PDF Basic Computation

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11 1. Divisibility

(a) When the last 2 digits of a number are divisible by 4, then the number is divisible by 4.

(b) When a number is even and is divisible by 3, then the number is divisible by 6.

(c) When the last 3 digits of a number are divisible by 8, then the number is divisible by 8.

(d) When the sum of the digits of a number is divisible by 9, then the number is divisible by 9.

2. H.C.F. and L.C.M.

(a) Prime factorization is a number written as the product of all its prime factors.

For example, 540 = 2 × 2 × 3 × 3 × 3 × 5.

(b) The first common multiple of two or more numbers is called the least common multiple (L.C.M.) of the numbers.

For example, the L.C.M. of 4 and 6 is 12.

(c) Among all the common factors of two or more numbers, the greatest one is called the highest common factor (H.C.F.) of the numbers.

For example, the H.C.F. of 20 and 12 is 4.

3. Operation of Numbers

(a) Multiplication and division must be completed before addition and subtraction.

(b) If there are brackets in an expression, complete the parts within the brackets first.

Calculate 5 × [30 – 2 × (2 + 4)].

Solution:

5 × [30 – 2 × (2 + 4)] = 5 × (30 – 2 × 2 + 4)

= 5 × 30

= 150

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The operation in brackets should be completed first, that is,

5 × [30 – 2 × (2 + 4)] = 5 × (30 – 2 × 6)

= 90

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Wow! Mathematics Summer Fun (New Syllabus Edition) S.1 – S.2

3. (a) Round off 449.049 to 1 decimal place.

(b) Round off 0.005 476 to 2 significant figures.

4. (a) Round off 92.479 85 to 3 significant figures.

(b) Round up 92.479 85 to the nearest integer.

(c) Round down 92.479 85 to 2 decimal places.

Estimate the following expressions by rounding off the numbers to the nearest thousand (5 – 6).

5. 4932 + 57 362 – 2237 6. 64 832 – 26 337 – 31 218

≈ + – ≈ – –

= =

Estimate the following expressions by rounding off the numbers to 2 significant figures (7 – 8).

7. 247 + 289 − 498 8. 247 × 4.03 – 79.85

9. Estimate the value of 7248 + 8957 + 4653 – 10 572 by (a) rounding up each of the numbers to the nearest thousand;

(b) rounding down each of the numbers to the nearest thousand.

10. Estimate the value of 248.32 × 15.67 – 2797 by

(a) rounding up each of the numbers to 2 significant figures;

(b) rounding down each of the numbers to 2 significant figures.

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19. The price of a melon in a fruit stall is $48. 32 melons are sold. The owner of the fruit stall estimates that the revenue from selling the melons is at least $1200. Do you agree? Explain your answer.

20. The table shows the numbers of visitors of a theme park last week:

Day Sun Mon Tue Wed Thu Fri Sat

Number of

visitors 13 827 4793 5832 4159 6317 7133 9874

(a) By rounding off the numbers to the nearest thousand, estimate the total number of visitors of the theme park last week.

(b) The manager estimates that the total number of visitors is greater than 55 000. Do you agree? Explain your answer.

21. Mr. Lee takes 130 minutes (correct to the nearest 10 minutes) to drive from city A to city B. Which of the following may be the actual time for the journey?

A. 121 minutes B. 125 minutes C. 135 minutes D. 139 minutes

22. 0.037 672 =

A. 0.0376 (cor. to 3 sig. fig.).

B. 0.0377 (cor. to 3 sig. fig.).

C. 0.0376 (cor. to 4 sig. fig.).

D. 0.03770 (cor. to 4 sig. fig.).

TSA

23. Find 4.5 ÷ 2.3 and give the answer correct to 3 decimal places.

A. 1.95 B. 1.96 C. 1.956 D. 1.957

24. If x = 42.50 (cor. to 4 sig. fig.), then which of the following may be the value of x?

A. 42.489 46 B. 42.490 92 C. 42.504 97 D. 42.510 07

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Multiple-choice Questions

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8383 Preparing for the New School Year

Try it now

Preparing for the New School Year

A. Change of Subjects of Formulas

1. Subject of a Formula

If there is only one variable on one side such that it is expressed in terms of other variables, then that variable is called the subject of the formula.

For example, in the formula x = 2y + 3z, x is the subject of the formula.

2. Change of Subject

The subject of a formula may be changed from one variable to another.

For example, make y the subject of the formula x = 2y + 3z.

x = 2y + 3z

x – 3z = 2y Subtract 3z from both sides.

y = x – 3z

2 Divide both sides by 2.

1. Make a the subject of the formula 4b = a – 5c.

2. (a) Make b the subject of the formula P = 2(15 + b).

(b) If P = 80, find the value of b.

Learning video

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We can make a compass by following the procedures below.

1. Materials required: Metal needle, a magnet, a styrofoam or a cork

2. Rub the needle with the magnet more than 20 times in the same direction instead of back and forth. The needle will then be magnetized after this step.

3. Insert the needle in the styrofoam or the cork so that it is in the middle of the needle.

4. Place the needle with the styrofoam or the cork into a bowl of water.

5. The magnetized needle will align itself with the earth’s magnetic field to point from north to south.

6. Compare the direction of the needle with a compass or a compass app in your smartphone.

Note:

1. The needle in the bowl will slowly spin either clockwise or anticlockwise to point from north to south. If it does not, rub the needle again to magnetize it.

2. Since we cannot distinguish which end of the needle points to the south, we may use a real compass to identify it.

3. Repeat several times with different directions of rubbing the needle. What do you observe?

4. Suggest a way to improve the accuracy of the above setup.

1. Making a simple compass

A compass can help us to move in the correct direction especially when you are camping. Making a magnetic compass is easy and its working principle bases on Earth’s magnetic field.

Let’s explore

STEM Exploration

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