Exam-Style Problems

Stage 9 - Q1 - 2 marks

19587

Multiply and simplify.

\[\frac{11}{4}\times\frac{8}{9}\]

Hint

A factor in any numerator can cancel with a factor in any denominator.

Stage 9 - Q2 - 2 marks

19588

Multiply and simplify.

\[\frac{31}{12}\times\frac{6}{7}\]

Hint

A factor in any numerator can cancel with a factor in any denominator.

Stage 9 - Q3 - 2 marks

19589

Multiply and simplify.

\[\frac{37}{14}\times\frac{7}{15}\]

Hint

A factor in any numerator can cancel with a factor in any denominator.

Stage 9 - Q4 - 2 marks

19590

Multiply and simplify.

\[\frac{37}{16}\times\frac{24}{35}\]

Hint

A factor in any numerator can cancel with a factor in any denominator.

Stage 9 - Q5 - 3 marks

19591

A tray contains 108 seedlings. \(\frac{5}{9}\) of them are planted. How many are planted?

Hint

“Of” means multiply in this context.

Stage 9 - Q6 - 3 marks

19592

A rectangle measures \(3\) m by \(\frac{11}{4}\) m. Find its exact area.

Hint

Cancel only factors, not terms joined by addition.

Stage 9 - Q7 - 3 marks

19593

Can you cancel 4 in \(\frac{4+1}{4}\) to get 2? Explain and correct.

Hint

Cancellation applies to products of factors.

Stage 9 - Q8 - 3 marks

19594

Find this product efficiently.

\[\frac{2}{3}\times\frac{15}{2}\times\frac{6}{5}\]

Hint

No rounding or decimal conversion is needed.

Stage 9 - Q9 - 4 marks

19595

Order \(\frac{7}{6}\times\frac{7}{8}\), \(\frac{7}{6}\) and \(\frac{7}{6}\times\frac{9}{8}\) without calculating the products.

Hint

Compare each multiplier with 1.

Stage 9 - Q10 - 5 marks

19596

Challenge: The product is \(\frac{5}{6}\times\frac{6}{7}\times\cdots\times\frac{12}{13}\). One factor is omitted and the product becomes \(\frac{45}{104}\). Identify the omitted factor and justify.

Hint

First find the complete telescoping product.