Note: In this page, fractions are written with diagonal bars. For example 2/3 is the fraction whose numerator is 2 and denominator is 3.
5 1/2 is a mixed number meaning 5 + 1/2.

3 1/2 + 5 1/3 =
Solution
Add whole numbers together and fractions together
3 1/2 + 5 1/3 = (3 + 5) + (1/2 + 1/3)
Write fractions with the same denominator
= 8 + (3/6 + 2/6) = 8 5/6

It takes Julia 1/2 hour to wash, comb her hair and put on her clothes, and 1/4 hour to have her breakfast. How much time does it take Julia to be ready for school?
Solution
The total time for Julia to be ready for school is
1/2 + 1/4
Write fractions with the same denominator
= 2/4 + 1/4 = 3/4 of an hour.

Which two fractions are equivalent?
 5/2 and 2/5
 4/3 and 8/6
 1/4 and 2/4

2/3 and 1/3
Solution
It is easier to compare fractions if they are written with the same denominator
5/2 and 2/5 with same denominator become 25/10 and 4/10
4/3 and 8/6 with same denominator become 8/6 and 8/6
Fractions 4/3 and 8/6 are equivalent because when written with common denominator both denominators and numerators are equal.

5 2/3  3 1/2 =
Solution
Subtract whole numbers together and fractions together
5 2/3  3 1/2 = (5  3) + (2/3  1/2)
Write fractions with the same denominator
= 2 + (4/6  3/6) = 2 1/6

Billy ate 1 1/4 pizzas and John ate 1 2/3 pizzas. How much more pizza did John eat than Billy?
.
Solution
John ate more than Billy and the difference is given by
1 2/3  1 1/4 = (1  1) + (2/3  1/4)
Write fractions with the same denominator
= 0 + (8/12  3/12) = 5/12
John ate 5/12 of a pizza more than Billy.

5/2 ÷ 3/4 =
.
Solution
To divide two fractions, you multiply the first one by the multiplicative inverse of the second
5/2 ÷ 3/4 = 5/2 × 4/3 = 20/6 = 10/3

5 ÷ 1/7 =
Solution
To divide two fractions, you multiply the first one by the multiplicative inverse of the second
5 ÷ 1/7 = 5/1 × 7/1 = 35/1 = 35

2/5 × 3/7 =
Solution
Multiply numerators and denominators
2/5 × 3/7 = (2 × 3)/(5 × 7) = 6/35

To have a + 1 3/4 = 2, a must be equal to
Solution
The above may written as
a + 1 + 3/4 = 2
we need to have
a + 3/4 = 1 so that a + 1 + 3/4 = 2
To have
a + 3/4 = 1 we need to have a = 1/4
Check
a + 1 3/4 = 1/4 + 1 + 3/4 = 1 + (1/4 + 3/4) = 1 + 4/4 = 1 + 1 = 2

What fraction is the shaded part?
.
Solution
There are two whole shaded items above and one shaded at 3/4. Hence the mixed number
2 3/4 represents the shaded parts.

True or false 2 1/2 = 2 x 1/2?
Solution
False: 2 1/2 is a mixed number and is equal to
2 1/2 = 1 + 1/2

Tina works 15 hours a week (Monday to Friday). Last week she worked 3 1/2 hours on Monday, 4 hours on Tuesday, 2 1/6 hours on Wednesday and 1 1/2 on Thursday. How many hours did she work on Friday?
.
Solution
We do not know how many hours she worked on Friday let us say n hours. The total (addition) for the 5 days is 15 hours. Let us add all hours for 5 days
3 1/2 + 4 + 2 1/6 + 1 1/2 + n = 15
Add whole numbers together and fractions together
(3 + 4 + 2 + 1) + (1/2 + 1/6 + 1/2) + n = 15
10 + (1/2 + 1/2 + 1/6) + n = 15
10 + (1 + 1/6) + n = 15
11 + 1/6 + n = 15
For 11 + 1/6 + n = 15 to have right hand side and left hand side equal, n must be equal to 3 and 5/6. Check
11 + 1/6 + (3 + 5/6) = (11 + 3) + (1/6 + 5/6) = 14 + 6/6 = 14 + 1 = 15

Which point on the number line represents 1 7/10?
.
Solution
1 7/10 in decimal form is
1 7/10 = 1 + 7/10 = 1 + 0.7 = 1.7 and corresponds to point W.

Write 2 1/3 as a fraction.
Solution
2 1/3 as a fraction is
2 1/3 = 2 + 1/3
common denominator
= 6/3 + 1/3 = 7/3

Write 31/8 as a mixed number.
Solution
Write 31 as the highest multiple of 8 plus a number smaller than 8
31/8 = (24 + 7)/8 = 3 + 7/8 = 3 7/8

3 × 1/4 =
 3 1/4
 1/4 + 1/4 + 1/4
 1/4

12
Solution
3 1/4 may be written as
3 1/4 = 3 + 1/4 and hence is not equal to 3 × 1/4
1/4 + 1/4 + 1/4 may be written as follows
1/4 + 1/4 + 1/4 = 3/4 = 3 × 1/3

3 1/4 =
Solution
3 1/4 is equal to
3 + 1/4

True or false 2/5 > 3/8?
Solution
Rewrite the two fractions with the same denominator. The same denominator is the LCM of 5 and 8. First list the first few multiples of 5 and 8 until we obtain a common multiple
5: 5, 10, 15, 20, 25, 30, 35, 40
8: 8, 16, 24, 32, 40
2/5 = 16/40 and 3/8 = 15/40
16/40 is greater than 15/40 and therefore 2/5 is greater than 3/8 and the above statement is true.

Order from least to greatest the fractions 3/5 , 7/6 , 1/3 , 4/9.
Solution
Note that 1 of the given fractions 7/6 has its numerator greater than its denominator and hence it is greater than 1. The remaining 3 have their numerators smaller than their denominators and therefore are all smaller than 1. 7/6 is the largest fraction. The remaining 3 fractions 3/5 , 1/3 , 4/9 can be compared by first writing them with the same denominator. The common denominator may be the lowest multiple of 5, 3 and 9
5: 5, 10, 15, 25, 30, 35, 40, 45
3: 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45
9: 9,18,27,36,45
3/5 = 27/45
1/3 = 15/45
4/9 = 20/45
We now order the fractions from least to the greatest
1/3 , 4/9 , 3/5 , 7/6

Write 2/3 of 4 as a mixed number.
Solution
2/3 of 4 is equal to
2/3 × 4 = 8/3 = (6 + 2)/3 = 6/3 + 2/3 = 2 2/3

How many minutes in 2/3 of an hour?
Solution
one hour is equal to 60 minutes. Hence 2/3 of an hour is equal to
2/3 × 60 = 2 × 60 / 3 = 120 / 3 = 40 minutes

What fraction of the large square is red?
What fraction of the large square is blue?
What fraction of the large square is orange?
What fraction of the large square is green?
What fraction of the large square is black?
What fraction of the large square is yellow?
Solution
The large square is divided into 16 small square. Hence every small square is 1/16 of the large square.
red: 4 small squares = 4 × 1/16 = 4/16 = 1/4
blue: 1 small square = 1 × 1/16 = 1/16
orange: half a small square = 1/2 of 1/16 = 1/2 × 1/16 = 1/32
green: 1 small square and 1/2 of a small square = 1/16 + 1/2 × 1/16 = 1/16 + 1/32 = 3/32
black: 3 small squares = 3 × 1/16 = 3/16
yellow: 3 small squares = 3 × 1/16 = 3/16

