Sec 1 Mathematics Integers, Rational & Real Numbers topical questions

Work out each of the following.

1. (a)(−9) + 4[1]
2. (b)(−2) × (−7)[1]
3. (c)6 − (−5)[1]

Write 7/8 as a decimal, and write 0.4 as a fraction in its simplest form.

Arrange in ascending order: 0.7, −2, 3/5, −1.5, 1.

Evaluate 1 1/3 × 3/8.

Work out each of the following.

1. (a)(−7) × 6[1]
2. (b)(−36) ÷ (−9)[1]
3. (c)(−1)¹⁰⁰[1]

Work out 3/4 + 2/3, giving your answer as a mixed number.

A submarine sits at −45 m relative to sea level. It rises 18 m, then dives 30 m, then rises 12 m.

1. (a)Find its final depth.[2]
2. (b)Did the submarine end higher or lower than it started? Explain how you know.[2]

Work out 2 2/5 ÷ 6/25, giving your answer as a mixed number.

a is the number exactly halfway between −4 and 3, and b is the number exactly halfway between a and 3.

1. (a)Find a.[1]
2. (b)Find b.[1]
3. (c)How many halves (units of 0.5) are there between a and 3?[1]

A chicken rice recipe uses 3/4 kg of rice. Auntie Rosnah has 2 1/2 kg of rice in her stall bin.

1. (a)How many full recipes can she cook?[3]
2. (b)How much rice is left over? Give your answer in kg.[1]

A small online store records three monthly results as signed values (profit positive, loss negative): −$450, +$280 and −$120.

1. (a)Find the net result over the three months.[2]
2. (b)How much profit in a fourth month would bring the store back to breaking even?[1]

x is an integer with −3 < x ≤ 2, and y is an integer with y ≥ 1. State all the possible values of the product x × y that are negative.

Show that 0.999… (recurring) equals 1.

Three students discuss the number 0.12112111211112… (each block of 1s grows by one). Amara says it is rational because it has a pattern; Bala says it is irrational; Cai says every non-terminating decimal is irrational.

For each number below, state whether it is rational or irrational, giving a reason in each case: √16, √17, 22/7, 0.121212… (recurring).