Operations on Decimals Exercises – Set 2

This is our second set of exercises on operations on decimals.

Perform the indicated operation.

1.) 1.5 + 0.7
2.) 10.5 + 3.08 + 4.026
3.) 0.8 – 0.2
4.) 8.06 – 3.215
5.) 5.7 – 0.9
6.) .22 × .6
7.) 5.02 × 1.2
8.) 8.1 ÷ 0.009
9.) .63 ÷ 30
10.) .7 ÷ .005

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Addition of Fractions Exercises – Set 2

Add the following fractions.

1.) \dfrac{1}{7} + \dfrac{2}{7}

2.) \dfrac{1}{12} + \dfrac{5}{12}

3.) \dfrac{7}{15} + \dfrac{2}{15} + \dfrac{6}{15}

4.) \dfrac{1}{3} + \dfrac{1}{4}

5.) \dfrac{2}{9} + \dfrac{1}{3}

6.) \dfrac{3}{8} + \dfrac{1}{4}

7.) 8 \dfrac{2}{3} + \dfrac{3}{2}

8.) \dfrac{1}{2} + \dfrac{2}{3} + \dfrac{3}{4}

9.) 7 \dfrac{2}{7} + 6 \dfrac{3}{14}

10.) 3 \dfrac{1}{4} + 2 \dfrac{1}{8}

Answer key and solution:

1.) \dfrac{3}{7}

2.) \dfrac{6}{12} = \dfrac{1}{2}

3.) \dfrac{15}{15} = 1

4.) \dfrac{7}{12}

Solution:

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Conversion of Units Part 1: Centimeters, Meters, Kilometers

Converting from one unit to another is one of the skills that you should learn before taking the Civil Service Examinations. It sometimes makes calculations easier and therefore saves time.

In this series, I will discuss the different methods that can be used in converting from one unit to another. I will illustrate several examples such as conversion among centimeters (cm), meters (m) and kilometers (km). Take note that the methods used here can also be used in conversion of other units of measure.

It is important that you memorize some standard conversions such as the following:

1 m = 100 cm

1 km = 1000 m

1 kg = 1000 g

1 ft = 30 cm

1 ft = 12 inches

1 mile = 1.6 km  » Read more

Multiplication and Division of Fractions Exercises – Set 1

Week 4

1. 3/4 x 1/2

2. 2/7 x 7/10

3. 4 1/5 x 2/3

4. 8 x 3/4

5. 1 2/3 x 2 3/4 x 11/12

6. 2/5 ÷ 4/5

7. 3/4 ÷ 8

8. 9 ÷ 3/4

9. 5 1/6 ÷ 3/31

10. 2 5/6 ÷ 4 3/5

Answers:

1. 3/8 3/4 x 1/2 = 3/8

2. 1/5

Solution

2/7 x 7/10 = 14/70 = 1/5

3. 2 4/5

Solution

4 1/5 x 2/3
= 21/5 x 2/3 = 42/15
= 2 12/15 = 2 4/5

4. 6

Solution

8 x 3/4 = 8/1 x 3/4
= 24/4 = 6

5. 4 29/144

Solution
1 2/3 x 2 3/4 x 11/12
= 5/3 x 11/4 x 11/12
= 605/144
= 4 29/144

6. 1/2

Solution

2/5 x 5/4 = 10/20 = 1/2

7. 3/32

Solution
3/4 ÷ 8
= 3/4 x 1/8
= 3/32

8. 12

Solution

9 ÷ 3/4 = 9/1 x 4/3 = 36/3 = 12

9. 5 1/6 ÷ 31/3
= 31/6 x 3/31
= 961/18 = 53 7/18

10. 8/35

2 5/6 ÷ 4 3/5 = 17/6 ÷ 23/5
= 17/6 x 5/23 = 85/138

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Subtraction of Fractions Exercises – Set 1

Find the difference of the following:

1.) \dfrac{8}{11} - \dfrac{3}{11}

2.) \dfrac{7}{16} - \dfrac{3}{16}

3.) \dfrac{4}{5} - \dfrac{3}{4}

4.) 7 - \dfrac{4}{9}

5.) 8 \dfrac{9}{10} - \dfrac{3}{10}

6.) 6 \dfrac{2}{7} - \dfrac{5}{7}

7.) 4 \dfrac{1}{3} - \dfrac{1}{6}

8.) 6 \dfrac{3}{5} - 2 \dfrac{3}{4}

9.) 11 \dfrac{2}{3} - 7

10.) 9 \dfrac{2}{5} - \dfrac{11}{9}

Answers:

1.) \dfrac{5}{11}

2.) \dfrac{1}{4}

Solution
\dfrac{7}{16} - \dfrac{3}{6} = \dfrac{4}{16} = \dfrac{1}{4}

3.) \dfrac{1}{20}

Solution
LCD: 20
\dfrac{4}{5} - \dfrac{3}{4} = \dfrac{16}{20} - \dfrac{15}{20} = \dfrac{1}{20}

4.) 6 \dfrac{5}{9}

Solution

We can decompose 7 into 6 and 9/9.

6 \dfrac{9}{9} - \dfrac{4}{9} = 6 \dfrac{5}{9}

5.) 8 \dfrac{3}{5}

Solution
8 \dfrac{9}{10} - \dfrac{3}{10} = 8 \dfrac{6}{10} = 8 \dfrac{3}{5}

6.) 5 \dfrac{4}{7}

Solution
5 \dfrac{9}{7} - \dfrac{5}{7} = 5 \dfrac{4}{7}

7.) 4 \dfrac{1}{6}

Solution
LCD: 6
4 \dfrac{1}{3} - \dfrac{1}{6} = 4 \dfrac{2}{6} - \dfrac{1}{6} = 4 \dfrac{1}{6}

8.) 3 \dfrac{17}{20}

Solution
LCD: 20
5 \dfrac{8}{5} - 2 \dfrac{3}{4} = 5 \dfrac{32}{20} - 2 \dfrac{15}{20} = 3 \dfrac{17}{20}

9.) 4 \dfrac{2}{3}

Solution
11 \dfrac{2}{3} - 7 = 4 \dfrac{2}{3}

10.) 8 \dfrac{8}{45}

Solution
9 \dfrac{2}{5} - \dfrac{11}{9} = 8 \dfrac{7}{5} - \dfrac{11}{9}

LCD: 45
8 \dfrac{63}{45} - \dfrac{55}{45} = 8 \dfrac{8}{45}

 

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