Math

QuestionCalculate 7÷19107 \div 1 \frac{9}{10} and choose the correct answer: A) 1970-\frac{19}{70}, B) 64156 \frac{4}{15}, C) 313193 \frac{13}{19}, D) 6126 \frac{1}{2}.

Studdy Solution

STEP 1

Assumptions1. We are dividing7 by19/10. The division operation is defined as the inverse of multiplication

STEP 2

First, we need to convert the mixed number19/10 into an improper fraction. A mixed number is a whole number and a fraction combined into one "mixed" number. An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number).
1910=10×1+9101 \frac{9}{10} = \frac{10 \times1 +9}{10}

STEP 3

Calculate the improper fraction.
1910=10×1+910=19101 \frac{9}{10} = \frac{10 \times1 +9}{10} = \frac{19}{10}

STEP 4

Now we need to divide7 by19/10. Remember that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
7÷1910=7×10197 \div \frac{19}{10} =7 \times \frac{10}{19}

STEP 5

Now, multiply7 by10/19.
7×1019=70197 \times \frac{10}{19} = \frac{70}{19}

STEP 6

Now, we need to convert the improper fraction70/19 into a mixed number. We do this by dividing the numerator by the denominator.
7019=31319\frac{70}{19} =3 \frac{13}{19}So, the answer is C) 313193 \frac{13}{19}.

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