Write each fraction in its simplest form: \frac{8}{16} = \frac{8 \div 8}{16 \div 8} = \frac{1}{2} b) \frac{12}{36} = \frac{12 \div 12}{36 \div 12} = \frac{1}{3} c) \frac{13}{26} j) \frac{13}{39} e) \frac{18}{48} f) \frac{30}{45} h) \frac{16}{56} i) \frac{20}{28} k) \frac{24}{36} l) \frac{36}{48} \frac{33}{88} = \frac{33 \div 11}{88 \div 11} = \frac{3}{8} \frac{24}{32} Complete:
The Correct Answer and Explanation is:
Here are the simplified forms of the given fractions:
- c) 1326=13÷1326÷13=12\frac{13}{26} = \frac{13 ÷ 13}{26 ÷ 13} = \frac{1}{2}
- j) 1339=13÷1339÷13=13\frac{13}{39} = \frac{13 ÷ 13}{39 ÷ 13} = \frac{1}{3}
- e) 1848=18÷648÷6=38\frac{18}{48} = \frac{18 ÷ 6}{48 ÷ 6} = \frac{3}{8}
- f) 3045=30÷1545÷15=23\frac{30}{45} = \frac{30 ÷ 15}{45 ÷ 15} = \frac{2}{3}
- h) 1656=16÷856÷8=27\frac{16}{56} = \frac{16 ÷ 8}{56 ÷ 8} = \frac{2}{7}
- i) 2028=20÷428÷4=57\frac{20}{28} = \frac{20 ÷ 4}{28 ÷ 4} = \frac{5}{7}
- k) 2436=24÷1236÷12=23\frac{24}{36} = \frac{24 ÷ 12}{36 ÷ 12} = \frac{2}{3}
- l) 3648=36÷1248÷12=34\frac{36}{48} = \frac{36 ÷ 12}{48 ÷ 12} = \frac{3}{4}
- 2432=24÷832÷8=34\frac{24}{32} = \frac{24 ÷ 8}{32 ÷ 8} = \frac{3}{4}
Explanation
To simplify a fraction, we reduce it to an equivalent form with the smallest possible numerator and denominator. The idea is to divide both parts of the fraction by their greatest common divisor (GCD), which is the largest number that divides both values exactly.
For instance, take 3045\frac{30}{45}. We determine that the GCD of 30 and 45 is 15. Dividing both by 15, we get 23\frac{2}{3}, which is the simplified form. This reduced fraction represents the same ratio but in a more compact and easily understandable format.
Simplifying helps in many real-life and academic scenarios. It improves the clarity of measurements, sharpens calculation accuracy, and makes comparison between fractions much easier. Imagine adding 2028\frac{20}{28} and 1656\frac{16}{56}. Simplifying them to 57\frac{5}{7} and 27\frac{2}{7}, respectively, makes the sum much more straightforward.
This process also links directly to factoring. When we simplify 3648\frac{36}{48}, we identify that both numbers share a factor of 12. Recognizing common factors not only simplifies fractions but strengthens number sense, which is essential for mastering ratios, proportions, algebraic expressions, and even unit conversions.
Overall, simplifying fractions is a foundational skill in mathematics that teaches us about the relationships between numbers, enhances computation, and sets the stage for deeper mathematical understanding.
