## Browse Tag: civil service exam math practice problems

These are the answers and solutions to the Week 3 Practice Exercises and Problems.

Solutions to Practice Exercise 1

a.) 2 1/5 + 3 2/5

We can add the whole numbers first, 2 + 1 = 3. Then, add the fractions: 1/5 + 2/5 = 3/5.
We then combine the whole number and the fraction, so the answer is 3 3/5.

b.) 8 1/4 + 2 3/4

We can add the whole numbers first, 8 + 2 = 10. Then, add the fractions: 1/4 + 3/4 = 4/4 = 1
We then add 10 + 1 = 11.

c.) 5 + 2 1/4

We can just add the whole numbers: 5 + 2 = 7. Then, we append the fraction. So the correct answer is 7 ¼.

d.) 5 1/2 + 1/5

We just add the fractions and combine the sum with the whole number 5 later. To add dissimilar fractions, we get the LCM of the denominators. The LCM of 2 and 5 is 10.

The equivalent fraction of ½ = 5/10.
The equivalent fraction of 1/5 = 2/10.
5/10 + 2/10 = 7/10

We now append 5. So, the correct answer is 5 7/10.

e.) 3 1/3 + 4 1/4 + 5 1/5

Just like in (d), we can separately add the whole numbers and then add the fractions.

Whole numbers: 3 + 4 + 5 = 12

To add dissimilar fractions, we get the LCM of the denominators. The LCM of 3, 4, and 5 is 60.

The equivalent fraction of 1/3 = 20/60.
The equivalent fraction of 1/4 = 15/60.
The equivalent fraction of 1/5 = 12/60.

20/60 + 15/60 +12/60 = 47/60

Appending the whole number, the final answer is 12 47/60.

Solutions to Practice Exercises 2

a.) 4 6/7 – 3/7

Solution

We just subtract the fractions and append the whole number. 6/7 – 3/7 = 3/7. So, the final answer is 4 3/7.

b.) 8 – 3/4

Solution

One strategy here is to borrow 1 from 8 and make the fraction 4/4. This means that 8 becomes 7 4/4.
So, 7 4/4 – ¾ = 7 ¼.

c.) 12 – 5 2/9

Solution

Our minuend is a whole number, so we can make a fraction out of it. To do this, we can borrow 1 from 12 and make the fraction 9/9. This means that 12 becomes 11 9/9.
So, 11 9/9 – 5 2/9 = 6 7/9.

d.) 7 3/10 – 7/10

We cannot subtract 3/10 – 7/10, so we borrow 1 from 7 and make the fraction 6 10/10. But since we already have 3/10, we add it to 6 10/10 making it 6 13/10.
So, 6 13/10 – 7/10 = 6 6/10 = 6 3/5.

e.) 6 1/5 – 3/4

Another strategy in subtracting fractions is to convert mixed fractions to improper fractions. The improper fraction equivalent of 6 1/5 is 31/5. Then, we find the LCM of 5 and 4 which is 20.

Now, the equivalent fraction of 31/5 is 124/20.
The equivalent fraction of 3/4 = 15/20.
124/20 – 15/20 = 109/20

Converting 109/20 to mixed fraction, we have 5 9/20.

f.) 9 3/8 – 4 5/7

9 3/8 – 4 5/7 = 8 3/8+8/8 – 4 5/7 = 8 11/8 – 4 5/7

The LCM of 8 and 7 is 56, so

4 77-40/56 = 4 37/56.

Solutions to Practice Problems

1.) 1 3/5 + 4/5 = 1 7/5 = 2 2/5

2.) Converting the improper fractions, we have
2 5/8= 21/8
1 5/6 = 11/6.

This means that we need to perform.
21/8-11/6.

Since they are dissimilar fractions, we get their LCM which is 48.
(126-88)/48= 38/48 reduce lowest term by dividing the numerator and denominator by 2, we get 19/24

3.) 2 5/6 – 17/8 = 17/6 – 17/8

LCD: 24
68/24 – 51/24 = 17/24

4.) 3/8 + 1/4
LCD: 8
3/8 + 2/8 = 5/8

Whole pizza – 5/8
8/8 – 5/8
= 3/8

5.) d = 3 4/15 + 5/8
d= 49/15 + 5/8
d= (49(8)+5(15))/120
d= (392+75)/120
d= 467/120
d=3 107/120