Question 19 of 58beginner🔧 ApplyNumerical2 marks

Simplify the following using the distributive property: 79(67−34).\frac{7}{9}\left(\frac{6}{7} - \frac{3}{4}\right).

Correct Answer

112\frac{1}{12}

Exercise: Exercise Set 3.3 | Q: 7 | (Page 10)
For More Understanding

Explanation

The distributive property of rational numbers states that for any rational numbers p, q, and r, p(q - r) = pq - pr. We apply this property to multiply the term outside the brackets by each term inside, and then find the difference between the resulting products.

Solution Steps

  1. Apply the distributive property: 79(67−34)=(79×67)−(79×34)\frac{7}{9}\left(\frac{6}{7} - \frac{3}{4}\right) = \left(\frac{7}{9} \times \frac{6}{7}\right) - \left(\frac{7}{9} \times \frac{3}{4}\right)

  2. Multiply the fractions: (4263)−(2136)=23−712\left(\frac{42}{63}\right) - \left(\frac{21}{36}\right) = \frac{2}{3} - \frac{7}{12}

  3. Make the denominators equal: The LCM of 3 and 12 is 12. Convert 23\frac{2}{3} to have denominator 12: 2×43×4=812\frac{2 \times 4}{3 \times 4} = \frac{8}{12}

  4. Subtract the fractions: 812−712=112\frac{8}{12} - \frac{7}{12} = \frac{1}{12}

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