2.1 Fractions 1 : Simplifying & Equivalent – National 5 Maths Lessons @MrThomasMaths (Nat 5 / N5)

The video concludes by recommending practice questions from page 125, specifically question 6 for equivalent fractions and question 8 for simplifying fractions, in the TJ Nat 4 book book one, to solidify understanding of both concepts.

The video begins by recapping equivalent fractions. Using shaded shapes, it demonstrates that 1/3, 2/6, and 4/12 all represent the same amount, making them equivalent fractions. It then explains that to change one fraction into an equivalent one, you multiply both the numerator (top number) and denominator (bottom number) by the same number.

The video provides examples of creating equivalent fractions. For instance, to find an equivalent of 1/2, one can multiply both the numerator and denominator by any whole number (e.g., by 4 to get 4/8, or by 7 to get 7/14). This process involves making the numbers bigger while maintaining the same fractional value.

Additional examples are shown with the fraction 5/8. By multiplying both the numerator and denominator by 3, we get 15/24. Multiplying by 9 yields 45/72. Another example shows multiplying by 34 to get 170/272, emphasizing that any common multiplier creates an equivalent fraction.

The video transitions to simplifying fractions, which is the reverse process of creating equivalent fractions. Instead of multiplying, you divide both the numerator and denominator by the same number. The goal is to make the numbers smaller and the fraction simpler, such as changing 2/6 to 1/3 by dividing by 2.

An example demonstrates simplifying 12/15. Both 12 and 15 are divisible by 3. Dividing both by 3 results in 4/5. It's crucial to check if the simplified fraction can be reduced further; in this case, 4 and 5 share no common factors other than 1.

Another example involves simplifying 21/56. Identifying that both numbers are divisible by 7, dividing them yields 3/8. The video reiterates the importance of ensuring the fraction is fully simplified by checking for any further common divisors.

The video presents multiple methods for simplifying 24/32. One method is to divide both by 8 directly, resulting in 3/4. Another method shows a step-by-step division by smaller common factors: dividing by 2 to get 12/16, then by 2 again to get 6/8, and finally by 2 to arrive at 3/4. It also mentions dividing by 4 as an intermediate step. The key takeaway is that different paths lead to the same fully simplified fraction.