To determine which equation can be represented using the number line described, we can analyze each option based on the relationship between the fractions and their division.
-
Three-fourths divided by one-eighth = 6: To evaluate this, we calculate \( \frac{3/4}{1/8} \): \[ \frac{3/4}{1/8} = \frac{3}{4} \times \frac{8}{1} = \frac{3 \times 8}{4 \times 1} = \frac{24}{4} = 6 \] This equation is correct.
-
One-eighth divided by three-fourths = 6: Calculate \( \frac{1/8}{3/4} \): \[ \frac{1/8}{3/4} = \frac{1}{8} \times \frac{4}{3} = \frac{4}{24} = \frac{1}{6} \] This is incorrect.
-
6 divided by three-fourths = one-eighth: Calculate \( \frac{6}{3/4} \): \[ \frac{6}{3/4} = 6 \times \frac{4}{3} = \frac{24}{3} = 8 \] This is incorrect.
-
6 divided by one-eighth = three-fourths: Calculate \( \frac{6}{1/8} \): \[ \frac{6}{1/8} = 6 \times 8 = 48 \] This is also incorrect.
Out of the options presented, only the first one is valid:
Three-fourths divided by one-eighth = 6.
This can indeed be represented on the number line as it shows the process of dividing the fraction \( \frac{3}{4} \) by \( \frac{1}{8} \), which relates directly to the marks and increments depicted on the number line.
4 answers