Fractions and Square Root Practice Questions

Most High School tests as well as Nursing Entrance tests, and Armed Services tests include either fractions and square root practice questions, or both.

Basic Math

1. Which one of the following is a finite decimal?

a. ⁸⁴/₆₃₀
b. ⁶/₃₅
c. ³/₂₂
d. ¹³/₁₂₈
e. ⁷/₂₁₆

2. Calculate   69% of 33.

a. 22
b. 22.5
c. 23.5
d. 22.75
e. 22.77

3. Which of the following is located between ⁷/₁₁ and ⁵/₇ ?

a. 0.6
b. ¹³/>₁₇
c. ²/₃
d. ¹¹/₁₅
e. ³/₄

4. 

a. 1.2
b. 0.2
c. ³/₄
d. 1.5
e. 1 ²/₃

5. Which of the following is less than a third?

a. ⁸⁴/₂₃₁
b. ⁶/₃₅
c.> ³/₂₂
d. Answers a,b,c
e. Answers b,c

6. Which of the following numbers is the largest?

a. 1
b. √2
c. 3/2
d. 1.1
e. 160%

7. Which of the following numbers is the smallest?

a. 1
b. √2
c. 3/2
d. 1.1
e. 160%

8. Calculate 1 + 0.125 + 3/4

a. 1.625
b. 1.755
c. 1
d.1 ⁷/₈
e.2

9. Calculate ²/₉ of 23,531,445.

a. 5,229,210
b. 33,435,720
c. 2,451,316
d. 13,483,540
e. 18,590,200

1. d
2. e
3. c
4. a
5. e
6. e
7. a
8. d
9.a

1. Not simplifying fractions first.  Always simplify fractions to the simples form before adding, subtracting or other operations.

2. Not understanding common denominators.

To add or subtract fractions, they must have the same denominator. For example, to add 1/2 and 3/4, a common denominator is needed. The common denominator 4, because 4 is a multiple of both 2 and 4.
So, you would convert 1/2 to 2/4 and add it to 3/4 to get 2/4 + 3/4 = 5/4

3. Errors with mixed numbers and converting to improper fractions or vice versa.

Referring to the problem above, 5/4 is an improper fraction, since 5 (the numerator) is larger than 4 (the denominator).  This can be converted to a mixed number – 5/4 = 4/4 + 1/4, and we know 4/4 = 1

so – 1 + 1/4 = 1 1/4.

4. Errors with equivalent fractions and reducing to the simplest form.

Here is question – Does 2/4 = 1/2 ?    YES!   we can reduce 2/4 by dividing the numerator (top)  and the denominator (bottom) by 2.  so 2/4 divided by 2/2 = 1/2.

5. Errors canceling common factors in fractions.

Cancelling out common factors works like this – 2/4 X 4/8    These are divisible by 2 so we divide by 2 in the top of one side and bottom of the other –  1/4 X 4/4

We can do the same again with the bottom of the first fraction and the top of the second – 1/1 X 1/4   and since 1/1 = 1  we have 1 X 1/4 = 1/4.

6. Errors with basic arithmetic operations (addition, subtraction, multiplication, and division) with fractions.  Fractions Practice

7. Solving word problems involving fractions.  How to Solve Word Problems  Word Problem Practice

8. Errors converting percent, decimals, and fractions. Converting Fractions and Decimal