Adding and subtracting with like denominators Transitional Reasoning Download PDF

Questions

1. 1.

   A ceramicist is preparing a specialty glaze mixture that requires a total of $\frac{19}{20}$ kilogram of powdered minerals. The recipe specifies $\frac{8}{20}$ kilogram of silica, and the amount of feldspar needed is $\frac{3}{20}$ kilogram less than the amount of silica. The remaining portion of the mixture consists of kaolin clay. What fraction of a kilogram of kaolin clay must the ceramicist add to complete the mixture?

   • A) $\frac{11}{20}$ kilogram
   • B) $\frac{8}{20}$ kilogram
   • C) $\frac{6}{20}$ kilogram
   • D) $\frac{5}{20}$ kilogram
2. 2.

   In a science workshop, Liam and Maya each receive an identical strip of copper tape to build circuits. Liam uses $\frac{5}{18}$ of his strip for an electromagnet and $\frac{4}{18}$ of it for a switch connection. Maya uses $\frac{7}{18}$ of her strip for an LED circuit and $\frac{6}{18}$ of it for a buzzer alarm. How much more of her strip did Maya use than Liam used of his?

   • A) $\frac{2}{18}$
   • B) $\frac{3}{18}$
   • C) $\frac{4}{18}$
   • D) $\frac{5}{18}$
3. 3.

   A nature trail is divided into 14 equal-length checkpoint segments. A walking club completes $\frac{5}{14}$ of the trail before noon and another $\frac{6}{14}$ of the trail in the early afternoon. Due to maintenance on the path, the club must turn back $\frac{3}{14}$ of the trail to wait at a rest pavilion. What fraction of the full trail remains between their waiting location and the final finish line?

   • A) $\frac{3}{14}$
   • B) $\frac{5}{14}$
   • C) $\frac{8}{14}$
   • D) $\frac{6}{14}$
4. 4.

   A community water cistern is partitioned into 16 equal volume sections. At sunrise, the cistern holds $\frac{13}{16}$ of its total capacity. During the day, garden irrigation consumes $\frac{9}{16}$ of the cistern's capacity, and an automated pump refills $\frac{5}{16}$ of the capacity in the evening. How much additional water, expressed as a fraction of the total capacity, is required to fill the cistern completely to $\frac{16}{16}$?

   • A) $\frac{7}{16}$
   • B) $\frac{9}{16}$
   • C) $\frac{4}{16}$
   • D) $\frac{3}{16}$
5. 5.

   A school garden is divided into 12 equal planting sections. Students plant leafy vegetables in $\frac{4}{12}$ of the garden and root vegetables in $\frac{5}{12}$ of the garden during the morning session. After an inspection in the afternoon, they remove $\frac{2}{12}$ of the garden's planted sections due to weed overgrowth. What fraction of the school garden remains planted?

   • A) $\frac{11}{12}$
   • B) $\frac{7}{12}$
   • C) $\frac{3}{12}$
   • D) $\frac{7}{24}$