2412n = \frac{24}{12}

STEP 4

Calculate the value of n.
n=2412=2n = \frac{24}{12} =2

STEP 5

Now that we have the value of n, we can find the new numerator by multiplying the original numerator by n.
New numerator=−7×nNew\, numerator = -7 \times n

STEP 6

Plug in the value of n to calculate the new numerator.
New numerator=−×2New\, numerator = - \times2

STEP 7

Calculate the new numerator.
New numerator=−7×2=−14New\, numerator = -7 \times2 = -14So, −712=−1424\frac{-7}{12}=\frac{-14}{24} when simplified.

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