CONVERTING MIXED FRACTION INTO IMPROPER FRACTION

To convert mixed fraction to improper fraction, we will follow the steps given below.

Rewrite the mixed number as an improper fraction.

Problem 1 :

1  2/3

Solution :

=  1  2/3

= (3 × 1 + 2)/3

= (3 + 2)/3

= 5/3

Problem 2 :

1  2/5

Solution :

= 1  2/5

= (5 × 1 + 2)/5

= (5 + 2)/5

= 7/5

Problem 3 :

2  1/4

Solution :

= 2  1/4

= (4 × 2 + 1)/4

= (8 + 1)/4

= 9/4

Problem 4 :

2  5/6

Solution :

= 2  5/6

= (6 × 2 + 5)/6

= (12 + 5)/6

= 17/6

Problem 5 :

2  7/9

Solution :

= 2  7/9

= = (9 × 2 + 7)/9

= (18 + 7)/9

= 25/9

Problem 6 :

2  5/7

Solution :

= 2  5/7

= (7 × 2 + 5)/7

= (14 + 5)/7

= 19/7

Problem 7 :

3  4/7

Solution :

= 3  4/7

= (7 × 3 + 4)/7

= (21 + 4)/7

= 25/7

Problem 8 :

3  5/9

Solution :

= 3  5/9

= (9 × 3 + 5)/9

= (27 + 5)/9

= 32/9

Problem 9 :

Ms. Panvini gave her students a test with twenty math problems. The table shows the fraction of correct answers for each of the five students who finished the test first.

Which comparison is true?

a) 9/10 < 4/5        b) 17/20 < 9/10        c) 9/10 < 3/4      d) 17/20 < 1/2

Problem 10 :

Kendrick used 4  5/8 bags of dirt in a garden of roses and 9  1/8 bags of dirt in a garden of wildflowers. Which equation can be used to find the number of bags of dirt Kendrick used?

a)  4/8 + 5/8 + 9/8 + 1/8 = 19/8          b)  9/8 + 10/8 = 19/16

c)  20/8 + 9/8 = 3  5/8      d) 4 + 9 + 5/8 + 1/8 = 13  6/8

Solution :

Total number of bags = 4   5/8 + 9  1/8

Adding the whole numbers and adding the fraction parts.

= 4 + 9 + 5/8 + 1/8

= 13 + (5 + 1)/8

= 13   6/8

So, option d is correct.

Problem 11 :

Which fraction belongs in the ___  to make this comparison true?

3/7 > ___

a)  1/4     b)  2/3     c)  1/2     d) 3/5

Solution :

To compare the fractions, we should find the least common multiple of 2, 3, 4, 5 and 7

least common multiple = 2 x 3 x 2 x 5 x 7

= 420

• 3/7 x 60/60 = 180/420
• 1/4 x 105/105 = 105/420
• 2/3 x 140/140 = 280/420
• 1/2 x 210/210 = 210/420
• 3/5 x 84/84 = 252/420

180/420 > 105/420

3/7 > 1/4

So, option a is correct.

Problem 12 :

Which equation shows a decimal and a fraction that are equivalent?

a)  23.5 = 23 5/100      b) 23.55 = 23  55/100     c)  23.05 = 23  5/10

d) 23.5 = 23  50/100

Solution :

Problem 13 :

The model is shaded to represent a decimal number less than one.

Which value is represented by the shaded part of the model?

a) Two and seven-tenths       b) Twenty-seven

c)  Twenty-seven-hundredths     d) Two and seven-hundredths

Solution :

Number of squares shaded = 20 + 7

= 27

Number of square shaded = 27/100

Twenty seven hundredths is the answer, option c is correct.

Problem 14 :

The shaded parts of the model represent the combined fraction of a small pie that 2/ 9 Darrell and Nani ate. Darrell ate of the pie.

What fraction of the pie did Nani eat?

a)  5/9     b)  3/9      c) 2/9      d) 4/9

Solution :

Total number of equal parts = 9

Number of parts shaded = 5

So, the fractional part that is shaded is 5/9.

Problem 15 :

This chart shows four comparisons.

Which of these comparisons are true?

a) Only W      b) Only X and Z       c) Only W, Y, and Z     d) None of these

Solution :

Comparision in Y :

8/12 < 9/12

Since the denominator is the same, comparision can be done and Y is true

Comparision in Z :

8/12 < 6/8

LCM(12, 8) = 24

8/12 x 2/2 = 16/24

6/8 x 3/3 = 18/24

16/24 < 18/24

8/12 < 6/8

Z is true.

So, option c is correct.

Problem 16 :

Paul threw a baseball 18.7 meters. Which fraction is equivalent to 18.7?

a)  18   7/100    b)  18/70     c)  18  7/10     d) 187/100

Solution :

Option c is correct.