Note: In this page, fractions are written with diagonal bars. For example 1/3 is the fraction whose numerator is 1 and denominator is 3.
6 1/3 is a mixed number meaning 6 + 1/3.

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 made up of 16 small squares. There are 4 red small squares. Hence the fraction of the large square that is red is given by

4 / 16

Divide numerator and denominator by 4 to reduce the fraction to

= 1 / 4

There is one blue square. Hence the fraction of the large square that is blue is given by

1 / 16

There is one half of a square that is orange. Hence the fraction of the large square that is orange is given by

half of 1 / 16 = (1/2) (1/16) = 1 / 32

There is one and one half of a small square that are green. Hence the fraction of the large square that is green is given by

1 / 16 + (1/2)(1 / 16) = 1 / 16 + 1 / 32

= 2 / 32 + 1 / 32 = 3 / 32 , common denominator and addition

There are 3 small square that are black. Hence the fraction of the large square that is black is given by

3 / 16

There are 3 small square that are yellow. Hence the fraction of the large square that is yellow is given by

3 / 16

What fraction is the shaded part?

.

Solution

There are two whole items and 3 / 4 of one item. Hence the part that is shaded is given by

2 + 3/4 = 2 3/4 (mixed number)

Which point on the number line represents 1 1/5?

.

Solution

Note that 1 1/5 is larger than 1 and smaller than 2. Each small division on the number line represent 1 / 10. Hence point R represents

1 and 2/10

= 1 2/10

= 1 1/5 , reduce fraction 2/10 = 1/5

Point R represents 1 1/5

3 1/2 + 5 1/2 =

Solution

Add whole numbers together and fractions together

3 1/2 + 5 1/2 = (3 + 5) + (1/2 + 1/2)

= 8 + 2/2 = 8 + 1 = 9

1/2 + 1/14 =

Write to the same denominator before you add fractions

Change the mixed numbers 3 1/4 and 5 1/3 to fractions and then divide.

3 1/4 = 13 / 4

5 1/3 = 16 / 3

hence

3 1/4 ÷ 5 1/3 = 13 / 4 ÷ 16 / 3

= 13 / 4 × 3 / 16 = 39 / 64

4 2/7 × 5 3/5 =

Solution

Change the mixed numbers 4 2/7 and 5 3/5 to fractions and then multiply.

4 2/7 = 30 / 7

5 3/5 = 28 / 5

hence

4 2/7 × 5 3/5 = 30 / 7 × 28 / 5

= (30 × 28) / (7 × 5) = 24

To have F + 2 5/7 = 4, F must be equal to

Solution

In order to have F + 2 5/7 = 4, F must be equal to

F = 4 - 2 5/7 = 2 - 5/7

= 14 / 7 - 5 / 7

= 9 / 7 = 1 2/7

Tom runs 3/4 of an hour every Monday, 30 minutes every Tuesday, half an hour every Wednesday, 1 1/4 hours every Thursday and 2/3 of an hour on Friday. How many hours does Tom run from Monday to Friday?
.

Solution

Find the time in minutes for each day.

Monday: 3 / 4 of an hour = (3 / 4) × 60 = 180 / 4 = 45 minutes

Order from least to greatest: 5 3/4 , 3 4/5 , 3 1/5 , 4 5/6.

Solution

The mixed number with the smallest whole number is the smallest. Hence 3 1/5 is the smallest and 3 4/5 is the second smallest. The next largest is 4 5/6 and the largest is 5 3/4. Hence the order from least to greatest is given by

3 1/5 , 3 4/5 , 4 5/6 , 5 3/4

Order from least to greatest: 7 2/3 , 7 3/5 , 7 3/4 , 7 6/11.

Solution

The given mixed numbers all have the same whole number and the fractional parts are not easy to compare either. The best way to compare these mixed numbers is to compare their fractional parts and to compare their fractional parts we need to write to the lowest common denominator 660.