18. Algebraic Fractions (Foundation)

Question 1:

Express the following as single fractions.

Give your answers in their simplest forms.

1(a) \dfrac{m}{3}+\dfrac{m}{4}

ANSWER: Multiple Choice (Type 1)

A: \dfrac{5m}{12}

B: \dfrac{7m}{12}

C: \dfrac{3m}{5}

D: \dfrac{11m}{12}

Answer: \dfrac{7m}{12}

Workings:

\dfrac{m}{3}+\dfrac{m}{4}=\dfrac{4m}{12}+\dfrac{3m}{12}=\dfrac{7m}{12}

Marks = 1

1(b) \dfrac{x}{16}+\dfrac{7x}{4}

ANSWER: Multiple Choice (Type 1)

A: \dfrac{29x}{14}

B: \dfrac{29x}{18}

C: \dfrac{29x}{12}

D: \dfrac{29x}{16}

Answer: D

Workings:

\dfrac{x}{16}+\dfrac{7x}{4}=\dfrac{x}{16}+\dfrac{28x}{16}=\dfrac{29x}{16}

Marks = 1

1(c) \dfrac{25x}{27}+\dfrac{2x}{9}

ANSWER: Multiple Choice (Type 1)

A: \dfrac{29x}{27}

B: \dfrac{31x}{27}

C: \dfrac{33x}{27}

D: \dfrac{35x}{27}

Answer: \dfrac{31x}{27}

Workings:

\dfrac{25x}{27}+\dfrac{2x}{9}=\dfrac{25x}{27}+\dfrac{6x}{27}=\dfrac{31x}{27}

Marks = 1

Question 2:

Express the following as single fractions.

Give your answers in their simplest forms.

2(a) \dfrac{4y}{7}-\dfrac{6y}{35}

ANSWER: Multiple Choice (Type 1)

A: \dfrac{y}{5}

B: \dfrac{2y}{5}

C: \dfrac{3y}{5}

D: \dfrac{4y}{5}

Answer: B

Workings:

\dfrac{4y}{7}-\dfrac{6y}{35}=\dfrac{20y}{35}-\dfrac{6y}{35}=\dfrac{14}{35}=\dfrac{2y}{5}

Marks = 1

2(b) \dfrac{10x}{3}-\dfrac{3}{9}

ANSWER: Multiple Choice (Type 1)

A: \dfrac{10x-1}{3}

B: \dfrac{10x-2}{3}

C:  \dfrac{10x-3}{3}

D: \dfrac{10x-4}{3}

Answer: A

Workings:

Marks = 1

2(c) \dfrac{10}{y}-\dfrac{4}{5}

ANSWER: Multiple Choice (Type 1)

A: \dfrac{50-3y}{5y}

B: \dfrac{50-4y}{5y}

C: \dfrac{50-6y}{5y}

D: \dfrac{50-7y}{5y}

Answer: B

Workings:

\dfrac{10}{y}-\dfrac{4}{5}=\dfrac{50}{5y}-\dfrac{4y}{5y}=\dfrac{50-4y}{5y}

Marks = 1