GCD Practice Exercises with Solutions on Youtube

Find the GCD/GCF of the following numbers.

1. 12, 18
2. 14, 35
3. 20,28
4. 25, 30, 40
5. 7, 12
6. 48, 72
7. 42, 60, 72
8. 24, 36
9. 12, 16
10. 18, 30, 54

Answers

1. 6
2. 7
3. 4
4. 5
5. 1
6. 12
7. 6
8. 12
9. 4
10. 6

Solutions to numbers 1-2
Solutions to numbers 3-5
Solutions to numbers 6-7
Solutions to numbers 8-10

Week 3 Review Answers and Solutions

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

Practice Test on Dividing Integers

In the previous post we have discussed how to divide integers. Operations on real numbers, particularly integers, is one of the scopes of the Civil Service Examinations both Professional and Subprofessional.  You must master these operations because you will use them in solving equations and word problems in Algebra. 

Test your skill by answering the exercises below. Recall that a divided by b is the same as a times reciprocal of b.

Practice Test on Dividing Integers

1.) -35 ÷ 7

2.) 38 ÷ -19  » Read more



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