Identify, Name and Write Equivalent Fractions of a Given Fraction, Represented Visually, Including Tenths and Hundredths 3 - Reasoning

The task at hand requires students to match given fractions to their equivalent visual representations and to justify their answers. The fractions presented are 1/10, 3/5, and 4/7, along with their equivalent forms 10/100, 21/35, and 56/98 respectively. To determine the equivalence, students are to apply their understanding of fraction simplification and equivalence.

For diagram A, the fraction 1/10 is matched with 10/100. This equivalence is proven by dividing both the numerator (top number) and the denominator (bottom number) of 10/100 by 10, which simplifies to 1/10. Similarly, diagram B corresponds to the fraction 3/5, which is equivalent to 21/35. This can be shown by dividing both the numerator and denominator of 21/35 by 7. Lastly, diagram C is matched with 4/7, which is equivalent to 56/98, and this is proven by dividing both parts of 56/98 by 14. Through these calculations, students can visually and numerically confirm the equivalence of the given fractions.